JS8.cpp

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#include "JS8.h"
#include "JS8_Include/commons.h"
#include "JS8_Mode/FrequencyTracker.h"
#include "JS8_Mode/whitening_processor.h"
#include "ldpc_feedback.h"
#include "soft_combiner.h"
 
#include <QDebug>
#include <QLoggingCategory>
#include <QtGlobal>
 
#include <algorithm>
#include <atomic>
#include <boost/crc.hpp>
#include <boost/math/ccmath/round.hpp>
#include <boost/multi_index/key.hpp>
#include <boost/multi_index/ordered_index.hpp>
#include <boost/multi_index/ranked_index.hpp>
#include <boost/multi_index_container.hpp>
#include <chrono>
#include <cmath>
#include <complex>
#include <concepts>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <fftw3.h>
#include <initializer_list>
#include <limits>
#include <memory>
#include <mutex>
#include <numbers>
#include <numeric>
#include <optional>
#include <sstream>
#include <stdexcept>
#include <string_view>
#include <unordered_map>
#include <utility>
#include <vector>
#include <vendor/Eigen/Dense>
 
Q_DECLARE_LOGGING_CATEGORY(decoder_js8);
 
// A C++ conversion of the Fortran JS8 encoding and decoder function.
// Some notes on the conversion:
//
//   1. Names of variables and functions as much as possible match those
//      of the Fortran routines, for ease in cross-referencing during the
//      debug comparison phase of testing. You don't have to like them; I
//      don't like them either, frankly, but it's the reasonable approach
//      to the problem as of this writing; we can make 'em pretty later.
//
//   2. The BP decoder should be a faithful reproduction of the Fortran
//      version, albeit modified for the column-major vs. row-major
//      differences between the two languages.
//
//   3. The OSD decoder is no longer used, and the depth is now fixed at
//      2, instead of being variable 1 to 4.
//
//   4. The Fortran version didn't compute the 40% rank consistently in
//      syncjs8(); this version does. It wasn't typically off by much, but
//      it was reliably not going to be at 40%. Hopefully, this change will
//      result in more predictable first-pass candidate selection.
//
//   5. The Fortran version was very subject to Runge's phenomenon when
//      computing the baseline in baselinejs8(), and was using a ton of
//      data points below the 10% threshold for the polynomial determination.
//      Neither of these seemed to be helpful, so in contrast we're using
//      a number of Chebyshev nodes proportional to the desired polynomial
//      terms.
//
//   6. The Fortran version normalized `s1` by dividing by the median in
//      js8dec(), but did so in a naive manner, not checking for a median
//      of zero. Testing indicates that the normalization does not appear
//      to contribute to decoder yield, so it's been removed.
//
//   7. Translating array indices from the world of Fortran to that of C++
//      is no one's fun task. If you see things that aren't behaving as
//      expected, look at the Fortran code and compare the array indexing;
//      would not be surprised in the least to have off-by-one errors here.
 
/******************************************************************************/
// Compilation Utilities
/******************************************************************************/
 
namespace {
// Full-range cosine function using symmetries of cos(x). std::cos
// isn't constexpr until C++20, and we're targeting C++17 at the
// moment. We only use this function during compilation; std::cos
// is the better choice at runtime. Once we move to requiring a
// C++20 compiler, we can just use std::cos.
 
constexpr double cos_approx(double x) {
    constexpr auto RAD_360 = std::numbers::pi * 2;
    constexpr auto RAD_180 = std::numbers::pi;
    constexpr auto RAD_90 = std::numbers::pi / 2;
 
    // Polynomial approximation of cos(x) for x in [0, RAD_90],
    // Accuracy here in theory is 1e-18, but double precision
    // itself is only 1-e16, so within the domain of doubles,
    // this should be extremely accurate.
 
    constexpr auto poly = [](double const x) {
        constexpr std::array coefficients = {
            1.0,                           // Coefficient for x^0
            -0.49999999999999994,          // Coefficient for x^2
            0.041666666666666664,          // Coefficient for x^4
            -0.001388888888888889,         // Coefficient for x^6
            0.000024801587301587,          // Coefficient for x^8
            -0.00000027557319223986,       // Coefficient for x^10
            0.00000000208767569878681,     // Coefficient for x^12
            -0.00000000001147074513875176, // Coefficient for x^14
            0.0000000000000477947733238733 // Coefficient for x^16
        };
 
        auto const x2 = x * x;
        auto const x4 = x2 * x2;
        auto const x6 = x4 * x2;
        auto const x8 = x4 * x4;
        auto const x10 = x8 * x2;
        auto const x12 = x8 * x4;
        auto const x14 = x12 * x2;
        auto const x16 = x8 * x8;
 
        return coefficients[0] + coefficients[1] * x2 + coefficients[2] * x4 +
               coefficients[3] * x6 + coefficients[4] * x8 +
               coefficients[5] * x10 + coefficients[6] * x12 +
               coefficients[7] * x14 + coefficients[8] * x16;
    };
 
    // Reduce x to [0, RAD_360)
 
    x -= static_cast<long long>(x / RAD_360) * RAD_360;
 
    // Map x to [0, RAD_180]
 
    if (x > RAD_180)
        x = RAD_360 - x;
 
    // Map x to [0, RAD_90] and evaluate the polynomial;
    // flip the sign for angles in the second quadrant.
 
    return x > RAD_90 ? -poly(RAD_180 - x) : poly(x);
};
} // end anonymous namespace
 
/******************************************************************************/
// Constants
/******************************************************************************/
 
namespace {
/* COMMON PARAMETERS */
 
// !Common
//
// parameter (KK=87)                     !Information bits (75 + CRC12)
// parameter (ND=58)                     !Data symbols
// parameter (NS=21)                     !Sync symbols (3 @ Costas 7x7)
// parameter (NN=NS+ND)                  !Total channel symbols (79)
// parameter (ASYNCMIN=1.5)              !Minimum Sync
// parameter (NFSRCH=5)                  !Search frequency range in Hz (i.e.,
// +/- 2.5 Hz) parameter (NMAXCAND=300)              !Maximum number of
// candidate signals
 
// Parameter    Value   Description
// KK   87  Number of information bits (75 message bits + 12 CRC bits).
// ND   58  Number of data symbols in the JS8 transmission.
// NS   21  Number of synchronization symbols (3 Costas arrays of size 7).
// NN   79  Total number of channel symbols (NN = NS + ND).
// ASYNCMIN 1.5 Minimum sync value for successful decoding.
// NFSRCH   5   Search frequency range in Hz (±2.5 Hz).
// NMAXCAND 300 Maximum number of candidate signals.
 
constexpr int N = 174;           // Total bits
constexpr int K = 87;            // Message bits
constexpr int M = N - K;         // Check bits
constexpr int KK = 87;           // Information bits (75 + CRC12)
constexpr int ND = 58;           // Data symbols
constexpr int NS = 21;           // Sync symbols (3 @ Costas 7x7)
constexpr int NN = NS + ND;      // Total channel symbols (79)
constexpr float ASYNCMIN = 1.5f; // Minimum sync
constexpr int NFSRCH = 5; // Search frequency range in Hz (i.e., +/- 2.5 Hz)
constexpr std::size_t NMAXCAND = 300; // Maxiumum number of candidate signals
constexpr int NFILT = 1400;           // Filter length
constexpr int NROWS = 8;
constexpr int NFOS = 2;
constexpr int NSSY = 4;
constexpr int NP = 3200;
constexpr int NP2 = 2812;
constexpr float TAU = 2.0f * std::numbers::pi_v<float>;
constexpr auto ZERO = std::complex<float>{0.0f, 0.0f};
// Key for the constants that follow:
// Key for the constants that follow:
//
//   NSUBMODE - ID of the submode
//   NCOSTAS  - Which JS8 Costas Arrays to use
//   NSPS     - Number of samples per second
//   NTXDUR   - Duration of the transmission in seconds.
//   NDOWNSPS - Number of samples per symbol after downsampling.
//   NDD      - Parameter used in waveform tapering and related calculations.
//   XXX JZ       - Range of symbol offsets considered during decoding. ASTART
//   - Start delay in seconds for decoding. BASESUB  - XXX NMAX     - Samples in
//   input wave NSTEP    - Rough time-sync step size NHSYM    - Number of symbol
//   spectra (1/4-sym steps) NDOW     - Downsample factor to 32 samples per
//   symbol NQSYMBOL - Downsample factor of a quarter symbol
 
/* A MODE DECODER */
 
struct ModeA {
    // Static constants
    inline static constexpr int NSUBMODE = 0;
    inline static constexpr auto NCOSTAS = JS8::Costas::Type::ORIGINAL;
    inline static constexpr int NSPS = JS8A_SYMBOL_SAMPLES;
    inline static constexpr int NTXDUR = JS8A_TX_SECONDS;
    inline static constexpr int NDOWNSPS = 32;
    inline static constexpr int NDD = 100;
    inline static constexpr int JZ = 62;
    inline static constexpr float ASTART = 0.5f;
    inline static constexpr float BASESUB = 40.0f;
 
    // Derived parameters
    inline static constexpr float AZ = (12000.0f / NSPS) * 0.64f;
    inline static constexpr int NMAX = NTXDUR * JS8_RX_SAMPLE_RATE;
    inline static constexpr int NFFT1 = NSPS * NFOS;
    inline static constexpr int NSTEP = NSPS / NSSY;
    inline static constexpr int NHSYM = NMAX / NSTEP - 3;
    inline static constexpr int NDOWN = NSPS / NDOWNSPS;
    inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
    inline static constexpr int NDFFT1 = NSPS * NDD;
    inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
    inline static constexpr int NP2 = NN * NDOWNSPS;
    inline static constexpr float TSTEP = NSTEP / 12000.0f;
    inline static constexpr int JSTRT = ASTART / TSTEP;
    inline static constexpr float DF = 12000.0f / NFFT1;
};
 
/* B MODE DECODER */
 
struct ModeB {
    // Static constants
    inline static constexpr int NSUBMODE = 1;
    inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
    inline static constexpr int NSPS = JS8B_SYMBOL_SAMPLES;
    inline static constexpr int NTXDUR = JS8B_TX_SECONDS;
    inline static constexpr int NDOWNSPS = 20;
    inline static constexpr int NDD = 100;
    inline static constexpr int JZ = 144;
    inline static constexpr float ASTART = 0.2f;
    inline static constexpr float BASESUB = 39.0f;
 
    // Derived parameters
    inline static constexpr float AZ = (12000.0f / NSPS) * 0.8f;
    inline static constexpr int NMAX = NTXDUR * JS8_RX_SAMPLE_RATE;
    inline static constexpr int NFFT1 = NSPS * NFOS;
    inline static constexpr int NSTEP = NSPS / NSSY;
    inline static constexpr int NHSYM = NMAX / NSTEP - 3;
    inline static constexpr int NDOWN = NSPS / NDOWNSPS;
    inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
    inline static constexpr int NDFFT1 = NSPS * NDD;
    inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
    inline static constexpr int NP2 = NN * NDOWNSPS;
    inline static constexpr float TSTEP = NSTEP / 12000.0f;
    inline static constexpr int JSTRT = ASTART / TSTEP;
    inline static constexpr float DF = 12000.0f / NFFT1;
};
 
/* C MODE DECODER */
 
struct ModeC {
    // Static constants
    inline static constexpr int NSUBMODE = 2;
    inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
    inline static constexpr int NSPS = JS8C_SYMBOL_SAMPLES;
    inline static constexpr int NTXDUR = JS8C_TX_SECONDS;
    inline static constexpr int NDOWNSPS = 12;
    inline static constexpr int NDD = 120;
    inline static constexpr int JZ = 172;
    inline static constexpr float ASTART = 0.1f;
    inline static constexpr float BASESUB = 38.0f;
 
    // Derived parameters
    inline static constexpr float AZ = (12000.0f / NSPS) * 0.6f;
    inline static constexpr int NMAX = NTXDUR * JS8_RX_SAMPLE_RATE;
    inline static constexpr int NFFT1 = NSPS * NFOS;
    inline static constexpr int NSTEP = NSPS / NSSY;
    inline static constexpr int NHSYM = NMAX / NSTEP - 3;
    inline static constexpr int NDOWN = NSPS / NDOWNSPS;
    inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
    inline static constexpr int NDFFT1 = NSPS * NDD;
    inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
    inline static constexpr int NP2 = NN * NDOWNSPS;
    inline static constexpr float TSTEP = NSTEP / 12000.0f;
    inline static constexpr int JSTRT = ASTART / TSTEP;
    inline static constexpr float DF = 12000.0f / NFFT1;
};
 
/* E MODE DECODER */
 
// Note that the original used 28 for NTXDUR and 90 for NDD, but the
// corresponding C++ mainline side used 30 for NTXDUR, so for the
// moment, we're matching that here, which seems logical at present.
 
struct ModeE {
    // Static constants
    inline static constexpr int NSUBMODE = 4;
    inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
    inline static constexpr int NSPS = JS8E_SYMBOL_SAMPLES;
    inline static constexpr int NTXDUR =
        JS8E_TX_SECONDS; // XXX was 28 in Fortran
    inline static constexpr int NDOWNSPS = 32;
    inline static constexpr int NDD = 94; // XXX was 90 in Fortran
    inline static constexpr int JZ = 32;
    inline static constexpr float ASTART = 0.5f;
    inline static constexpr float BASESUB = 42.0f;
 
    // Derived parameters
    inline static constexpr float AZ = (12000.0f / NSPS) * 0.64f;
    inline static constexpr int NMAX = NTXDUR * JS8_RX_SAMPLE_RATE;
    inline static constexpr int NFFT1 = NSPS * NFOS;
    inline static constexpr int NSTEP = NSPS / NSSY;
    inline static constexpr int NHSYM = NMAX / NSTEP - 3;
    inline static constexpr int NDOWN = NSPS / NDOWNSPS;
    inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
    inline static constexpr int NDFFT1 = NSPS * NDD;
    inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
    inline static constexpr int NP2 = NN * NDOWNSPS;
    inline static constexpr float TSTEP = NSTEP / 12000.0f;
    inline static constexpr int JSTRT = ASTART / TSTEP;
    inline static constexpr float DF = 12000.0f / NFFT1;
};
 
/* I MODE DECODER */
 
struct ModeI {
    // Static constants
    inline static constexpr int NSUBMODE = 8;
    inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
    inline static constexpr int NSPS = JS8I_SYMBOL_SAMPLES;
    inline static constexpr int NTXDUR = JS8I_TX_SECONDS;
    inline static constexpr int NDOWNSPS = 12;
    inline static constexpr int NDD = 125;
    inline static constexpr int JZ = 250;
    inline static constexpr float ASTART = 0.1f;
    inline static constexpr float BASESUB = 36.0f;
 
    // Derived parameters
    inline static constexpr float AZ = (12000.0f / NSPS) * 0.64f;
    inline static constexpr int NMAX = NTXDUR * JS8_RX_SAMPLE_RATE;
    inline static constexpr int NFFT1 = NSPS * NFOS;
    inline static constexpr int NSTEP = NSPS / NSSY;
    inline static constexpr int NHSYM = NMAX / NSTEP - 3;
    inline static constexpr int NDOWN = NSPS / NDOWNSPS;
    inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
    inline static constexpr int NDFFT1 = NSPS * NDD;
    inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
    inline static constexpr int NP2 = NN * NDOWNSPS;
    inline static constexpr float TSTEP = NSTEP / 12000.0f;
    inline static constexpr int JSTRT = ASTART / TSTEP;
    inline static constexpr float DF = 12000.0f / NFFT1;
};
 
// Tunable settings; degree of the polynomial used for the baseline
// curve fit, and the percentile of the span at which to sample. In
// general, a 5th degree polynomial and the 10th percentile should
// be optimal.
 
constexpr auto BASELINE_DEGREE = 5;
constexpr auto BASELINE_SAMPLE = 10;
 
// Define the closed range in Hz that we'll consider to be the window
// for baseline determination.
 
constexpr auto BASELINE_MIN = 500;
constexpr auto BASELINE_MAX = 2500;
 
// We're going to do a pairwise Estrin's evaluation of the polynomial
// coefficients, so it's critical that the degree of the polynomial is
// odd, resulting in an even number of coefficients.
 
static_assert(BASELINE_DEGREE & 1, "Degree must be odd");
static_assert(BASELINE_SAMPLE >= 0 && BASELINE_SAMPLE <= 100,
              "Sample must be a percentage");
 
// Since we know the degree of the polynomial, and thus the number of
// nodes that we're going to use, we can do all the trigonometry work
// required to calculate the Chebyshev nodes in advance, by computing
// them over the range [0, 1]; we can then scale these at runtime to
// a span of any size by simple multiplication.
//
// Downside to this with C++17 is that std::cos() is not yet constexpr,
// as it is in C++20, so we must provide our own implementation until
// then.
 
constexpr auto BASELINE_NODES = []() {
    // Down to the actual business of generating Chebyshev nodes
    // suitable for scaling; once we move to C++20 as the minimum
    // compiler, we can remove the cos() function above and instead
    // call std::cos() here, as it's required to be constexpr in
    // C++20 and above, and presumably it'll be of high quality.
 
    auto nodes = std::array<double, BASELINE_DEGREE + 1>{};
    constexpr auto slice = std::numbers::pi / (2.0 * nodes.size());
 
    for (std::size_t i = 0; i < nodes.size(); ++i) {
        nodes[i] = 0.5 * (1.0 - cos_approx(slice * (2.0 * i + 1)));
    }
 
    return nodes;
}();
} // end anonymous namespace
 
/******************************************************************************/
// Local Types
/******************************************************************************/
 
namespace {
// Accumulation of rounding errors in IEEE 754 values can be a problem
// when summing large numbers of small values; a Kahan summation class
// by which to compensate for them.
//
// Fortran, or at least, gfortran, will use this technique under the
// covers in various scenarios. While it'd be reasonable to expect it
// to be used in sum(), that's typically not the case.
//
// However, for example, it'll use it here for the value that goes into
// win(i), and naive summation in C++ will as a result not produce the
// same values without using compensation.
//
//   subroutine nuttal_window(win,n)
//     real win(n)
//     pi=4.0*atan(1.0)
//     a0=0.3635819
//     a1=-0.4891775;
//     a2=0.1365995;
//     a3=-0.0106411;
//     do i=1,n
//         win(i)=a0+a1*cos(2*pi*(i-1)/(n))+ &
//             a2*cos(4*pi*(i-1)/(n))+ &
//             a3*cos(6*pi*(i-1)/(n))
//     enddo
//     return
//   end subroutine nuttal_window
 
template <std::floating_point T> class KahanSum {
    T m_sum;          // Accumulated sum
    T m_compensation; // Compensation for lost low-order bits
 
  public:
    KahanSum(T sum = T(0)) : m_sum(sum), m_compensation(T(0)) {}
 
    KahanSum &operator=(T const sum) {
        m_sum = sum;
        m_compensation = T(0);
 
        return *this;
    }
 
    KahanSum &operator+=(T const value) {
        T const y = value - m_compensation; // Correct the value
        T const t = m_sum + y;              // Perform the sum
 
        m_compensation = (t - m_sum) - y; // Update compensation
        m_sum = t;                        // Update the sum
 
        return *this;
    }
 
    operator T() const { return m_sum; }
};
 
// Management of dynamic FFTW plan storage.
 
class FFTWPlanManager {
  public:
    enum class Type { DS, BB, CF, CB, SD, CS, count };
 
    // Disallow copying and moving
 
    FFTWPlanManager(FFTWPlanManager const &) = delete;
    FFTWPlanManager &operator=(FFTWPlanManager const &) = delete;
    FFTWPlanManager(FFTWPlanManager &&) = delete;
    FFTWPlanManager &operator=(FFTWPlanManager &&) = delete;
 
    // Constructor
 
    FFTWPlanManager() { m_plans.fill(nullptr); }
 
    // Destructor
 
    ~FFTWPlanManager() {
        std::lock_guard<std::mutex> lock(fftw_mutex);
 
        for (auto &plan : m_plans) {
            if (plan)
                fftwf_destroy_plan(plan);
        }
    }
 
    // Accessor
 
    fftwf_plan const &operator[](Type const type) const noexcept {
        return m_plans[static_cast<std::size_t>(type)];
    }
 
    // Manipulator
 
    fftwf_plan &operator[](Type const type) noexcept {
        return m_plans[static_cast<std::size_t>(type)];
    }
 
    // Iteration support
 
    auto begin() noexcept { return m_plans.begin(); }
    auto end() noexcept { return m_plans.end(); }
    auto begin() const noexcept { return m_plans.begin(); }
    auto end() const noexcept { return m_plans.end(); }
 
  private:
    // Data members
 
    std::array<fftwf_plan, static_cast<std::size_t>(Type::count)> m_plans;
};
 
// Encapsulates the first-order search results provided by syncjs8().
 
struct Sync {
    float freq;
    float step;
    float sync;
 
    // Constructor for convenience.
 
    Sync(float const freq, float const step, float const sync)
        : freq(freq), step(step), sync(sync) {}
};
 
// Tag structs so that we can refer to multi index container indices
// by a descriptive tag instead of by the index of the index. These
// don't need to be anything but a name.
 
namespace Tag {
struct Freq {};
struct Rank {};
struct Sync {};
} // namespace Tag
 
// Container indexing Sync objects in useful ways, used by syncjs8().
 
namespace MI = boost::multi_index;
using SyncIndex = MI::multi_index_container<
    Sync, MI::indexed_by<
              MI::ordered_non_unique<MI::tag<Tag::Freq>, MI::key<&Sync::freq>>,
              MI::ranked_non_unique<MI::tag<Tag::Rank>, MI::key<&Sync::sync>>,
              MI::ordered_non_unique<MI::tag<Tag::Sync>, MI::key<&Sync::sync>,
                                     std::greater<>>>>;
 
// Represents a decoded message, i.e., the 3-bit message type
// and the 12 bytes that result from decoding a message.
 
class Decode {
  public:
    int type;
    std::string data;
 
    Decode(int type, std::string data) : type(type), data(std::move(data)) {}
 
    bool operator==(Decode const &) const noexcept = default;
 
    struct Hash {
        std::size_t operator()(Decode const &decode) const noexcept {
            std::size_t const h1 = std::hash<int>{}(decode.type);
            std::size_t const h2 = std::hash<std::string>{}(decode.data);
            return h1 ^ (h2 + 0x9e3779b9 + (h1 << 6) + (h1 >> 2));
        }
    };
 
    using Map = std::unordered_map<Decode, int, Hash>;
};
 
/******************************************************************************/
// Belief Propagation Decoder
/******************************************************************************/
 
namespace {
constexpr int BP_MAX_ROWS = 7;        // Max rows per column in Nm
constexpr int BP_MAX_CHECKS = 3;      // Max checks per bit in Mn
constexpr int BP_MAX_ITERATIONS = 30; // Max iterations in BP decoder
 
constexpr std::array<std::array<int, BP_MAX_CHECKS>, N> Mn = {
    {{0, 24, 68},  {1, 4, 72},   {2, 31, 67},  {3, 50, 60},  {5, 62, 69},
     {6, 32, 78},  {7, 49, 85},  {8, 36, 42},  {9, 40, 64},  {10, 13, 63},
     {11, 74, 76}, {12, 22, 80}, {14, 15, 81}, {16, 55, 65}, {17, 52, 59},
     {18, 30, 51}, {19, 66, 83}, {20, 28, 71}, {21, 23, 43}, {25, 34, 75},
     {26, 35, 37}, {27, 39, 41}, {29, 53, 54}, {33, 48, 86}, {38, 56, 57},
     {44, 73, 82}, {45, 61, 79}, {46, 47, 84}, {58, 70, 77}, {0, 49, 52},
     {1, 46, 83},  {2, 24, 78},  {3, 5, 13},   {4, 6, 79},   {7, 33, 54},
     {8, 35, 68},  {9, 42, 82},  {10, 22, 73}, {11, 16, 43}, {12, 56, 75},
     {14, 26, 55}, {15, 27, 28}, {17, 18, 58}, {19, 39, 62}, {20, 34, 51},
     {21, 53, 63}, {23, 61, 77}, {25, 31, 76}, {29, 71, 84}, {30, 64, 86},
     {32, 38, 50}, {36, 47, 74}, {37, 69, 70}, {40, 41, 67}, {44, 66, 85},
     {45, 80, 81}, {48, 65, 72}, {57, 59, 65}, {60, 64, 84}, {0, 13, 20},
     {1, 12, 58},  {2, 66, 81},  {3, 31, 72},  {4, 35, 53},  {5, 42, 45},
     {6, 27, 74},  {7, 32, 70},  {8, 48, 75},  {9, 57, 63},  {10, 47, 67},
     {11, 18, 44}, {14, 49, 60}, {15, 21, 25}, {16, 71, 79}, {17, 39, 54},
     {19, 34, 50}, {22, 24, 33}, {23, 62, 86}, {26, 38, 73}, {28, 77, 82},
     {29, 69, 76}, {30, 68, 83}, {21, 36, 85}, {37, 40, 80}, {41, 43, 56},
     {46, 52, 61}, {51, 55, 78}, {59, 74, 80}, {0, 38, 76},  {1, 15, 40},
     {2, 30, 53},  {3, 35, 77},  {4, 44, 64},  {5, 56, 84},  {6, 13, 48},
     {7, 20, 45},  {8, 14, 71},  {9, 19, 61},  {10, 16, 70}, {11, 33, 46},
     {12, 67, 85}, {17, 22, 42}, {18, 63, 72}, {23, 47, 78}, {24, 69, 82},
     {25, 79, 86}, {26, 31, 39}, {27, 55, 68}, {28, 62, 65}, {29, 41, 49},
     {32, 36, 81}, {34, 59, 73}, {37, 54, 83}, {43, 51, 60}, {50, 52, 71},
     {57, 58, 66}, {46, 55, 75}, {0, 18, 36},  {1, 60, 74},  {2, 7, 65},
     {3, 59, 83},  {4, 33, 38},  {5, 25, 52},  {6, 31, 56},  {8, 51, 66},
     {9, 11, 14},  {10, 50, 68}, {12, 13, 64}, {15, 30, 42}, {16, 19, 35},
     {17, 79, 85}, {20, 47, 58}, {21, 39, 45}, {22, 32, 61}, {23, 29, 73},
     {24, 41, 63}, {26, 48, 84}, {27, 37, 72}, {28, 43, 80}, {34, 67, 69},
     {40, 62, 75}, {44, 48, 70}, {49, 57, 86}, {47, 53, 82}, {12, 54, 78},
     {76, 77, 81}, {0, 1, 23},   {2, 5, 74},   {3, 55, 86},  {4, 43, 52},
     {6, 49, 82},  {7, 9, 27},   {8, 54, 61},  {10, 28, 66}, {11, 32, 39},
     {13, 15, 19}, {14, 34, 72}, {16, 30, 38}, {17, 35, 56}, {18, 45, 75},
     {20, 41, 83}, {21, 33, 58}, {22, 25, 60}, {24, 59, 64}, {26, 63, 79},
     {29, 36, 65}, {31, 44, 71}, {37, 50, 85}, {40, 76, 78}, {42, 55, 67},
     {46, 73, 81}, {39, 51, 77}, {53, 60, 70}, {45, 57, 68}}};
 
struct CheckNode {
    int valid_neighbors;
    std::array<int, BP_MAX_ROWS> neighbors;
};
 
constexpr std::array<CheckNode, M> Nm = {{{6, {0, 29, 59, 88, 117, 146, 0}},
                                          {6, {1, 30, 60, 89, 118, 146, 0}},
                                          {6, {2, 31, 61, 90, 119, 147, 0}},
                                          {6, {3, 32, 62, 91, 120, 148, 0}},
                                          {6, {1, 33, 63, 92, 121, 149, 0}},
                                          {6, {4, 32, 64, 93, 122, 147, 0}},
                                          {6, {5, 33, 65, 94, 123, 150, 0}},
                                          {6, {6, 34, 66, 95, 119, 151, 0}},
                                          {6, {7, 35, 67, 96, 124, 152, 0}},
                                          {6, {8, 36, 68, 97, 125, 151, 0}},
                                          {6, {9, 37, 69, 98, 126, 153, 0}},
                                          {6, {10, 38, 70, 99, 125, 154, 0}},
                                          {6, {11, 39, 60, 100, 127, 144, 0}},
                                          {6, {9, 32, 59, 94, 127, 155, 0}},
                                          {6, {12, 40, 71, 96, 125, 156, 0}},
                                          {6, {12, 41, 72, 89, 128, 155, 0}},
                                          {6, {13, 38, 73, 98, 129, 157, 0}},
                                          {6, {14, 42, 74, 101, 130, 158, 0}},
                                          {6, {15, 42, 70, 102, 117, 159, 0}},
                                          {6, {16, 43, 75, 97, 129, 155, 0}},
                                          {6, {17, 44, 59, 95, 131, 160, 0}},
                                          {6, {18, 45, 72, 82, 132, 161, 0}},
                                          {6, {11, 37, 76, 101, 133, 162, 0}},
                                          {6, {18, 46, 77, 103, 134, 146, 0}},
                                          {6, {0, 31, 76, 104, 135, 163, 0}},
                                          {6, {19, 47, 72, 105, 122, 162, 0}},
                                          {6, {20, 40, 78, 106, 136, 164, 0}},
                                          {6, {21, 41, 65, 107, 137, 151, 0}},
                                          {6, {17, 41, 79, 108, 138, 153, 0}},
                                          {6, {22, 48, 80, 109, 134, 165, 0}},
                                          {6, {15, 49, 81, 90, 128, 157, 0}},
                                          {6, {2, 47, 62, 106, 123, 166, 0}},
                                          {6, {5, 50, 66, 110, 133, 154, 0}},
                                          {6, {23, 34, 76, 99, 121, 161, 0}},
                                          {6, {19, 44, 75, 111, 139, 156, 0}},
                                          {6, {20, 35, 63, 91, 129, 158, 0}},
                                          {6, {7, 51, 82, 110, 117, 165, 0}},
                                          {6, {20, 52, 83, 112, 137, 167, 0}},
                                          {6, {24, 50, 78, 88, 121, 157, 0}},
                                          {7, {21, 43, 74, 106, 132, 154, 171}},
                                          {6, {8, 53, 83, 89, 140, 168, 0}},
                                          {6, {21, 53, 84, 109, 135, 160, 0}},
                                          {6, {7, 36, 64, 101, 128, 169, 0}},
                                          {6, {18, 38, 84, 113, 138, 149, 0}},
                                          {6, {25, 54, 70, 92, 141, 166, 0}},
                                          {7, {26, 55, 64, 95, 132, 159, 173}},
                                          {6, {27, 30, 85, 99, 116, 170, 0}},
                                          {6, {27, 51, 69, 103, 131, 143, 0}},
                                          {6, {23, 56, 67, 94, 136, 141, 0}},
                                          {6, {6, 29, 71, 109, 142, 150, 0}},
                                          {6, {3, 50, 75, 114, 126, 167, 0}},
                                          {6, {15, 44, 86, 113, 124, 171, 0}},
                                          {6, {14, 29, 85, 114, 122, 149, 0}},
                                          {6, {22, 45, 63, 90, 143, 172, 0}},
                                          {6, {22, 34, 74, 112, 144, 152, 0}},
                                          {7, {13, 40, 86, 107, 116, 148, 169}},
                                          {6, {24, 39, 84, 93, 123, 158, 0}},
                                          {6, {24, 57, 68, 115, 142, 173, 0}},
                                          {6, {28, 42, 60, 115, 131, 161, 0}},
                                          {6, {14, 57, 87, 111, 120, 163, 0}},
                                          {7, {3, 58, 71, 113, 118, 162, 172}},
                                          {6, {26, 46, 85, 97, 133, 152, 0}},
                                          {5, {4, 43, 77, 108, 140, 0, 0}},
                                          {6, {9, 45, 68, 102, 135, 164, 0}},
                                          {6, {8, 49, 58, 92, 127, 163, 0}},
                                          {6, {13, 56, 57, 108, 119, 165, 0}},
                                          {6, {16, 54, 61, 115, 124, 153, 0}},
                                          {6, {2, 53, 69, 100, 139, 169, 0}},
                                          {6, {0, 35, 81, 107, 126, 173, 0}},
                                          {5, {4, 52, 80, 104, 139, 0, 0}},
                                          {6, {28, 52, 66, 98, 141, 172, 0}},
                                          {6, {17, 48, 73, 96, 114, 166, 0}},
                                          {6, {1, 56, 62, 102, 137, 156, 0}},
                                          {6, {25, 37, 78, 111, 134, 170, 0}},
                                          {6, {10, 51, 65, 87, 118, 147, 0}},
                                          {6, {19, 39, 67, 116, 140, 159, 0}},
                                          {6, {10, 47, 80, 88, 145, 168, 0}},
                                          {6, {28, 46, 79, 91, 145, 171, 0}},
                                          {6, {5, 31, 86, 103, 144, 168, 0}},
                                          {6, {26, 33, 73, 105, 130, 164, 0}},
                                          {5, {11, 55, 83, 87, 138, 0, 0}},
                                          {6, {12, 55, 61, 110, 145, 170, 0}},
                                          {6, {25, 36, 79, 104, 143, 150, 0}},
                                          {6, {16, 30, 81, 112, 120, 160, 0}},
                                          {5, {27, 48, 58, 93, 136, 0, 0}},
                                          {6, {6, 54, 82, 100, 130, 167, 0}},
                                          {6, {23, 49, 77, 105, 142, 148, 0}}}};
 
// Belief Propagation Decoder
 
int bpdecode174(std::array<float, N> const &llr, std::array<int8_t, K> &decoded,
                std::array<int8_t, N> &cw) {
    // Initialize messages and variables
    std::array<std::array<float, BP_MAX_CHECKS>, N> tov =
        {}; // Messages to variable nodes
    std::array<std::array<float, BP_MAX_ROWS>, M> toc =
        {}; // Messages to check nodes
    std::array<std::array<float, BP_MAX_ROWS>, M> tanhtoc =
        {}; // Tanh of messages
 
    std::array<float, N> zn = {}; // Bit log likelihood ratios
    std::array<int, M> synd = {}; // Syndrome for checks
 
    int ncnt = 0;
    int nclast = 0;
 
    // Initialize toc (messages from bits to checks)
    for (int i = 0; i < M; ++i) {
        for (int j = 0; j < Nm[i].valid_neighbors; ++j) {
            toc[i][j] = llr[Nm[i].neighbors[j]];
        }
    }
 
    // Iterative decoding
    for (int iter = 0; iter <= BP_MAX_ITERATIONS; ++iter) {
        // Update bit log likelihood ratios
        for (int i = 0; i < N; ++i) {
            zn[i] =
                llr[i] + std::accumulate(tov[i].begin(),
                                         tov[i].begin() + BP_MAX_CHECKS, 0.0f);
        }
 
        // Check if we have a valid codeword
        for (int i = 0; i < N; ++i)
            cw[i] = zn[i] > 0 ? 1 : 0;
 
        int ncheck = 0;
        for (int i = 0; i < M; ++i) {
            synd[i] = 0;
            for (int j = 0; j < Nm[i].valid_neighbors; ++j) {
                synd[i] += cw[Nm[i].neighbors[j]];
            }
            if (synd[i] % 2 != 0)
                ++ncheck;
        }
 
        if (ncheck == 0) {
            // Extract decoded bits (last N-M bits of codeword)
            std::copy(cw.begin() + M, cw.end(), decoded.begin());
 
            // Count errors
            int nerr = 0;
            for (int i = 0; i < N; ++i) {
                if ((2 * cw[i] - 1) * llr[i] < 0.0f) {
                    ++nerr;
                }
            }
 
            return nerr;
        }
 
        // Early stopping criterion
        if (iter > 0) {
            int nd = ncheck - nclast;
            ncnt = (nd < 0) ? 0 : ncnt + 1;
            if (ncnt >= 5 && iter >= 10 && ncheck > 15) {
                return -1;
            }
        }
        nclast = ncheck;
 
        // Send messages from bits to check nodes
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < Nm[i].valid_neighbors; ++j) {
                int ibj = Nm[i].neighbors[j];
                toc[i][j] = zn[ibj];
                for (int k = 0; k < BP_MAX_CHECKS; ++k) {
                    if (Mn[ibj][k] == i) {
                        toc[i][j] -= tov[ibj][k];
                    }
                }
            }
        }
 
        // Send messages from check nodes to variable nodes
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < 7;
                 ++j) { // Fixed range [0, 7) to match Fortran's 1:7, could be
                        // nrw[j], or 7 logically
                tanhtoc[i][j] = std::tanh(-toc[i][j] / 2.0f);
            }
        }
 
        for (int i = 0; i < N; ++i) {
            for (int j = 0; j < BP_MAX_CHECKS; ++j) {
                int ichk = Mn[i][j];
                if (ichk >= 0) {
                    float Tmn = 1.0f;
                    for (int k = 0; k < Nm[ichk].valid_neighbors; ++k) {
                        if (Nm[ichk].neighbors[k] != i) {
                            Tmn *= tanhtoc[ichk][k];
                        }
                    }
                    tov[i][j] = 2.0f * std::atanh(-Tmn);
                }
            }
        }
    }
 
    return -1; // Decoding failed
}
} // namespace
 
/******************************************************************************/
// Local Routines
/******************************************************************************/
 
namespace {
constexpr std::string_view alphabet =
    "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-+";
 
static_assert(alphabet.size() == 64);
 
// Function that either translates valid JS8 message characters to their
// corresponding 6-bit word value, or throws. This will end up doing a
// direct index operation into a 256-byte table, the creation of which
// must be constexpr under C++17.
 
constexpr auto alphabetWord = []() {
    constexpr std::uint8_t invalid = 0xff;
 
    constexpr auto words = []() {
        std::array<std::uint8_t, 256> words{};
 
        for (auto &word : words)
            word = invalid;
 
        for (std::size_t i = 0; i < alphabet.size(); ++i) {
            words[static_cast<std::uint8_t>(alphabet[i])] =
                static_cast<std::uint8_t>(i);
        }
 
        return words;
    }();
 
    return [words](char const value) {
        if (auto const word = words[value]; word != invalid) {
            return word;
        }
 
        throw std::runtime_error("Invalid character in message");
    };
}();
 
// Sanity check key bounds of the 6-bit encoding table.
 
static_assert(alphabetWord('0') == 0);
static_assert(alphabetWord('A') == 10);
static_assert(alphabetWord('a') == 36);
static_assert(alphabetWord('-') == 62);
static_assert(alphabetWord('+') == 63);
 
template <typename T> std::uint16_t CRC12(T const &range) {
    return boost::augmented_crc<12, 0xc06>(range.data(), range.size()) ^ 42;
}
 
bool checkCRC12(std::array<std::int8_t, KK> const &decoded) {
    std::array<uint8_t, 11> bits = {};
 
    for (std::size_t i = 0; i < decoded.size(); ++i) {
        if (decoded[i])
            bits[i / 8] |= (1 << (7 - (i % 8)));
    }
 
    // Extract the received CRC-12.
 
    uint16_t crc = (static_cast<uint16_t>(bits[9] & 0x1F) << 7) |
                   (static_cast<uint16_t>(bits[10]) >> 1);
 
    // Clear bits that correspond to the CRC in the last bytes.
 
    bits[9] &= 0xE0;
    bits[10] = 0x00;
 
    // Compute CRC and indicate if we have a match.
 
    return crc == CRC12(bits);
}
 
std::string extractmessage174(std::array<int8_t, KK> const &decoded) {
    std::string message;
 
    // Ensure received CRC matches computed CRC.
 
    if (checkCRC12(decoded)) {
        message.reserve(12);
 
        // Decode the message from the 72 data bits
 
        std::array<uint8_t, 12> words;
 
        for (std::size_t i = 0; i < 12; ++i) {
            words[i] = (decoded[i * 6 + 0] << 5) | (decoded[i * 6 + 1] << 4) |
                       (decoded[i * 6 + 2] << 3) | (decoded[i * 6 + 3] << 2) |
                       (decoded[i * 6 + 4] << 1) | (decoded[i * 6 + 5] << 0);
        }
 
        // Map 6-bit words to the alphabet
 
        for (auto const word : words)
            message += alphabet[word];
    }
 
    return message;
}
 
// Parity matrix for JS8 message generation.
//
// This should be 952 bytes in size; to store an 87x87 matrix of bits,
// you need 7569 bits, which requires 119 64-bit values, or 952 bytes.
//
// Background here is that this is a low-density parity check code (LDPC),
// generated using the PEG algorithm. In short, true values in a row i of
// the matrix define which of the 87 message bits must be summed, modulo
// 2, to produce the ith parity check bit. Decent references on this are:
//
//   1. https://wsjt.sourceforge.io/FT4_FT8_QEX.pdf
//   2. https://inference.org.uk/mackay/PEG_ECC.html
//   3. https://github.com/Lcrypto/classic-PEG-
//
// The data used was harvested from the original 'ldpc_174_87_params.f90',
// but you'll note that the rows have been reordered here, because this
// isn't Fortran; C++ is row-major, not column-major.
 
constexpr auto parity = []() {
    constexpr std::size_t Rows = 87;
    constexpr std::size_t Cols = 87;
 
    using ElementType = std::uint64_t;
    constexpr std::size_t ElementSize =
        std::numeric_limits<ElementType>::digits;
 
    constexpr auto matrix = []() {
        constexpr std::array<std::string_view, Rows> Data = {
            "23bba830e23b6b6f50982e", "1f8e55da218c5df3309052",
            "ca7b3217cd92bd59a5ae20", "56f78313537d0f4382964e",
            "6be396b5e2e819e373340c", "293548a138858328af4210",
            "cb6c6afcdc28bb3f7c6e86", "3f2a86f5c5bd225c961150",
            "849dd2d63673481860f62c", "56cdaec6e7ae14b43feeee",
            "04ef5cfa3766ba778f45a4", "c525ae4bd4f627320a3974",
            "41fd9520b2e4abeb2f989c", "7fb36c24085a34d8c1dbc4",
            "40fc3e44bb7d2bb2756e44", "d38ab0a1d2e52a8ec3bc76",
            "3d0f929ef3949bd84d4734", "45d3814f504064f80549ae",
            "f14dbf263825d0bd04b05e", "db714f8f64e8ac7af1a76e",
            "8d0274de71e7c1a8055eb0", "51f81573dd4049b082de14",
            "d8f937f31822e57c562370", "b6537f417e61d1a7085336",
            "ecbd7c73b9cd34c3720c8a", "3d188ea477f6fa41317a4e",
            "1ac4672b549cd6dba79bcc", "a377253773ea678367c3f6",
            "0dbd816fba1543f721dc72", "ca4186dd44c3121565cf5c",
            "29c29dba9c545e267762fe", "1616d78018d0b4745ca0f2",
            "fe37802941d66dde02b99c", "a9fa8e50bcb032c85e3304",
            "83f640f1a48a8ebc0443ea", "3776af54ccfbae916afde6",
            "a8fc906976c35669e79ce0", "f08a91fb2e1f78290619a8",
            "cc9da55fe046d0cb3a770c", "d36d662a69ae24b74dcbd8",
            "40907b01280f03c0323946", "d037db825175d851f3af00",
            "1bf1490607c54032660ede", "0af7723161ec223080be86",
            "eca9afa0f6b01d92305edc", "7a8dec79a51e8ac5388022",
            "9059dfa2bb20ef7ef73ad4", "6abb212d9739dfc02580f2",
            "f6ad4824b87c80ebfce466", "d747bfc5fd65ef70fbd9bc",
            "612f63acc025b6ab476f7c", "05209a0abb530b9e7e34b0",
            "45b7ab6242b77474d9f11a", "6c280d2a0523d9c4bc5946",
            "f1627701a2d692fd9449e6", "8d9071b7e7a6a2eed6965e",
            "bf4f56e073271f6ab4bf80", "c0fc3ec4fb7d2bb2756644",
            "57da6d13cb96a7689b2790", "a9fa2eefa6f8796a355772",
            "164cc861bdd803c547f2ac", "cc6de59755420925f90ed2",
            "a0c0033a52ab6299802fd2", "b274db8abd3c6f396ea356",
            "97d4169cb33e7435718d90", "81cfc6f18c35b1e1f17114",
            "481a2a0df8a23583f82d6c", "081c29a10d468ccdbcecb6",
            "2c4142bf42b01e71076acc", "a6573f3dc8b16c9d19f746",
            "c87af9a5d5206abca532a8", "012dee2198eba82b19a1da",
            "b1ca4ea2e3d173bad4379c", "b33ec97be83ce413f9acc8",
            "5b0f7742bca86b8012609a", "37d8e0af9258b9e8c5f9b2",
            "35ad3fb0faeb5f1b0c30dc", "6114e08483043fd3f38a8a",
            "cd921fdf59e882683763f6", "95e45ecd0135aca9d6e6ae",
            "2e547dd7a05f6597aac516", "14cd0f642fc0c5fe3a65ca",
            "3a0a1dfd7eee29c2e827e0", "c8b5dffc335095dcdcaf2a",
            "3dd01a59d86310743ec752", "8abdb889efbe39a510a118",
            "3f231f212055371cf3e2a2"};
 
        constexpr std::size_t Total = (Rows * Cols + ElementSize - 1);
        constexpr std::size_t Count = Total / ElementSize;
        constexpr std::array<std::uint8_t, 4> Masks = {0x8, 0x4, 0x2, 0x1};
 
        std::array<ElementType, Count> data{};
 
        for (std::size_t row = 0; row < Rows; ++row) {
            std::size_t col = 0;
 
            for (auto const c : Data[row]) {
                std::uint8_t const value =
                    (c >= '0' && c <= '9')   ? c - '0'
                    : (c >= 'a' && c <= 'f') ? c - 'a' + 10
                    : (c >= 'A' && c <= 'F') ? c - 'A' + 10
                                             : throw "Invalid hex";
 
                for (auto const mask : Masks) {
                    if (col >= Cols)
                        break;
                    if (value & mask) {
                        auto const index = row * Cols + col;
                        data[index / ElementSize] |=
                            (ElementType(1) << (index % ElementSize));
                    }
                    ++col;
                }
            }
        }
        return data;
    }();
 
    return [matrix](std::size_t const row, std::size_t const col) {
        auto const index = row * Cols + col;
        return (matrix[index / ElementSize] >> (index % ElementSize)) & 1;
    };
}();
} // namespace
 
/******************************************************************************/
// DecodeMode Template Class
/******************************************************************************/
 
// Mode-parameterized decode class.
 
namespace {
template <typename Mode> class DecodeMode {
    // Data members
 
    std::array<float, Mode::NFFT1> nuttal;
    std::array<std::array<std::array<std::complex<float>, Mode::NDOWNSPS>, 7>,
               3>
        csyncs;
    alignas(64) std::array<std::complex<float>, Mode::NDOWNSPS> csymb;
    alignas(64) std::array<std::complex<float>, Mode::NMAX> filter;
    alignas(64) std::array<std::complex<float>, Mode::NMAX> cfilt;
    alignas(64) std::array<std::complex<float>, Mode::NDFFT1 / 2 + 1> ds_cx;
    alignas(64) std::array<std::complex<float>, Mode::NFFT1 / 2 + 1> sd;
    alignas(64) std::array<std::complex<float>, NP> cd0;
    std::array<float, Mode::NMAX> dd;
    std::array<std::array<float, Mode::NHSYM>, Mode::NSPS> s;
    std::array<float, Mode::NSPS> savg;
    FFTWPlanManager plans;
    SyncIndex sync;
    js8::SoftCombiner<N> m_softCombiner;
    bool m_enableFreqTracking = true;
    bool m_enableTimingTracking = true;
    float m_llrErasureThreshold = js8::llrErasureThreshold();
    bool m_enableLdpcFeedback = js8::ldpcFeedbackEnabled();
    int m_maxLdpcPasses = js8::ldpcFeedbackMaxPasses();
 
    using Plan = FFTWPlanManager::Type;
 
    static constexpr auto Costas = JS8::Costas::array(Mode::NCOSTAS);
 
    // Fore and aft tapers to reduce spectral leakage during the
    // downsampling process. We can compute these at compile time.
 
    static constexpr auto Taper = [] {
        std::array<std::array<float, Mode::NDD + 1>, 2> taper{};
 
        for (size_t i = 0; i <= Mode::NDD; ++i) {
            float const value =
                0.5f *
                (1.0f + cos_approx(i * std::numbers::pi_v<float> / Mode::NDD));
 
            taper[1][i] = value;             // TailTaper (original taper)
            taper[0][Mode::NDD - i] = value; // HeadTaper (reversed taper)
        }
 
        return taper;
    }();
 
    // Baseline computation support.
 
    using Points = Eigen::Matrix<double, BASELINE_NODES.size(), 2>;
    using Vandermonde =
        Eigen::Matrix<double, BASELINE_NODES.size(), BASELINE_NODES.size()>;
    using Coefficients = Eigen::Vector<double, BASELINE_NODES.size()>;
 
    Points p;
    Vandermonde V;
    Coefficients c;
 
    // Polynomial evaluation using Estrin's method, loop is unrolled at
    // compile time. A compiler should emit SIMD instructions from what
    // it sees here when the optimizer is involved, but even without it,
    // we'll likely see fused multiply-add instructions.
 
    inline auto evaluate(float const x) const {
        return [this]<Eigen::Index... I>(
                   float const x, std::integer_sequence<Eigen::Index, I...>) {
            auto baseline = 0.0;
            auto exponent = 1.0;
 
            ((baseline += (c[I * 2] + c[I * 2 + 1] * x) * exponent,
              exponent *= x * x),
             ...);
 
            return static_cast<float>(baseline);
        }(x, std::make_integer_sequence<Eigen::Index,
                                        Coefficients::SizeAtCompileTime / 2>{});
    }
 
    std::optional<Decode> js8dec(bool const syncStats, bool const lsubtract,
                                 float &f1, float &xdt, int &nharderrors,
                                 float &xsnr, JS8::Event::Emitter emitEvent) {
        constexpr float FR = 12000.0f / Mode::NFFT1; // Frequency resolution
        constexpr float FS2 = 12000.0f / Mode::NDOWN;
        constexpr float DT2 = 1.0f / FS2;
 
        float const coarseStartHz = f1;
        float const coarseStartDt = xdt;
 
        auto const index =
            static_cast<int>(std::round(f1 / FR)); // Closest index
        float const scaled_value =
            0.1f * (savg[index] - Mode::BASESUB); // Adjust and scale
        float const xbase =
            std::pow(10.0f, scaled_value); // Convert to linear scale
 
        float delfbest = 0.0f;
        int ibest = 0;
 
        // Downsample the signal and prepare for processing.
 
        js8_downsample(f1);
 
        // Initial guess for the start of the signal.
 
        int i0 = static_cast<int>(std::round((xdt + Mode::ASTART) * FS2));
        float smax = 0.0f;
 
        // Search for the best synchronization offset.
 
        for (int idt = i0 - Mode::NQSYMBOL; idt <= i0 + Mode::NQSYMBOL; ++idt) {
            float const sync = syncjs8d(idt, 0.0f);
 
            if (sync > smax) {
                smax = sync;
                ibest = idt;
            }
        }
 
        // Improved estimate for DT.
 
        float const xdt2 = ibest * DT2;
 
        // Fine frequency synchronization
 
        i0 = static_cast<int>(std::round(xdt2 * FS2));
        smax = 0.0f;
 
        for (int ifr = -NFSRCH; ifr <= NFSRCH; ++ifr) {
            float const delf = ifr * 0.5f;
            float const sync = syncjs8d(i0, delf);
 
            if (sync > smax) {
                smax = sync;
                delfbest = delf;
            }
        }
 
        // Frequency tweaking.
 
        float const dphi = -delfbest * ((2.0f * std::numbers::pi_v<float>) /
                                        FS2); // Phase increment
        std::complex<float> const wstep =
            std::polar(1.0f, dphi);           // Step for phase rotation
        std::complex<float> w = {1.0f, 0.0f}; // Cumlative phase
 
        for (int i = 0; i < NP2; ++i) {
            w *= wstep;  // Update cumulative phase
            cd0[i] *= w; // Apply phase shift
        }
 
        // Adjust the frequency and time offset.
 
        xdt = xdt2;
        f1 += delfbest;
 
        float const sync = syncjs8d(i0, 0.0f);
 
        std::array<std::array<float, NN>, NROWS> s2;
 
        js8::FrequencyTracker freqTracker;
        if (m_enableFreqTracking) {
            freqTracker.reset(0.0, FS2);
        } else {
            freqTracker.disable();
        }
 
        // Scale timing clamp relative to samples per symbol so short-symbol
        // modes aren't allowed outsized shifts (e.g., 12-sample JS8 40 formerly "Turbo").
        double const timingMaxShift =
            std::clamp(0.08 * static_cast<double>(Mode::NDOWNSPS), 0.5, 2.0);
 
        js8::TimingTracker timingTracker;
        if (m_enableTimingTracking) {
            timingTracker.reset(0.0, 0.15, 0.35, timingMaxShift);
        } else {
            timingTracker.disable();
        }
 
        auto const estimateResidualHz =
            [&](int expectedTone) -> std::optional<float> {
            if (!freqTracker.enabled())
                return std::nullopt;
 
            if (expectedTone < 0 || expectedTone + 1 >= Mode::NDOWNSPS)
                return std::nullopt;
 
            float const m0 = std::norm(csymb[expectedTone]);
            float const mplus = std::norm(csymb[expectedTone + 1]);
            float const mminus =
                expectedTone > 0 ? std::norm(csymb[expectedTone - 1]) : 0.0f;
 
            if (m0 <= 0.0f)
                return std::nullopt;
 
            float const ratio = m0 / (mplus + mminus + 1e-12f);
            if (ratio < 1.5f)
                return std::nullopt;
 
            float const denom = mminus - 2.0f * m0 + mplus;
            if (std::abs(denom) < 1e-9f)
                return std::nullopt;
 
            float delta = 0.5f * (mminus - mplus) / denom;
            delta = std::clamp(delta, -0.5f, 0.5f);
 
            return delta * (FS2 / Mode::NDOWNSPS);
        };
 
        auto const logTracker = [&](char const *tag) {
            if (decoder_js8().isDebugEnabled()) {
                if (freqTracker.enabled()) {
                    qCDebug(decoder_js8)
                        << "freqTracker" << tag << "coarseHz" << coarseStartHz
                        << "fineHz" << f1 << "refinedHz"
                        << f1 + static_cast<float>(freqTracker.currentHz())
                        << "avgStepHz"
                        << static_cast<float>(freqTracker.averageStepHz());
                }
 
                if (timingTracker.enabled()) {
                    qCDebug(decoder_js8)
                        << "timingTracker" << tag << "coarseDt" << coarseStartDt
                        << "fineDt" << xdt << "refinedDt"
                        << xdt + static_cast<float>(
                                     timingTracker.currentSamples() * DT2)
                        << "avgStepSmpl"
                        << static_cast<float>(
                               timingTracker.averageStepSamples());
                }
            }
        };
 
        auto const goertzelEnergy =
            [&](int start, int expectedTone) -> std::optional<float> {
            if (start < 0 || start + Mode::NDOWNSPS > NP2)
                return std::nullopt;
 
            std::array<std::complex<float>, Mode::NDOWNSPS> tmp;
            std::copy(cd0.begin() + start, cd0.begin() + start + Mode::NDOWNSPS,
                      tmp.begin());
 
            if (freqTracker.enabled()) {
                freqTracker.apply(tmp.data(), Mode::NDOWNSPS);
            }
 
            auto const wstep = std::polar(
                1.0f, static_cast<float>(-TAU * expectedTone / Mode::NDOWNSPS));
            auto phase = std::complex<float>{1.0f, 0.0f};
            std::complex<float> acc{0.0f, 0.0f};
 
            for (auto const &sample : tmp) {
                acc += sample * std::conj(phase);
                phase *= wstep;
            }
 
            return std::norm(acc);
        };
 
        for (int k = 0; k < NN; ++k) {
            // Calculate the starting index for the current symbol.
 
            int const i1Base = ibest + k * Mode::NDOWNSPS;
            int const timingShift = timingTracker.enabled()
                                        ? static_cast<int>(std::round(
                                              timingTracker.currentSamples()))
                                        : 0;
            int i1 = i1Base + timingShift;
 
            if (i1 < 0) {
                i1 = 0;
            } else if (i1 + Mode::NDOWNSPS > NP2) {
                i1 = NP2 - Mode::NDOWNSPS;
            }
 
            csymb.fill(ZERO);
 
            if (i1 >= 0 && i1 + Mode::NDOWNSPS <= NP2) {
                std::copy(cd0.begin() + i1, cd0.begin() + i1 + Mode::NDOWNSPS,
                          csymb.begin());
 
                if (freqTracker.enabled()) {
                    freqTracker.apply(csymb.data(), Mode::NDOWNSPS);
                }
            }
 
            fftwf_execute(plans[Plan::CS]);
 
            // Normalize and take the magnitude of the first 8 points.
 
            for (int i = 0; i < NROWS; ++i) {
                s2[i][k] = std::abs(csymb[i]) / 1000.0f;
            }
 
            if (freqTracker.enabled() || timingTracker.enabled()) {
                bool const isPilot =
                    (k < 7) || (k >= 36 && k < 43) || (k >= 72 && k < 79);
 
                if (isPilot) {
                    int costasBlock = 0;
                    int costasColumn = k;
 
                    if (k >= 36 && k < 43) {
                        costasBlock = 1;
                        costasColumn = k - 36;
                    } else if (k >= 72 && k < 79) {
                        costasBlock = 2;
                        costasColumn = k - 72;
                    }
 
                    int const expectedTone = Costas[costasBlock][costasColumn];
 
                    if (auto const residual =
                            estimateResidualHz(expectedTone)) {
                        freqTracker.update(*residual);
                    }
 
                    if (timingTracker.enabled()) {
                        auto const e0 = goertzelEnergy(i1, expectedTone);
                        auto const eEarly =
                            goertzelEnergy(i1 - 1, expectedTone);
                        auto const eLate = goertzelEnergy(i1 + 1, expectedTone);
 
                        float const toneMag = s2[expectedTone][k];
 
                        if (e0 && eEarly && eLate && toneMag > 1e-6f) {
                            float const denom = *e0 + 1e-6f;
                            float const grad = (*eLate - *eEarly) / denom;
 
                            // Smaller steps; favor stability.
                            double const weight = std::clamp(
                                static_cast<double>(toneMag / 5.0f), 0.0, 1.0);
                            double const errorSamples = std::clamp(
                                0.25 * static_cast<double>(grad), -1.0, 1.0);
 
                            timingTracker.update(errorSamples, weight);
                        }
                    }
                }
            }
        }
 
        // Sync quality check using Costas tone patterns.
 
        int nsync = 0;
 
        for (std::size_t costas = 0; costas < Costas.size(); ++costas) {
            auto const offset = costas * 36;
 
            for (std::size_t column = 0; column < 7; ++column) {
                // Find the row containing the maximum value in the
                // current column.
 
                auto const max_row = std::distance(
                    s2.begin(),
                    std::max_element(s2.begin(), s2.end(),
                                     [index = offset + column](
                                         auto const &rowA, auto const &rowB) {
                                         return rowA[index] < rowB[index];
                                     }));
 
                // Check if the max row matches the Costas pattern.
 
                if (Costas[costas][column] == max_row)
                    ++nsync;
            }
        }
 
        // If the sync quality isn't at least 7, this one's a loser.
 
        if (nsync <= 6) {
            logTracker("sync_fail");
            return std::nullopt;
        }
 
        if (syncStats)
            emitEvent(
                JS8::Event::SyncState{JS8::Event::SyncState::Type::CANDIDATE,
                                      Mode::NSUBMODE,
                                      f1,
                                      xdt,
                                      {.candidate = nsync}});
 
        std::array<std::array<float, ND>, NROWS> s1;
 
        // Fill s1 from s2, excluding the Costas arrays.
 
        for (int row = 0; row < NROWS; ++row) {
            std::copy(s2[row].begin() + 7, s2[row].begin() + 36,
                      s1[row].begin());
            std::copy(s2[row].begin() + 43, s2[row].begin() + 72,
                      s1[row].begin() + 29);
        }
 
        // Identify winning tones (max magnitude) for each data symbol.
        std::array<int, ND> symbolWinners = {};
 
        for (int j = 0; j < ND; ++j) {
            int winner = 0;
            float best = s1[0][j];
 
            for (int i = 1; i < NROWS; ++i) {
                if (s1[i][j] > best) {
                    best = s1[i][j];
                    winner = i;
                }
            }
 
            symbolWinners[j] = winner;
        }
 
        auto const whitening = js8::WhiteningProcessor<NROWS, ND, N>::process(
            s1, symbolWinners, m_llrErasureThreshold,
            decoder_js8().isDebugEnabled());
 
        auto llr0 = whitening.llr0;
        auto llr1 = whitening.llr1;
 
        // Only apply a second erasure threshold pass if whitening didn't
        // already zero low-magnitude LLRs using the configured threshold.
        if (!whitening.erasureApplied) {
            std::size_t erasuresAfterThreshold = 0;
            double sumAbsPreErasure = 0.0;
            double sumAbsPostErasure = 0.0;
 
            auto const applyErasureThreshold = [&](auto &llr) {
                for (auto const value : llr)
                    sumAbsPreErasure += std::abs(value);
 
                if (m_llrErasureThreshold > 0.0f) {
                    for (auto &value : llr) {
                        if (std::abs(value) < m_llrErasureThreshold) {
                            value = 0.0f;
                            ++erasuresAfterThreshold;
                        }
 
                        sumAbsPostErasure += std::abs(value);
                    }
                } else {
                    for (auto const value : llr)
                        sumAbsPostErasure += std::abs(value);
                }
            };
 
            applyErasureThreshold(llr0);
            applyErasureThreshold(llr1);
 
            if (decoder_js8().isDebugEnabled()) {
                auto const total =
                    static_cast<double>(llr0.size() + llr1.size());
                double const avgPre =
                    total > 0.0 ? sumAbsPreErasure / total : 0.0;
                double const avgPost =
                    total > 0.0 ? sumAbsPostErasure / total : 0.0;
 
                qCDebug(decoder_js8)
                    << "LLR erasure threshold" << m_llrErasureThreshold
                    << "erasures:" << erasuresAfterThreshold
                    << "avg|LLR| pre/post:" << avgPre << avgPost;
            }
        }
 
        auto const ttl = std::chrono::seconds{Mode::NTXDUR * 2};
 
        m_softCombiner.flush(ttl);
 
        auto const key =
            m_softCombiner.makeKey(Mode::NSUBMODE, f1, xdt, llr0, llr1);
        auto combined = m_softCombiner.combine(key, llr0, llr1, ttl);
 
        auto llr0Combined = combined.llr0;
        auto llr1Combined = combined.llr1;
 
        std::array<int8_t, K> decoded;
        std::array<int8_t, N> cw;
 
        int totalLdpcPasses = 0;
        bool usedFeedbackPass = false;
        bool feedbackTurnedSuccess = false;
        int feedbackConfident = 0;
        int feedbackUncertain = 0;
 
        auto const tryDecode = [&](std::array<float, N> const &llrInput,
                                   int ipass) -> std::optional<Decode> {
            nharderrors = bpdecode174(llrInput, decoded, cw);
            xsnr = -99.0f;
 
            if (std::all_of(cw.begin(), cw.end(),
                            [](int x) { return x == 0; })) {
                return std::nullopt;
            }
 
            if (nharderrors >= 0 && nharderrors < 60 &&
                !(sync < 2.0f && nharderrors > 35) &&
                !(ipass > 2 && nharderrors > 39) &&
                !(ipass == 4 && nharderrors > 30)) {
                if (checkCRC12(decoded)) {
                    if (syncStats)
                        emitEvent(JS8::Event::SyncState{
                            JS8::Event::SyncState::Type::DECODED,
                            Mode::NSUBMODE,
                            f1,
                            xdt2,
                            {.decoded = sync}});
 
                    auto message = extractmessage174(decoded);
 
                    int const i3bit =
                        (decoded[72] << 2) | (decoded[73] << 1) | decoded[74];
 
                    std::array<int, NN> itone;
 
                    JS8::encode(i3bit, Costas, message.data(), itone.data());
 
                    if (lsubtract)
                        subtractjs8(genjs8refsig(itone, f1), xdt2);
 
                    float xsig = 0.0f;
 
                    for (std::size_t i = 0; i < itone.size(); ++i) {
                        xsig += std::pow(s2[itone[i]][i], 2);
                    }
 
                    xsnr =
                        std::max(10.0f * std::log10(std::max(
                                             xsig / xbase - 1.0f, 1.259e-10f)) -
                                     32.0f,
                                 -60.0f); // XXX was -28.0f in Fortran
 
                    m_softCombiner.markDecoded(combined.key);
 
                    logTracker("decoded");
                    return std::make_optional<Decode>(i3bit, message);
                }
            } else {
                nharderrors = -1;
            }
 
            return std::nullopt;
        };
 
        // Loop over decoding passes
        for (int ipass = 1; ipass <= 4 && totalLdpcPasses < m_maxLdpcPasses;
             ++ipass) {
            auto &llr = ipass == 2 ? llr1Combined : llr0Combined;
 
            // Zero ranges for certain passes to mirror legacy behavior.
            if (ipass == 3)
                std::fill(llr0Combined.begin(), llr0Combined.begin() + 24,
                          0.0f);
            else if (ipass == 4)
                std::fill(llr0Combined.begin() + 24, llr0Combined.begin() + 48,
                          0.0f);
 
            std::array<float, N> llrPrimary = llr;
            if (auto result = tryDecode(llrPrimary, ipass)) {
                ++totalLdpcPasses;
                return result;
            }
            ++totalLdpcPasses;
 
            // Feedback refinement and second attempt, if enabled and budget
            // allows.
            if (m_enableLdpcFeedback && totalLdpcPasses < m_maxLdpcPasses) {
                std::array<float, N> llrRefined;
                int confident = 0;
                int uncertain = 0;
                js8::refineLlrsWithLdpcFeedback(
                    llrPrimary, cw, m_llrErasureThreshold, llrRefined,
                    confident, uncertain);
 
                if (decoder_js8().isDebugEnabled()) {
                    qCDebug(decoder_js8)
                        << "LDPC feedback pass"
                        << "ipass" << ipass << "confident" << confident
                        << "uncertain" << uncertain;
                }
 
                usedFeedbackPass = true;
                feedbackConfident += confident;
                feedbackUncertain += uncertain;
 
                if (auto result = tryDecode(llrRefined, ipass)) {
                    ++totalLdpcPasses;
                    feedbackTurnedSuccess = true;
                    if (decoder_js8().isDebugEnabled()) {
                        qCDebug(decoder_js8)
                            << "LDPC feedback succeeded on second pass"
                            << "ipass" << ipass << "confident"
                            << feedbackConfident << "uncertain"
                            << feedbackUncertain << "passes" << totalLdpcPasses;
                    }
                    return result;
                }
 
                ++totalLdpcPasses;
            }
        }
 
        if (decoder_js8().isDebugEnabled()) {
            qCDebug(decoder_js8)
                << "LDPC feedback summary"
                << "used" << usedFeedbackPass << "success"
                << feedbackTurnedSuccess << "confident" << feedbackConfident
                << "uncertain" << feedbackUncertain << "passes"
                << totalLdpcPasses;
        }
 
        logTracker("fail");
        return std::nullopt;
    }
 
    // Compute noise baseline. We differ quite a bit from the Fortran
    // implementation here.
    //
    // The Fortran version took `savg` as input; power scaled data from
    // `syncjs8`, and produced `sbase`, the noise baseline. To accomplish
    // that, it used up to 1000 lower envelope points for the polynomial
    // determination, which caused some oddities when the matrix was
    // ill-conditioned; we're just looking for a low-order polynomial
    // here, and a massively tall matrix isn't in general going to be
    // helpful there. Additionally, the methodology seemed to be very
    // susceptible to Runge's phenomenon.
    //
    // This approach instead uses a number of Chebyshev nodes proportional
    // to the polynomial degree, and we evaluate 2 kHz of `savg`, centered
    // around 1.5 kHz, to determine the polynomial, figuring that that's
    // going to be an optimal place to measure the 10% noise floor. We then
    // map the [ia, ib] range to the domain of the polynomial to compute
    // the baseline. Since `savg` would otherwise no longer be referenced
    // beyond this function, we dispense with `sbase` and instead overwrite
    // `savg` with the baseline.
 
    void baselinejs8(int const ia, int const ib) {
        // Data referenced in savg is defined by the closed range [bmin, bmax].
        // From this we can derive the size of the closed range and the number
        // of points in each of the arms on either side of a node. All of these
        // values can be computed at compile time.
 
        using boost::math::ccmath::round;
 
        constexpr auto bmin =
            static_cast<std::size_t>(round(BASELINE_MIN / Mode::DF));
        constexpr auto bmax =
            static_cast<std::size_t>(round(BASELINE_MAX / Mode::DF));
        constexpr auto size = bmax - bmin + 1;
        constexpr auto arm = size / (2 * BASELINE_NODES.size());
 
        // Loop invariants; beginning of the data range, sentinel one past the
        // end of the range.
 
        auto const data = savg.begin() + bmin;
        auto const end = data + size;
 
        // Convert savg range of interest from power scale to dB scale.
 
        std::transform(data, end, data, [](float const value) {
            return 10.0f * std::log10(value);
        });
 
        // Collect lower envelope points; use Chebyshev node interpolants
        // to reduce Runge's phenomenon oscillations.
 
        for (std::size_t i = 0; i < BASELINE_NODES.size(); ++i) {
            auto const node = size * BASELINE_NODES[i];
            auto const base = data + static_cast<int>(std::round(node));
            auto span = std::vector<float>(std::clamp(base - arm, data, end),
                                           std::clamp(base + arm, data, end));
 
            auto const n = span.size() * BASELINE_SAMPLE / 100;
 
            std::nth_element(span.begin(), span.begin() + n, span.end());
 
            p.row(i) << node, span[n];
        }
 
        // Extract x and y values from points and prepare the Vandermonde
        // matrix, initializing the first column with 1 (x^0); remaining
        // columns are filled with the Schur product.
 
        Eigen::VectorXd x = p.col(0);
        Eigen::VectorXd y = p.col(1);
 
        V.col(0).setOnes();
        for (Eigen::Index i = 1; i < V.cols(); ++i) {
            V.col(i) = V.col(i - 1).cwiseProduct(x);
        }
 
        // Solve the least squares problem for polynomial coefficients.
 
        c = V.colPivHouseholderQr().solve(y);
 
        // To map an index i in the range [ia, ib] to the polynomial's
        // input domain [0, size - 1]:
        //
        //      i  - ia
        //  x = ------- * (size - 1)
        //      ib - ia
 
        auto const mapIndex = [ia, ib, last = size - 1](int const i) {
            return (i - ia) * last / float(ib - ia);
        };
 
        // Replace savg with a computed baseline in the range [ia, ib].
        // This might be interpolation, which should be quite accurate,
        // or extrapolation, likely somewhat less so the further we get
        // from the polynomial fitting domain, but hopefully still good
        // enough for our purposes here.
 
        savg.fill(0.0f);
 
        for (int i = ia; i <= ib; ++i) {
            savg[i] = evaluate(mapIndex(i)) + 0.65f;
        }
    }
 
    // Extracted from the downsampling process; this step is part of the
    // frequency-domain filtering process for downsampling the JS8 signal.
    // After the FFT, the resulting frequency-domain data (ds_cx) can be
    // manipulated (e.g., band-pass filtered or shifted). Subsequent inverse
    // FFT operations convert the filtered data back to the time domain at
    // a lower sample rate, achieving the desired downsampling.
 
    void computeBasebandFFT() {
        // ds_dx is an array of complex<float>; we're going to do an in-place
        // FFT, so we'll interpret the first half of the array as if they were
        // floats, which they are.
 
        float *fftw_real = reinterpret_cast<float *>(ds_cx.data());
 
        // Copy in data and zero-pad any remainder; not all modes will have
        // a remainder.
 
        std::copy(dd.begin(), dd.end(), fftw_real);
        std::fill(fftw_real + dd.size(), fftw_real + Mode::NDFFT1, 0.0f);
 
        fftwf_execute(plans[Plan::BB]);
    }
 
    // This function extracts a narrow frequency band around the target
    // frequency f0, applies tapering to reduce spectral artifacts, aligns the
    // signal to the center frequency, performs an inverse FFT to convert the
    // data back into the time domain, and normalizes the result for further
    // processing in the JS8 decoding pipeline.
 
    void js8_downsample(float const f0) {
        // Frequency band extraction; identifies a narrow frequency band around
        // the target frequency (f0) based on a predefined range (8.5 baud above
        // and 1.5 baud below). The indices of this range in the
        // frequency-domain representation (ds_cx) are calculated (ib and it),
        // and the relevant frequency-domain samples are extracted into cd0.
 
        constexpr float DF = 12000.0f / Mode::NDFFT1;
        constexpr float BAUD = 12000.0f / Mode::NSPS;
 
        float const ft = f0 + 8.5f * BAUD;
        float const fb = f0 - 1.5f * BAUD;
        int const i0 = static_cast<int>(std::round(f0 / DF));
        int const it =
            std::min(static_cast<int>(std::round(ft / DF)), Mode::NDFFT1 / 2);
        int const ib = std::max(0, static_cast<int>(std::round(fb / DF)));
 
        std::size_t const NDD_SIZE = Mode::NDD + 1;
        std::size_t const RANGE_SIZE = it - ib + 1;
 
        std::fill_n(cd0.begin(), Mode::NDFFT2, ZERO);
 
        std::copy(ds_cx.begin() + ib, ds_cx.begin() + ib + RANGE_SIZE,
                  cd0.begin());
 
        // Tapering is applied to smooth the edges of the frequency band,
        // reducing spectral leakage during the inverse FFT. Reversed taper at
        // the beginning, normal taper at the end.
 
        auto const head = cd0.begin();
        auto const tail = cd0.begin() + RANGE_SIZE;
 
        std::transform(head, head + NDD_SIZE, Taper[0].begin(), head,
                       std::multiplies<>());
        std::transform(tail - NDD_SIZE, tail, Taper[1].begin(), tail - NDD_SIZE,
                       std::multiplies<>());
 
        // The extracted frequency band is aligned to the center of the
        // frequency domain representation (i0 - ib) via a cyclic shift using
        // std::rotate. This centers the desired signal.
 
        std::rotate(cd0.begin(), cd0.begin() + (i0 - ib),
                    cd0.begin() + Mode::NDFFT2);
 
        // An inverse FFT is performed on the frequency-domain data (cd0) to
        // transform it back into the time domain, effectively yielding a
        // downsampled, time-domain signal focused on the extracted narrow
        // frequency band.
 
        fftwf_execute(plans[Plan::DS]);
 
        // The resulting time-domain samples are normalized by a factor derived
        // from the input and output FFT sizes (Mode::NDFFT1 and Mode::NDFFT2),
        // ensuring consistency in the signal’s amplitude.
 
        float const factor =
            1.0f / std::sqrt(static_cast<float>(Mode::NDFFT1) * Mode::NDFFT2);
 
        std::transform(cd0.begin(), cd0.end(), cd0.begin(),
                       [factor](auto &value) { return value * factor; });
    }
 
    // Evaluate the synchronization power of signal segments, ranks potential
    // candidates, and extracts the most promising ones for further decoding.
    //
    // Detailed Steps:
    //
    // 1.  Compute Symbol Spectra:
    //
    //     - The signal is processed in overlapping segments, with each segment
    //     multiplied by
    //       a Nuttall window to reduce spectral leakage.
    //     - An FFT is performed on each windowed segment to obtain the
    //     frequency-domain
    //       representation.
    //     - The power spectrum of each segment is computed, and the average
    //     spectrum is
    //       accumulated across segments.
    //
    // 2.  Filter Edge Adjustments:
    //
    //     - Adjusts the frequency bounds (nfa and nfb) to ensure the analysis
    //     remains
    //       within valid and meaningful regions of the signal.
    //
    // 3.  Baseline Computation:
    //
    //     - The average spectrum is converted to a dB scale.
    //     - Baseline is computed to distinguish significant signal components
    //     from
    //       background noise.
    //
    // 4.  Synchronization Metric Calculation:
    //
    //     - For each frequency bin in the specified range, evaluates
    //     synchronization
    //       power using a Costas waveform.
    //     - Sync metric is computed over the index range, considering all
    //     combinations
    //       of Costas patterns.
    //     - The maximum sync value and its corresponding offset are recorded
    //     for each
    //       frequency bin.
    //
    // 5.  Normalization:
    //
    //     - The sync values are normalized to the 40th percentile value using a
    //     ranked
    //       index. This ensures a consistent scaling across different signals
    //       and noise levels.
    //
    // 6.  Candidate Extraction:
    //
    //     - Candidates with a strong sync metric (above a defined threshold)
    //     are extracted.
    //     - Near-duplicate candidates of lesser synchronization power, based on
    //     frequency
    //       proximity, are eliminated.
    //
    // 7.  Output:
    //
    //     - Returns a vector of the most promising signal candidates, sorted by
    // their
    //       synchronization power. It's expected that these will be re-sorted
    //       by the caller into a desirable order, but synchronization power
    //       order facilitates debugging this function.
    //
    // Note: The Fortran version of this routine would normalize `s` at the end
    // of this
    //       function, but I'm unsure why; nothing beyond this function
    //       references `s`, so it was effectively a somewhat expensive dead
    //       store. It's been eliminated in this version.
 
    std::vector<Sync> syncjs8(int nfa, int nfb) {
        // Compute symbol spectra
 
        savg.fill(0.0f);
 
        for (int j = 0; j < Mode::NHSYM; ++j) {
            int const ia = j * Mode::NSTEP;
            int const ib = ia + Mode::NFFT1;
 
            if (ib > Mode::NMAX)
                break;
 
            std::transform(dd.begin() + ia, dd.begin() + ib, nuttal.begin(),
                           reinterpret_cast<float *>(sd.data()),
                           std::multiplies<float>{});
 
            fftwf_execute(plans[Plan::SD]);
 
            // Compute power spectrum
 
            for (int i = 0; i < Mode::NSPS; ++i) {
                auto const power = std::norm(sd[i]);
                s[i][j] = power;
                savg[i] += power;
            }
        }
 
        // Filter edge sanity measures
 
        int const nwin = nfb - nfa;
 
        if (nfa < 100) {
            nfa = 100;
            if (nwin < 100)
                nfb = nfa + nwin;
        }
 
        if (nfb > 4910) {
            nfb = 4910;
            if (nwin < 100)
                nfa = nfb - nwin;
        }
 
        auto const ia =
            std::max(0, static_cast<int>(std::round(nfa / Mode::DF)));
        auto const ib = static_cast<int>(std::round(nfb / Mode::DF));
 
        // Convert average spectrum from power to db scale and compute
        // baseline from it; baseline replaces average spectrum.
 
        baselinejs8(ia, ib);
 
        // Compute and populate the sync index.
 
        sync.clear();
 
        for (int i = ia; i <= ib; ++i) {
            float max_value = -std::numeric_limits<float>::infinity();
            int max_index = -Mode::JZ;
 
            for (int j = -Mode::JZ; j <= Mode::JZ; ++j) {
                std::array<std::array<float, 3>, 2> t{};
 
                for (int p = 0; p < 3; ++p) {
                    for (int n = 0; n < 7; ++n) {
                        int const offset =
                            j + Mode::JSTRT + NSSY * n + p * 36 * NSSY;
 
                        if (offset >= 0 && offset < Mode::NHSYM) {
                            // Accumulate Costas pattern contributions.
 
                            t[0][p] += s[i + NFOS * Costas[p][n]][offset];
 
                            // Accumulate sum over all frequencies for this
                            // block.
 
                            for (int freq = 0; freq < 7; ++freq) {
                                t[1][p] += s[i + NFOS * freq][offset];
                            }
                        }
                    }
                }
 
                // Compute sync metric over the index range. We are at the
                // moment maintaining the Fortran summation methodology for
                // compatibility testing; there are more efficient ways to do
                // this, but IEEE 754 addition is a touchy thing, so we'll need
                // to ensure that any changes don't negatively affect result
                // precision.
 
                auto const compute_sync = [&t](int start, int end) {
                    float tx = 0.0f;
                    float t0 = 0.0f;
 
                    for (int i = start; i <= end; ++i) {
                        tx += t[0][i];
                        t0 += t[1][i];
                    }
 
                    return tx / ((t0 - tx) / 6.0f);
                };
 
                if (auto const sync_value =
                        std::max({compute_sync(0, 2), compute_sync(0, 1),
                                  compute_sync(1, 2)});
                    sync_value > max_value) {
                    max_value = sync_value;
                    max_index = j;
                }
            }
 
            sync.emplace(Mode::DF * i, Mode::TSTEP * (max_index + 0.5f),
                         max_value);
        }
 
        // If we found nothing, we're done here.
 
        if (sync.empty())
            return {};
 
        // Access the sync indices.
 
        auto &freqIndex = sync.get<Tag::Freq>();
        auto &rankIndex = sync.get<Tag::Rank>();
        auto &syncIndex = sync.get<Tag::Sync>();
 
        // Normalize to the 40th percentile using the frequency index,
        // which is stable under sync value mutation. One thing to note
        // here is that the Fortran version didn't seem to reliably
        // calculate the 40th percentile rank; sometimes high, other
        // times low, infrequently actually the 40th percentile value.
        // This method should be perfectly accurate in all cases.
 
        auto const normalize =
            [sync = rankIndex.nth(rankIndex.size() * 4 / 10)->sync](
                Sync &entry) { entry.sync /= sync; };
 
        for (auto it = freqIndex.begin(); it != freqIndex.end(); ++it) {
            freqIndex.modify(it, normalize);
        }
 
        // Extract candidates.
 
        std::vector<Sync> candidates;
 
        for (auto it = syncIndex.begin();
             it != syncIndex.end() && candidates.size() < NMAXCAND;
             it = syncIndex.begin()) {
            // Stop iteration if below threshold or invalid; as the
            // index is sorted by sync, any subsequent entries will
            // also be below the threshold or invalid.
 
            if (it->sync < ASYNCMIN || std::isnan(it->sync))
                break;
 
            // Good value, relatively strong; save the candidate.
 
            candidates.push_back(*it);
 
            // Remove the candidate and any near-duplicates based
            // on frequency. This invalidates `it`, so we reset it
            // to the index begin in the loop increment condition.
 
            freqIndex.erase(freqIndex.lower_bound(it->freq - Mode::AZ),
                            freqIndex.upper_bound(it->freq + Mode::AZ));
        }
 
        return candidates;
    }
 
    // Returns the total synchronization power, which is a measure of how well
    // the signal aligns with the Costas sequence after accounting for the
    // frequency adjustment. Used to identify the best alignment for further
    // decoding.
 
    float syncjs8d(int const i0, float const delf) {
        constexpr float BASE_DPHI = TAU * (1.0f / (12000.0f / Mode::NDOWN));
 
        // If delta frequency is non-zero, compute the frequency
        // adjustment array, otherwise, use what'll be an identity
        // transfrom when multiplied.
 
        std::array<std::complex<float>, Mode::NDOWNSPS> freqAdjust;
 
        if (delf != 0.0f) {
            float const dphi = BASE_DPHI * delf;
            float phi = 0.0f;
 
            // std::fmod() is almost like Fortran's mod(), but not quite;
            // Since delf can be negative, we must ensure that phi stays
            // within [0, TAU), which Fortran's mod() handles by itself.
 
            for (int i = 0; i < Mode::NDOWNSPS; ++i) {
                freqAdjust[i] = std::polar(1.0f, phi);
                if (phi = std::fmod(phi + dphi, TAU); phi < 0.0f) {
                    phi += TAU;
                }
            }
        } else {
            freqAdjust.fill(std::complex<float>{1.0f, 0.0f});
        }
 
        // Compute sync power by looping over the Costas indices for
        // each of the 3 Costas blocks, accumulating as we go.
 
        float sync = 0.0f;
 
        for (int i = 0; i < 3; ++i) {
            for (int j = 0; j < 7; ++j) {
                if (auto const offset =
                        36 * i * Mode::NDOWNSPS + i0 + j * Mode::NDOWNSPS;
                    offset >= 0 && offset + Mode::NDOWNSPS <= Mode::NP2) {
                    sync += std::norm(std::transform_reduce(
                        freqAdjust.begin(),    // Range start
                        freqAdjust.end(),      // Range end
                        cd0.begin() + offset,  // Data start
                        std::complex<float>{}, // Initial reduction value
                        std::plus<>{},         // Reduction by accumulation
                        [&](auto const &fa,    // Conjugate and multiply
                            auto const &cd) {
                            return cd *
                                   std::conj(
                                       fa * csyncs[i][j][&fa - &freqAdjust[0]]);
                        }));
                }
            }
        }
 
        return sync;
    }
 
    // Generate a reference signal, based on the provided tone sequence and
    // base frequency. The output is a vector of complex values representing
    // the signal in the time domain.
 
    std::vector<std::complex<float>>
    genjs8refsig(std::array<int, NN> const &itone, float const f0) {
        // Precompute the base frequency contribution; full circle in
        // radians, multipled by the base frequency, multiplied by the
        // sampling interval, i.e., the time step between samples, which
        // results in the base frequency phase increment. Start the
        // phase accumulator off at zero.
 
        float const BFPI = TAU * f0 * (1.0f / 12000.0f);
        auto phi = 0.0f;
 
        std::vector<std::complex<float>> cref;
        cref.reserve(NN * Mode::NSPS);
 
        for (int i = 0; i < NN; ++i) {
            // Compute phase increment for the tone; frequency offset is
            // determined by the tone value.
 
            float const dphi =
                BFPI + TAU * static_cast<float>(itone[i]) / Mode::NSPS;
 
            // Iterate over the samples per symbol to generate the time
            // domain signal.
 
            for (std::size_t is = 0; is < Mode::NSPS; ++is) {
                cref.push_back(std::polar(1.0f, phi));
                phi = std::fmod(phi + dphi, TAU);
            }
        }
 
        return cref;
    }
 
    // Subtract a JS8 signal
    //
    // Measured signal  : dd(t)    = a(t)cos(2*pi*f0*t+theta(t))
    // Reference signal : cref(t)  = exp( j*(2*pi*f0*t+phi(t)) )
    // Complex amp      : cfilt(t) = LPF[ dd(t)*CONJG(cref(t)) ]
    // Subtract         : dd(t)    = dd(t) - 2*REAL{cref*cfilt}
    //
    // Important to note that dt can be negative here.
 
    void subtractjs8(std::vector<std::complex<float>> const &cref,
                     float const dt) {
        auto const nstart = static_cast<int>(dt * 12000.0f);
        std::size_t const cref_start =
            (nstart < 0) ? static_cast<std::size_t>(-nstart) : 0;
        std::size_t const dd_start =
            (nstart > 0) ? static_cast<std::size_t>(nstart) : 0;
        auto const size =
            std::min(cref.size() - cref_start, dd.size() - dd_start);
 
        // Populate complex filter with the conjugate of the reference signal.
 
        for (std::size_t i = 0; i < size; ++i) {
            cfilt[i] = dd[dd_start + i] * std::conj(cref[cref_start + i]);
        }
 
        // Zero-fill the remainder, if any.
 
        std::fill(cfilt.begin() + size, cfilt.end(), ZERO);
 
        // FFT to the frequency domain.
 
        fftwf_execute(plans[Plan::CF]);
 
        // Apply the filter in the frequency domain.
 
        std::transform(cfilt.begin(), cfilt.end(), filter.begin(),
                       cfilt.begin(), std::multiplies<>());
 
        // Inverse FFT to return to the time domain.
 
        fftwf_execute(plans[Plan::CB]);
 
        // Subtract the reconstructed signal.
 
        for (std::size_t i = 0; i < size; ++i) {
            dd[dd_start + i] -=
                2.0f * std::real(cfilt[i] * cref[cref_start + i]);
        }
    }
 
  public:
    // Constructor
 
    DecodeMode() {
        m_enableFreqTracking =
            std::getenv("JS8_DISABLE_FREQ_TRACKING") == nullptr;
        m_enableTimingTracking =
            std::getenv("JS8_DISABLE_TIMING_TRACKING") == nullptr;
 
        // Intialize the Nuttal window. In theory, we can do this as a
        // constexpr function at compile time, but doing so yield results
        // slightly different than the Fortran version did, so for sanity
        // while testing, we'll opt for consistency. IEEE 754 is always a
        // bit brittle.
 
        constexpr float a0 = 0.3635819f;
        constexpr float a1 = -0.4891775f;
        constexpr float a2 = 0.1365995f;
        constexpr float a3 = -0.0106411f;
 
        // Computed Pi constant to match the Fortran version; we could
        // probably use std::numbers::pi_v<float> here, but for the
        // moment, matching Fortran exactly.
 
        float const pi = 4.0f * std::atan(1.0f);
        float sum = 0.0f;
 
        for (std::size_t i = 0; i < nuttal.size(); ++i) {
            // Naive summation here will exhibit substantial precision loss
            // relative to the Fortran version; we use Kahan summation to
            // compensate, which should yield results identical to Fortran.
 
            KahanSum value = a0;
 
            value += a1 * std::cos(2 * pi * i / nuttal.size());
            value += a2 * std::cos(4 * pi * i / nuttal.size());
            value += a3 * std::cos(6 * pi * i / nuttal.size());
 
            nuttal[i] = value;
            sum += value;
        }
 
        // Normalize the Nuttal window.
 
        for (auto &value : nuttal)
            value = value / sum * nuttal.size() / 300.0f;
 
        // Initialize Costas waveforms.
 
        for (int i = 0; i < 7; ++i) {
            float const dphia = TAU * Costas[0][i] / Mode::NDOWNSPS;
            float const dphib = TAU * Costas[1][i] / Mode::NDOWNSPS;
            float const dphic = TAU * Costas[2][i] / Mode::NDOWNSPS;
 
            float phia = 0.0f;
            float phib = 0.0f;
            float phic = 0.0f;
 
            for (int j = 0; j < Mode::NDOWNSPS; ++j) {
                csyncs[0][i][j] = std::polar(1.0f, phia);
                csyncs[1][i][j] = std::polar(1.0f, phib);
                csyncs[2][i][j] = std::polar(1.0f, phic);
 
                phia = std::fmod(phia + dphia, TAU);
                phib = std::fmod(phib + dphib, TAU);
                phic = std::fmod(phic + dphic, TAU);
            }
        }
 
        // Compute a Hann-like window directly into the real part of the
        // first NFILT + 1 elements in the filter, accumulating the sum
        // as we go.
 
        sum = 0.0f;
 
        for (int j = -NFILT / 2; j <= NFILT / 2; ++j) {
            int const index = j + NFILT / 2;
            float const value = std::pow(std::cos(pi * j / NFILT), 2);
 
            filter[index].real(value);
            sum += value;
        }
 
        // Now that we've got the sum, create actual complex numbers using
        // the normalized real values that we just populated and zero the
        // rest of the filter.
 
        std::fill(std::transform(filter.begin(), filter.begin() + NFILT + 1,
                                 filter.begin(),
                                 [sum](auto const value) {
                                     return std::complex<float>(
                                         value.real() / sum, 0.0f);
                                 }),
                  filter.end(), ZERO);
 
        // Shift to position the window.
 
        std::rotate(filter.begin(), filter.begin() + NFILT / 2,
                    filter.begin() + NFILT + 1);
 
        // Transform the filter into the frequency domain.
 
        fftwf_plan fftw_plan;
        {
            std::lock_guard<std::mutex> lock(fftw_mutex);
 
            fftw_plan = fftwf_plan_dft_1d(
                Mode::NMAX, reinterpret_cast<fftwf_complex *>(filter.data()),
                reinterpret_cast<fftwf_complex *>(filter.data()), FFTW_FORWARD,
                FFTW_ESTIMATE_PATIENT);
 
            if (!fftw_plan) {
                throw std::runtime_error("Failed to create FFT plan");
            }
        }
 
        fftwf_execute(fftw_plan);
 
        {
            std::lock_guard<std::mutex> lock(fftw_mutex);
            fftwf_destroy_plan(fftw_plan);
        }
 
        // Normalize the frequency domain representation.
 
        std::transform(filter.begin(), filter.end(), filter.begin(),
                       [factor = 1.0f / Mode::NMAX](auto value) {
                           return value * factor;
                       });
 
        // The rest of our FFT plans are always the same size and operate on the
        // same data, so we can reuse them as long as we're alive.
 
        std::lock_guard<std::mutex> lock(fftw_mutex);
 
        plans[Plan::DS] = fftwf_plan_dft_1d(
            Mode::NDFFT2, reinterpret_cast<fftwf_complex *>(cd0.data()),
            reinterpret_cast<fftwf_complex *>(cd0.data()), FFTW_BACKWARD,
            FFTW_ESTIMATE_PATIENT);
 
        plans[Plan::BB] = fftwf_plan_dft_r2c_1d(
            Mode::NDFFT1, reinterpret_cast<float *>(ds_cx.data()),
            reinterpret_cast<fftwf_complex *>(ds_cx.data()),
            FFTW_ESTIMATE_PATIENT);
 
        plans[Plan::CF] = fftwf_plan_dft_1d(
            Mode::NMAX, reinterpret_cast<fftwf_complex *>(cfilt.data()),
            reinterpret_cast<fftwf_complex *>(cfilt.data()), FFTW_FORWARD,
            FFTW_ESTIMATE_PATIENT);
 
        plans[Plan::CB] = fftwf_plan_dft_1d(
            Mode::NMAX, reinterpret_cast<fftwf_complex *>(cfilt.data()),
            reinterpret_cast<fftwf_complex *>(cfilt.data()), FFTW_BACKWARD,
            FFTW_ESTIMATE_PATIENT);
 
        plans[Plan::SD] = fftwf_plan_dft_r2c_1d(
            Mode::NFFT1, reinterpret_cast<float *>(sd.data()),
            reinterpret_cast<fftwf_complex *>(sd.data()),
            FFTW_ESTIMATE_PATIENT);
 
        plans[Plan::CS] = fftwf_plan_dft_1d(
            Mode::NDOWNSPS, reinterpret_cast<fftwf_complex *>(csymb.data()),
            reinterpret_cast<fftwf_complex *>(csymb.data()), FFTW_FORWARD,
            FFTW_ESTIMATE_PATIENT);
 
        for (auto plan : plans) {
            if (!plan)
                throw std::runtime_error("Failed to create FFT plan");
        }
    }
 
    // Decode entry point.
 
    std::size_t operator()(struct dec_data const &data, int const kpos,
                           int const ksz, JS8::Event::Emitter emitEvent) {
        // Copy the relevant frames for decoding
 
        auto const pos = std::max(0, kpos);
        auto const sz = std::max(0, ksz);
 
        assert(sz <= Mode::NMAX);
 
        if (data.params.syncStats)
            emitEvent(JS8::Event::SyncStart{pos, sz});
 
        auto const ddCopy = [](auto const begin, auto const end,
                               auto const to) {
            std::transform(begin, end, to, [](auto const value) {
                return static_cast<float>(value);
            });
        };
 
        dd.fill(0.0f);
 
        if ((JS8_RX_SAMPLE_SIZE - pos) < sz) {
            // Wrap case; split into two parts.
 
            int const firstsize = JS8_RX_SAMPLE_SIZE - pos;
            int const secondsize = sz - firstsize;
 
            ddCopy(std::begin(data.d2) + pos,
                   std::begin(data.d2) + pos + firstsize, dd.begin());
            ddCopy(std::begin(data.d2), std::begin(data.d2) + secondsize,
                   dd.begin() + firstsize);
        } else {
            // Non-wrapping case; copy directly.
 
            ddCopy(std::begin(data.d2) + pos, std::begin(data.d2) + pos + sz,
                   dd.begin());
        }
 
        Decode::Map decodes;
        auto const ttl = std::chrono::seconds{Mode::NTXDUR * 2};
        m_softCombiner.flush(ttl);
 
        for (int ipass = 1; ipass <= 3; ++ipass) {
            // Determine if there's anything worth considering in the signal.
            // If not, then we can just bail completely; more passes will not
            // yield more results. If we do have some candidates, sort them
            // by frequency, but put any that are close to nfqso up front.
 
            auto candidates = syncjs8(data.params.nfa, data.params.nfb);
 
            if (candidates.empty())
                break;
 
            std::sort(
                candidates.begin(), candidates.end(),
                [nfqso = data.params.nfqso](auto const &a, auto const &b) {
                    auto const a_dist = std::abs(a.freq - nfqso);
                    auto const b_dist = std::abs(b.freq - nfqso);
 
                    if (a_dist < 10.0f && b_dist >= 10.0f)
                        return true;
                    if (b_dist < 10.0f && a_dist >= 10.0f)
                        return false;
 
                    return std::tie(a_dist, a.freq) < std::tie(b_dist, b.freq);
                });
 
            // Recompute the baseband signal; subtraction during the last
            // pass might have changed the landscape.
 
            computeBasebandFFT();
 
            bool const subtract = ipass < 3;
            bool improved = false;
 
            for (auto [f1, xdt, sync] : candidates) {
                float xsnr = 0.0f;
                int nharderrors = -1;
 
                if (auto decode = js8dec(data.params.syncStats, subtract, f1,
                                         xdt, nharderrors, xsnr, emitEvent)) {
                    // We don't need to be emitting duplicate events for
                    // something that's effectively the same SNR as a previous
                    // event.
 
                    auto const snr = static_cast<int>(std::round(xsnr));
 
                    // If this decode is new, or it's a duplicate with a better
                    // SNR than what we had before, then our situation has
                    // improved and we must announce that we've had some
                    // success.
 
                    if (auto [it, inserted] =
                            decodes.try_emplace(std::move(*decode), snr);
                        inserted || it->second < snr) {
                        improved = true;
 
                        // Update the SNR if this is an improved decode.
 
                        if (!inserted)
                            it->second = snr;
 
                        // Emit decoded events on new or improved decodes.
 
                        emitEvent(JS8::Event::Decoded{
                            data.params.nutc, snr, xdt - Mode::ASTART, f1,
                            it->first.data, it->first.type,
                            1.0f - nharderrors / 60.0f, Mode::NSUBMODE});
                    }
                }
            }
 
            // If nothing from this pass improved our situation, there's no
            // point in trying any remaining passes.
 
            if (!improved)
                break;
        }
 
        // Let the caller know how many unique decodes we discovered, if any.
 
        return decodes.size();
    }
};
 
// Explicit template class instantiations; avoids compiler complaints
// about unused variables.
 
template class DecodeMode<ModeA>;
template class DecodeMode<ModeB>;
template class DecodeMode<ModeC>;
template class DecodeMode<ModeE>;
template class DecodeMode<ModeI>;
} // namespace
} // namespace
 
/******************************************************************************/
// Worker
/******************************************************************************/
 
namespace JS8 {
class Worker : public QObject {
    Q_OBJECT
 
    // Initialization of the decoders, in that they're heavy with
    // FFT plan creations, is non-trivial, so a handle-body class
    // to avoid initializing them on the main thread.
 
    class Impl {
        // To avoid data races, decode data is referenced here but is
        // actually located in the Worker that instantiates us, as it
        // must be possible to copy data for us before we're ready to
        // process it.
 
        struct dec_data &m_data;
 
        // Mode-specific decode strategy; we'll instantiate one of
        // these for each of the 5 modes; this class is an aggregate
        // of the 5 modes.
 
        struct DecodeEntry {
            std::variant<DecodeMode<ModeA>, DecodeMode<ModeB>,
                         DecodeMode<ModeC>, DecodeMode<ModeE>,
                         DecodeMode<ModeI>>
                decode;
            int mode;
            int &kpos;
            int &ksz;
 
            template <typename DecodeModeType>
            DecodeEntry(std::in_place_type_t<DecodeModeType>, int mode,
                        int &kpos, int &ksz)
                : decode(std::in_place_type<DecodeModeType>), mode(mode),
                  kpos(kpos), ksz(ksz) {}
        };
 
        // Since a strategy can be neither moved nor copied, we must
        // instantiate them in-place. Note that with the advent of the
        // multi-decoder, mode identifiers became a bitset instead of
        // integral values. The order defined here is the order that
        // the decode loop will run in; we're matching the Fortran
        // version here in terms of faster modes first.
 
        template <typename ModeType>
        DecodeEntry makeDecodeEntry(int shift, int &kpos, int &ksz) {
            return DecodeEntry(std::in_place_type<DecodeMode<ModeType>>,
                               1 << shift, kpos, ksz);
        }
 
        std::array<DecodeEntry, 5> m_decodes = {
            {makeDecodeEntry<ModeI>(4, m_data.params.kposI, m_data.params.kszI),
             makeDecodeEntry<ModeE>(3, m_data.params.kposE, m_data.params.kszE),
             makeDecodeEntry<ModeC>(2, m_data.params.kposC, m_data.params.kszC),
             makeDecodeEntry<ModeB>(1, m_data.params.kposB, m_data.params.kszB),
             makeDecodeEntry<ModeA>(0, m_data.params.kposA,
                                    m_data.params.kszA)}};
 
      public:
        // Constructor
 
        explicit Impl(struct dec_data &data) : m_data(data) {}
 
        // Execute a decoding pass, using the supplied event emitter to
        // emit events as they occur.
 
        void operator()(::JS8::Event::Emitter emitEvent) {
            // The multi-decoder can provide data for multiple modes at
            // the same time; specific decodes to be performed for this
            // pass are in the `nsubmodes` bitset.
 
            auto const set = m_data.params.nsubmodes;
            std::size_t sum = 0;
 
            // Let any interested parties know that we've started a run
            // for the set of modes requested.
 
            emitEvent(::JS8::Event::DecodeStarted{set});
 
            // Iterate through all the modes we're aware of, performing
            // a mode-specific decode pass if the mode is scheduled for
            // decoding during this pass.
 
            for (auto &entry : m_decodes) {
                if ((set & entry.mode) == entry.mode) {
                    std::visit(
                        [&](auto &&decode) {
                            sum += decode(m_data, entry.kpos, entry.ksz,
                                          emitEvent);
                        },
                        entry.decode);
                }
            }
 
            // Let any interested parties know the total number of decodes
            // performed during this run.
 
            emitEvent(::JS8::Event::DecodeFinished{sum});
        }
    };
 
    // Data members
 
    QSemaphore *m_semaphore;
    std::atomic<bool> m_quit = false;
    struct dec_data m_data;
 
  public:
    // Constructor
 
    explicit Worker(QSemaphore *semaphore, QObject *parent = nullptr)
        : QObject(parent), m_semaphore(semaphore) {}
 
    // Used to inform the worker that it's time to go; the next
    // time it wakes up due to the semaphore being released, it
    // will exit the runloop.
 
    void stop() { m_quit = true; }
 
    // Called by the owning Decoder to refresh the copy of the
    // decode data that the Worker implementation references.
 
    void copy() { m_data = dec_data; };
 
  signals:
 
    // Signal used to indicate that something of interest has
    // occurred during a decoding pass.
 
    void decodeEvent(::JS8::Event::Variant const &);
 
  public slots:
 
    // Runloop for the thread that the worker is scheduled on; this
    // is started by the Decoder when it's informed that the thread
    // has started. Performs decoding runs each time the semaphore
    // is released, until it's informed that it should quit.
 
    void run() {
        // Our thread has started, and we're now running on it, so
        // we're good to now allocate our implementation; we didn't
        // want that to happen on the main thread, as the FFT plans
        // can take a while. We only need the implementation while
        // we're running.
 
        std::unique_ptr<Impl> impl = std::make_unique<Impl>(m_data);
 
        // Wait until there's something that requires our attention,
        // which is going to either be needing to quit or needing to
        // perform a decoding pass.
 
        while (true) {
            m_semaphore->acquire();
 
            if (m_quit)
                break;
 
            (*impl)([this](::JS8::Event::Variant const &event) {
                emit decodeEvent(event);
            });
        }
    }
};
} // namespace JS8
 
/******************************************************************************/
// Public Interface - Decoding
/******************************************************************************/
 
#include "JS8.moc"
 
JS8::Decoder::Decoder(QObject *parent)
    : QObject(parent), m_semaphore(0), m_worker(new JS8::Worker(&m_semaphore)) {
    m_worker->moveToThread(&m_thread);
 
    connect(&m_thread, &QThread::started, m_worker, &JS8::Worker::run);
    connect(&m_thread, &QThread::finished, m_worker, &QObject::deleteLater);
    connect(m_worker, &JS8::Worker::decodeEvent, this, &Decoder::decodeEvent);
}
 
void JS8::Decoder::start(QThread::Priority priority) {
    m_thread.start(priority);
}
 
void JS8::Decoder::quit() {
    m_worker->stop();
    m_semaphore.release();
    m_thread.quit();
    m_thread.wait();
}
 
void JS8::Decoder::decode() {
    m_worker->copy();
    m_semaphore.release();
}
 
/******************************************************************************/
// Public Interface - Encoding
/******************************************************************************/
 
namespace JS8 {
// Port of the Fortran `genjs8` subroutine; from the 12 bytes of `message`,
// construct an 87-bit JS8 message and encode it into tones. Costas array
// to use supplied by the caller, as is the type of message, indicated by
// the lower 3 bits of `type`.
 
void encode(int const type, Costas::Array const &costas,
            const char *const message, int *const tones) {
    // Our initial goal here is an 87-bit message, for which a std::bitset
    // would be the obvious choice, but we've got to compute a checksum of
    // the first 75 bits; thus, an array instead.
    //
    // Message structure:
    //
    //     +----------+----------+----------+
    //     |          |          |  72 bits |  12 6-bit words
    //     |          |          +==========+
    //     |          | 87 bits  |   3 bits |  Frame type
    //     | 11 bytes |          +==========+
    //     |          |          |  12 bits |  12-bit BE checksum
    //     |          |----------+==========+
    //     |          |  1 bit   |   1 bit  |  Leftover bit in array
    //     +----------+----------+==========+
 
    std::array<std::uint8_t, 11> bytes = {};
 
    // Convert the 12 characters we've been handed to 6-bit words and pack
    // them into the byte array, 4 characters, 24 bits at a time, into the
    // 9 bytes [0,8], 72 bits total. Throws if handed an invalid character.
 
    for (int i = 0, j = 0; i < 12; i += 4, j += 3) {
        std::uint32_t words = (alphabetWord(message[i]) << 18) |
                              (alphabetWord(message[i + 1]) << 12) |
                              (alphabetWord(message[i + 2]) << 6) |
                              alphabetWord(message[i + 3]);
 
        bytes[j] = words >> 16;
        bytes[j + 1] = words >> 8;
        bytes[j + 2] = words;
    }
 
    // The bottom 3 bits of type are the frame type; these go into the
    // next 3 bits in the byte array, i.e., the first 3 bits of byte 9,
    // after which we'll be at 75 bits in total.
 
    bytes[9] = (type & 0b111) << 5;
 
    // We now need to compute the augmented CRC-12 of the complete
    // byte array, including the trailing zero bits that we've not
    // set yet.
 
    auto const crc = CRC12(bytes);
 
    // That CRC needs to occupy the next 12 bits of the array, i.e.,
    // the final 5 bits of byte 9, and the first 7 bits of byte 10.
 
    bytes[9] |= (crc >> 7) & 0x1F;
    bytes[10] = (crc & 0x7F) << 1;
 
    // That's it for our 87-bit message; we're now going to turn it
    // into two blocks of 29 3-bit words, which will in turn become
    // tones, the first block being parity for the second, bracketed
    // by the Costas arrays.
    //
    // Output structure:
    //
    //     +----------+----------+
    //     |          |  7 bytes |  Costas array A
    //     |          +==========+
    //     |          | 29 bytes |  Parity data
    //     |          +==========+
    //     | 79 bytes |  7 bytes |  Costas array B
    //     |          +==========+
    //     |          | 29 bytes |  Output data
    //     |          +==========+
    //     |          |  7 bytes |  Costas array C
    //     +----------+==========+
 
    auto costasData = tones;
    auto parityData = tones + 7;
    auto outputData = tones + 43;
 
    // Output the 3 Costas arrays at offsets 0, 36, and 72.
 
    for (auto const &array : costas) {
        std::copy(array.begin(), array.end(), costasData);
        costasData += 36;
    }
 
    // Our 87 bits are going to be morphed into two sets of 29 3-bit
    // words, the first one parity for the second; we're going to do
    // this in parallel.
 
    std::size_t outputBits = 0;
    std::size_t outputByte = 0;
    std::uint8_t outputMask = 0x80;
    std::uint8_t outputWord = 0;
    std::uint8_t parityWord = 0;
 
    for (std::size_t i = 0; i < 87; ++i) {
        // Compute parity for the current bit; inputs for parity computation
        // are the corresponding parity matrix row and each bit in the message;
        // the parity matrix row, referenced by `i`, contains 87 boolean values.
        // Each `true` value defines a message bit that must be summed, modulo
        // 2, to produce the parity check bit for the bit we're working on now.
        //
        // In short, if the parity matrix bit `(i, j)` and the message bit `j`
        // are both set, then we add 1 to the parity bits accumulator. If, after
        // processing all message bits the accumulated result is odd, then the
        // parity bit should be set for the current bit.
 
        std::size_t parityBits = 0;
        std::size_t parityByte = 0;
        std::uint8_t parityMask = 0x80;
 
        for (std::size_t j = 0; j < 87; ++j) {
            parityBits += parity(i, j) && (bytes[parityByte] & parityMask);
            parityMask =
                (parityMask == 1) ? (++parityByte, 0x80) : (parityMask >> 1);
        }
 
        // Accumulate the parity and output bits; this is the point at which
        // we perform the modulo 2 operation on the summed parity bits.
 
        parityWord = (parityWord << 1) | (parityBits & 1);
        outputWord =
            (outputWord << 1) | ((bytes[outputByte] & outputMask) != 0);
        outputMask =
            (outputMask == 1) ? (++outputByte, 0x80) : (outputMask >> 1);
 
        // If we're at a 3-bit boundary, output the words and reset.
 
        if (++outputBits == 3) {
            *parityData++ = parityWord;
            *outputData++ = outputWord;
            parityWord = 0;
            outputWord = 0;
            outputBits = 0;
        }
    }
}
} // namespace JS8
 
/******************************************************************************/