243 lines
8.6 KiB
C++
243 lines
8.6 KiB
C++
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#include "decode.h"
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#include <math.h>
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#include "constants.h"
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static float max2(float a, float b);
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static float max4(float a, float b, float c, float d);
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static void heapify_down(Candidate *heap, int heap_size);
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static void heapify_up(Candidate *heap, int heap_size);
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static void decode_symbol(const uint8_t *power, const uint8_t *code_map, int bit_idx, float *log174);
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static void decode_multi_symbols(const uint8_t *power, int num_bins, int n_syms, const uint8_t *code_map, int bit_idx, float *log174);
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// Localize top N candidates in frequency and time according to their sync strength (looking at Costas symbols)
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// We treat and organize the candidate list as a min-heap (empty initially).
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int find_sync(const uint8_t *power, int num_blocks, int num_bins, const uint8_t *sync_map, int num_candidates, Candidate *heap) {
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int heap_size = 0;
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// Here we allow time offsets that exceed signal boundaries, as long as we still have all data bits.
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// I.e. we can afford to skip the first 7 or the last 7 Costas symbols, as long as we track how many
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// sync symbols we included in the score, so the score is averaged.
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for (int alt = 0; alt < 4; ++alt) {
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for (int time_offset = -7; time_offset < num_blocks - FT8_NN + 7; ++time_offset) {
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for (int freq_offset = 0; freq_offset < num_bins - 8; ++freq_offset) {
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int score = 0;
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// Compute average score over sync symbols (m+k = 0-7, 36-43, 72-79)
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int num_symbols = 0;
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for (int m = 0; m <= 72; m += 36) {
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for (int k = 0; k < 7; ++k) {
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// Check for time boundaries
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if (time_offset + k + m < 0) continue;
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if (time_offset + k + m >= num_blocks) break;
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int offset = ((time_offset + k + m) * 4 + alt) * num_bins + freq_offset;
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const uint8_t *p8 = power + offset;
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score += 8 * p8[sync_map[k]] -
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p8[0] - p8[1] - p8[2] - p8[3] -
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p8[4] - p8[5] - p8[6] - p8[7];
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// int sm = sync_map[k];
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// score += 4 * (int)p8[sm];
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// if (sm > 0) score -= p8[sm - 1];
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// if (sm < 7) score -= p8[sm + 1];
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// if (k > 0) score -= p8[sm - 4 * num_bins];
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// if (k < 6) score -= p8[sm + 4 * num_bins];
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++num_symbols;
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}
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}
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score /= num_symbols;
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// If the heap is full AND the current candidate is better than
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// the worst in the heap, we remove the worst and make space
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if (heap_size == num_candidates && score > heap[0].score) {
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heap[0] = heap[heap_size - 1];
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--heap_size;
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heapify_down(heap, heap_size);
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}
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// If there's free space in the heap, we add the current candidate
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if (heap_size < num_candidates) {
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heap[heap_size].score = score;
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heap[heap_size].time_offset = time_offset;
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heap[heap_size].freq_offset = freq_offset;
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heap[heap_size].time_sub = alt / 2;
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heap[heap_size].freq_sub = alt % 2;
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++heap_size;
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heapify_up(heap, heap_size);
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}
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}
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}
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}
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return heap_size;
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}
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// Compute log likelihood log(p(1) / p(0)) of 174 message bits
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// for later use in soft-decision LDPC decoding
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void extract_likelihood(const uint8_t *power, int num_bins, const Candidate & cand, const uint8_t *code_map, float *log174) {
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int offset = (cand.time_offset * 4 + cand.time_sub * 2 + cand.freq_sub) * num_bins + cand.freq_offset;
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// Go over FSK tones and skip Costas sync symbols
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const int n_syms = 1;
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const int n_bits = 3 * n_syms;
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const int n_tones = (1 << n_bits);
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for (int k = 0; k < FT8_ND; k += n_syms) {
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int sym_idx = (k < FT8_ND / 2) ? (k + 7) : (k + 14);
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int bit_idx = 3 * k;
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// Pointer to 8 bins of the current symbol
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const uint8_t *ps = power + (offset + sym_idx * 4 * num_bins);
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decode_symbol(ps, code_map, bit_idx, log174);
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}
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// Compute the variance of log174
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float sum = 0;
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float sum2 = 0;
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float inv_n = 1.0f / FT8_N;
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for (int i = 0; i < FT8_N; ++i) {
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sum += log174[i];
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sum2 += log174[i] * log174[i];
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}
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float variance = (sum2 - sum * sum * inv_n) * inv_n;
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// Normalize log174 such that sigma = 2.83 (Why? It's in WSJT-X, ft8b.f90)
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// Seems to be 2.83 = sqrt(8). Experimentally sqrt(16) works better.
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float norm_factor = sqrtf(16.0f / variance);
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for (int i = 0; i < FT8_N; ++i) {
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log174[i] *= norm_factor;
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}
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}
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static float max2(float a, float b) {
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return (a >= b) ? a : b;
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}
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static float max4(float a, float b, float c, float d) {
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return max2(max2(a, b), max2(c, d));
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}
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static void heapify_down(Candidate *heap, int heap_size) {
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// heapify from the root down
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int current = 0;
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while (true) {
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int largest = current;
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int left = 2 * current + 1;
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int right = left + 1;
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if (left < heap_size && heap[left].score < heap[largest].score) {
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largest = left;
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}
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if (right < heap_size && heap[right].score < heap[largest].score) {
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largest = right;
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}
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if (largest == current) {
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break;
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}
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Candidate tmp = heap[largest];
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heap[largest] = heap[current];
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heap[current] = tmp;
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current = largest;
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}
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}
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static void heapify_up(Candidate *heap, int heap_size) {
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// heapify from the last node up
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int current = heap_size - 1;
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while (current > 0) {
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int parent = (current - 1) / 2;
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if (heap[current].score >= heap[parent].score) {
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break;
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}
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Candidate tmp = heap[parent];
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heap[parent] = heap[current];
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heap[current] = tmp;
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current = parent;
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}
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}
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// Compute unnormalized log likelihood log(p(1) / p(0)) of 3 message bits (1 FSK symbol)
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static void decode_symbol(const uint8_t *power, const uint8_t *code_map, int bit_idx, float *log174) {
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// Cleaned up code for the simple case of n_syms==1
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float s2[8];
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for (int j = 0; j < 8; ++j) {
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s2[j] = (float)power[code_map[j]];
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}
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log174[bit_idx + 0] = max4(s2[4], s2[5], s2[6], s2[7]) - max4(s2[0], s2[1], s2[2], s2[3]);
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log174[bit_idx + 1] = max4(s2[2], s2[3], s2[6], s2[7]) - max4(s2[0], s2[1], s2[4], s2[5]);
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log174[bit_idx + 2] = max4(s2[1], s2[3], s2[5], s2[7]) - max4(s2[0], s2[2], s2[4], s2[6]);
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}
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// Compute unnormalized log likelihood log(p(1) / p(0)) of bits corresponding to several FSK symbols at once
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static void decode_multi_symbols(const uint8_t *power, int num_bins, int n_syms, const uint8_t *code_map, int bit_idx, float *log174) {
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// The following section implements what seems to be multiple-symbol decode at one go,
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// corresponding to WSJT-X's ft8b.f90. Experimentally found not to be any better than
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// 1-symbol decode.
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const int n_bits = 3 * n_syms;
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const int n_tones = (1 << n_bits);
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float s2[n_tones];
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for (int j = 0; j < n_tones; ++j) {
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int j1 = j & 0x07;
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if (n_syms == 1) {
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s2[j] = (float)power[code_map[j1]];
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continue;
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}
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int j2 = (j >> 3) & 0x07;
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if (n_syms == 2) {
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s2[j] = (float)power[code_map[j2]];
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s2[j] += (float)power[code_map[j1] + 4 * num_bins];
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continue;
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}
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int j3 = (j >> 6) & 0x07;
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s2[j] = (float)power[code_map[j3]];
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s2[j] += (float)power[code_map[j2] + 4 * num_bins];
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s2[j] += (float)power[code_map[j1] + 8 * num_bins];
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}
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// No need to go back to linear scale any more. Works better in dB.
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// for (int j = 0; j < n_tones; ++j) {
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// s2[j] = powf(10.0f, 0.1f * s2[j]);
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// }
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// Extract bit significance (and convert them to float)
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// 8 FSK tones = 3 bits
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for (int i = 0; i < n_bits; ++i) {
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if (bit_idx + i >= FT8_N) {
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// Respect array size
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break;
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}
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uint16_t mask = (n_tones >> (i + 1));
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float max_zero = -1000, max_one = -1000;
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for (int n = 0; n < n_tones; ++n) {
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if (n & mask) {
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max_one = max2(max_one, s2[n]);
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}
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else {
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max_zero = max2(max_zero, s2[n]);
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}
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}
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log174[bit_idx + i] = max_one - max_zero;
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}
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}
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