#include "encode_v2.h" #include namespace ft8_v2 { // Define the LDPC sizes constexpr int N = 174; // Number of bits in the encoded message constexpr int K = 91; // Number of payload bits constexpr int M = N - K; // Number of checksum bits constexpr uint16_t POLYNOMIAL = 0x2757; // CRC-14 polynomial without the leading (MSB) 1 constexpr int K_BYTES = (K + 7) / 8; // Number of whole bytes needed to store K bits // Parity generator matrix for (174,91) LDPC code, stored in bitpacked format (MSB first) const uint8_t kGenerator[M][K_BYTES] = { { 0x83, 0x29, 0xce, 0x11, 0xbf, 0x31, 0xea, 0xf5, 0x09, 0xf2, 0x7f, 0xc0 }, { 0x76, 0x1c, 0x26, 0x4e, 0x25, 0xc2, 0x59, 0x33, 0x54, 0x93, 0x13, 0x20 }, { 0xdc, 0x26, 0x59, 0x02, 0xfb, 0x27, 0x7c, 0x64, 0x10, 0xa1, 0xbd, 0xc0 }, { 0x1b, 0x3f, 0x41, 0x78, 0x58, 0xcd, 0x2d, 0xd3, 0x3e, 0xc7, 0xf6, 0x20 }, { 0x09, 0xfd, 0xa4, 0xfe, 0xe0, 0x41, 0x95, 0xfd, 0x03, 0x47, 0x83, 0xa0 }, { 0x07, 0x7c, 0xcc, 0xc1, 0x1b, 0x88, 0x73, 0xed, 0x5c, 0x3d, 0x48, 0xa0 }, { 0x29, 0xb6, 0x2a, 0xfe, 0x3c, 0xa0, 0x36, 0xf4, 0xfe, 0x1a, 0x9d, 0xa0 }, { 0x60, 0x54, 0xfa, 0xf5, 0xf3, 0x5d, 0x96, 0xd3, 0xb0, 0xc8, 0xc3, 0xe0 }, { 0xe2, 0x07, 0x98, 0xe4, 0x31, 0x0e, 0xed, 0x27, 0x88, 0x4a, 0xe9, 0x00 }, { 0x77, 0x5c, 0x9c, 0x08, 0xe8, 0x0e, 0x26, 0xdd, 0xae, 0x56, 0x31, 0x80 }, { 0xb0, 0xb8, 0x11, 0x02, 0x8c, 0x2b, 0xf9, 0x97, 0x21, 0x34, 0x87, 0xc0 }, { 0x18, 0xa0, 0xc9, 0x23, 0x1f, 0xc6, 0x0a, 0xdf, 0x5c, 0x5e, 0xa3, 0x20 }, { 0x76, 0x47, 0x1e, 0x83, 0x02, 0xa0, 0x72, 0x1e, 0x01, 0xb1, 0x2b, 0x80 }, { 0xff, 0xbc, 0xcb, 0x80, 0xca, 0x83, 0x41, 0xfa, 0xfb, 0x47, 0xb2, 0xe0 }, { 0x66, 0xa7, 0x2a, 0x15, 0x8f, 0x93, 0x25, 0xa2, 0xbf, 0x67, 0x17, 0x00 }, { 0xc4, 0x24, 0x36, 0x89, 0xfe, 0x85, 0xb1, 0xc5, 0x13, 0x63, 0xa1, 0x80 }, { 0x0d, 0xff, 0x73, 0x94, 0x14, 0xd1, 0xa1, 0xb3, 0x4b, 0x1c, 0x27, 0x00 }, { 0x15, 0xb4, 0x88, 0x30, 0x63, 0x6c, 0x8b, 0x99, 0x89, 0x49, 0x72, 0xe0 }, { 0x29, 0xa8, 0x9c, 0x0d, 0x3d, 0xe8, 0x1d, 0x66, 0x54, 0x89, 0xb0, 0xe0 }, { 0x4f, 0x12, 0x6f, 0x37, 0xfa, 0x51, 0xcb, 0xe6, 0x1b, 0xd6, 0xb9, 0x40 }, { 0x99, 0xc4, 0x72, 0x39, 0xd0, 0xd9, 0x7d, 0x3c, 0x84, 0xe0, 0x94, 0x00 }, { 0x19, 0x19, 0xb7, 0x51, 0x19, 0x76, 0x56, 0x21, 0xbb, 0x4f, 0x1e, 0x80 }, { 0x09, 0xdb, 0x12, 0xd7, 0x31, 0xfa, 0xee, 0x0b, 0x86, 0xdf, 0x6b, 0x80 }, { 0x48, 0x8f, 0xc3, 0x3d, 0xf4, 0x3f, 0xbd, 0xee, 0xa4, 0xea, 0xfb, 0x40 }, { 0x82, 0x74, 0x23, 0xee, 0x40, 0xb6, 0x75, 0xf7, 0x56, 0xeb, 0x5f, 0xe0 }, { 0xab, 0xe1, 0x97, 0xc4, 0x84, 0xcb, 0x74, 0x75, 0x71, 0x44, 0xa9, 0xa0 }, { 0x2b, 0x50, 0x0e, 0x4b, 0xc0, 0xec, 0x5a, 0x6d, 0x2b, 0xdb, 0xdd, 0x00 }, { 0xc4, 0x74, 0xaa, 0x53, 0xd7, 0x02, 0x18, 0x76, 0x16, 0x69, 0x36, 0x00 }, { 0x8e, 0xba, 0x1a, 0x13, 0xdb, 0x33, 0x90, 0xbd, 0x67, 0x18, 0xce, 0xc0 }, { 0x75, 0x38, 0x44, 0x67, 0x3a, 0x27, 0x78, 0x2c, 0xc4, 0x20, 0x12, 0xe0 }, { 0x06, 0xff, 0x83, 0xa1, 0x45, 0xc3, 0x70, 0x35, 0xa5, 0xc1, 0x26, 0x80 }, { 0x3b, 0x37, 0x41, 0x78, 0x58, 0xcc, 0x2d, 0xd3, 0x3e, 0xc3, 0xf6, 0x20 }, { 0x9a, 0x4a, 0x5a, 0x28, 0xee, 0x17, 0xca, 0x9c, 0x32, 0x48, 0x42, 0xc0 }, { 0xbc, 0x29, 0xf4, 0x65, 0x30, 0x9c, 0x97, 0x7e, 0x89, 0x61, 0x0a, 0x40 }, { 0x26, 0x63, 0xae, 0x6d, 0xdf, 0x8b, 0x5c, 0xe2, 0xbb, 0x29, 0x48, 0x80 }, { 0x46, 0xf2, 0x31, 0xef, 0xe4, 0x57, 0x03, 0x4c, 0x18, 0x14, 0x41, 0x80 }, { 0x3f, 0xb2, 0xce, 0x85, 0xab, 0xe9, 0xb0, 0xc7, 0x2e, 0x06, 0xfb, 0xe0 }, { 0xde, 0x87, 0x48, 0x1f, 0x28, 0x2c, 0x15, 0x39, 0x71, 0xa0, 0xa2, 0xe0 }, { 0xfc, 0xd7, 0xcc, 0xf2, 0x3c, 0x69, 0xfa, 0x99, 0xbb, 0xa1, 0x41, 0x20 }, { 0xf0, 0x26, 0x14, 0x47, 0xe9, 0x49, 0x0c, 0xa8, 0xe4, 0x74, 0xce, 0xc0 }, { 0x44, 0x10, 0x11, 0x58, 0x18, 0x19, 0x6f, 0x95, 0xcd, 0xd7, 0x01, 0x20 }, { 0x08, 0x8f, 0xc3, 0x1d, 0xf4, 0xbf, 0xbd, 0xe2, 0xa4, 0xea, 0xfb, 0x40 }, { 0xb8, 0xfe, 0xf1, 0xb6, 0x30, 0x77, 0x29, 0xfb, 0x0a, 0x07, 0x8c, 0x00 }, { 0x5a, 0xfe, 0xa7, 0xac, 0xcc, 0xb7, 0x7b, 0xbc, 0x9d, 0x99, 0xa9, 0x00 }, { 0x49, 0xa7, 0x01, 0x6a, 0xc6, 0x53, 0xf6, 0x5e, 0xcd, 0xc9, 0x07, 0x60 }, { 0x19, 0x44, 0xd0, 0x85, 0xbe, 0x4e, 0x7d, 0xa8, 0xd6, 0xcc, 0x7d, 0x00 }, { 0x25, 0x1f, 0x62, 0xad, 0xc4, 0x03, 0x2f, 0x0e, 0xe7, 0x14, 0x00, 0x20 }, { 0x56, 0x47, 0x1f, 0x87, 0x02, 0xa0, 0x72, 0x1e, 0x00, 0xb1, 0x2b, 0x80 }, { 0x2b, 0x8e, 0x49, 0x23, 0xf2, 0xdd, 0x51, 0xe2, 0xd5, 0x37, 0xfa, 0x00 }, { 0x6b, 0x55, 0x0a, 0x40, 0xa6, 0x6f, 0x47, 0x55, 0xde, 0x95, 0xc2, 0x60 }, { 0xa1, 0x8a, 0xd2, 0x8d, 0x4e, 0x27, 0xfe, 0x92, 0xa4, 0xf6, 0xc8, 0x40 }, { 0x10, 0xc2, 0xe5, 0x86, 0x38, 0x8c, 0xb8, 0x2a, 0x3d, 0x80, 0x75, 0x80 }, { 0xef, 0x34, 0xa4, 0x18, 0x17, 0xee, 0x02, 0x13, 0x3d, 0xb2, 0xeb, 0x00 }, { 0x7e, 0x9c, 0x0c, 0x54, 0x32, 0x5a, 0x9c, 0x15, 0x83, 0x6e, 0x00, 0x00 }, { 0x36, 0x93, 0xe5, 0x72, 0xd1, 0xfd, 0xe4, 0xcd, 0xf0, 0x79, 0xe8, 0x60 }, { 0xbf, 0xb2, 0xce, 0xc5, 0xab, 0xe1, 0xb0, 0xc7, 0x2e, 0x07, 0xfb, 0xe0 }, { 0x7e, 0xe1, 0x82, 0x30, 0xc5, 0x83, 0xcc, 0xcc, 0x57, 0xd4, 0xb0, 0x80 }, { 0xa0, 0x66, 0xcb, 0x2f, 0xed, 0xaf, 0xc9, 0xf5, 0x26, 0x64, 0x12, 0x60 }, { 0xbb, 0x23, 0x72, 0x5a, 0xbc, 0x47, 0xcc, 0x5f, 0x4c, 0xc4, 0xcd, 0x20 }, { 0xde, 0xd9, 0xdb, 0xa3, 0xbe, 0xe4, 0x0c, 0x59, 0xb5, 0x60, 0x9b, 0x40 }, { 0xd9, 0xa7, 0x01, 0x6a, 0xc6, 0x53, 0xe6, 0xde, 0xcd, 0xc9, 0x03, 0x60 }, { 0x9a, 0xd4, 0x6a, 0xed, 0x5f, 0x70, 0x7f, 0x28, 0x0a, 0xb5, 0xfc, 0x40 }, { 0xe5, 0x92, 0x1c, 0x77, 0x82, 0x25, 0x87, 0x31, 0x6d, 0x7d, 0x3c, 0x20 }, { 0x4f, 0x14, 0xda, 0x82, 0x42, 0xa8, 0xb8, 0x6d, 0xca, 0x73, 0x35, 0x20 }, { 0x8b, 0x8b, 0x50, 0x7a, 0xd4, 0x67, 0xd4, 0x44, 0x1d, 0xf7, 0x70, 0xe0 }, { 0x22, 0x83, 0x1c, 0x9c, 0xf1, 0x16, 0x94, 0x67, 0xad, 0x04, 0xb6, 0x80 }, { 0x21, 0x3b, 0x83, 0x8f, 0xe2, 0xae, 0x54, 0xc3, 0x8e, 0xe7, 0x18, 0x00 }, { 0x5d, 0x92, 0x6b, 0x6d, 0xd7, 0x1f, 0x08, 0x51, 0x81, 0xa4, 0xe1, 0x20 }, { 0x66, 0xab, 0x79, 0xd4, 0xb2, 0x9e, 0xe6, 0xe6, 0x95, 0x09, 0xe5, 0x60 }, { 0x95, 0x81, 0x48, 0x68, 0x2d, 0x74, 0x8a, 0x38, 0xdd, 0x68, 0xba, 0xa0 }, { 0xb8, 0xce, 0x02, 0x0c, 0xf0, 0x69, 0xc3, 0x2a, 0x72, 0x3a, 0xb1, 0x40 }, { 0xf4, 0x33, 0x1d, 0x6d, 0x46, 0x16, 0x07, 0xe9, 0x57, 0x52, 0x74, 0x60 }, { 0x6d, 0xa2, 0x3b, 0xa4, 0x24, 0xb9, 0x59, 0x61, 0x33, 0xcf, 0x9c, 0x80 }, { 0xa6, 0x36, 0xbc, 0xbc, 0x7b, 0x30, 0xc5, 0xfb, 0xea, 0xe6, 0x7f, 0xe0 }, { 0x5c, 0xb0, 0xd8, 0x6a, 0x07, 0xdf, 0x65, 0x4a, 0x90, 0x89, 0xa2, 0x00 }, { 0xf1, 0x1f, 0x10, 0x68, 0x48, 0x78, 0x0f, 0xc9, 0xec, 0xdd, 0x80, 0xa0 }, { 0x1f, 0xbb, 0x53, 0x64, 0xfb, 0x8d, 0x2c, 0x9d, 0x73, 0x0d, 0x5b, 0xa0 }, { 0xfc, 0xb8, 0x6b, 0xc7, 0x0a, 0x50, 0xc9, 0xd0, 0x2a, 0x5d, 0x03, 0x40 }, { 0xa5, 0x34, 0x43, 0x30, 0x29, 0xea, 0xc1, 0x5f, 0x32, 0x2e, 0x34, 0xc0 }, { 0xc9, 0x89, 0xd9, 0xc7, 0xc3, 0xd3, 0xb8, 0xc5, 0x5d, 0x75, 0x13, 0x00 }, { 0x7b, 0xb3, 0x8b, 0x2f, 0x01, 0x86, 0xd4, 0x66, 0x43, 0xae, 0x96, 0x20 }, { 0x26, 0x44, 0xeb, 0xad, 0xeb, 0x44, 0xb9, 0x46, 0x7d, 0x1f, 0x42, 0xc0 }, { 0x60, 0x8c, 0xc8, 0x57, 0x59, 0x4b, 0xfb, 0xb5, 0x5d, 0x69, 0x60, 0x00 } }; // Column order (permutation) in which the bits in codeword are stored const uint8_t kColumn_order[N] = { 0, 1, 2, 3, 28, 4, 5, 6, 7, 8, 9, 10, 11, 34, 12, 32, 13, 14, 15, 16, 17, 18, 36, 29, 43, 19, 20, 42, 21, 40, 30, 37, 22, 47, 61, 45, 44, 23, 41, 39, 49, 24, 46, 50, 48, 26, 31, 33, 51, 38, 52, 59, 55, 66, 57, 27, 60, 35, 54, 58, 25, 56, 62, 64, 67, 69, 63, 68, 70, 72, 65, 73, 75, 74, 71, 77, 78, 76, 79, 80, 53, 81, 83, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119, 120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139, 140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159, 160,161,162,163,164,165,166,167,168,169,170,171,172,173 }; // Costas 7x7 tone pattern const uint8_t kCostas_map[7] = { 3,1,4,0,6,5,2 }; // Gray code map const uint8_t kGray_map[8] = { 0,1,3,2,5,6,4,7 }; // Returns 1 if an odd number of bits are set in x, zero otherwise uint8_t parity8(uint8_t x) { x ^= x >> 4; // a b c d ae bf cg dh x ^= x >> 2; // a b ac bd cae dbf aecg bfdh x ^= x >> 1; // a ab bac acbd bdcae caedbf aecgbfdh return (x) & 1; } // Encode a 91-bit message and return a 174-bit codeword. // The generator matrix has dimensions (87,87). // The code is a (174,91) regular ldpc code with column weight 3. // The code was generated using the PEG algorithm. // Arguments: // [IN] message - array of 91 bits stored as 12 bytes (MSB first) // [OUT] codeword - array of 174 bits stored as 22 bytes (MSB first) void encode174(const uint8_t *message, uint8_t *codeword) { // Here we don't generate the generator bit matrix as in WSJT-X implementation // Instead we access the generator bits straight from the binary representation in kGenerator // For reference: // codeword(1:K)=message // codeword(K+1:N)=pchecks // printf("Encode "); // for (int i = 0; i < K_BYTES; ++i) { // printf("%02x ", message[i]); // } // printf("\n"); // Fill the codeword with message and zeros, as we will only update binary ones later for (int j = 0; j < (7 + N) / 8; ++j) { codeword[j] = (j < K_BYTES) ? message[j] : 0; } uint8_t col_mask = (0x80 >> (K % 8)); // bitmask of current byte uint8_t col_idx = K_BYTES - 1; // index into byte array // Compute the first part of itmp (1:M) and store the result in codeword for (int i = 0; i < M; ++i) { // do i=1,M // Fast implementation of bitwise multiplication and parity checking // Normally nsum would contain the result of dot product between message and kGenerator[i], // but we only compute the sum modulo 2. uint8_t nsum = 0; for (int j = 0; j < K_BYTES; ++j) { uint8_t bits = message[j] & kGenerator[i][j]; // bitwise AND (bitwise multiplication) nsum ^= parity8(bits); // bitwise XOR (addition modulo 2) } // Check if we need to set a bit in codeword if (nsum % 2) { // pchecks(i)=mod(nsum,2) codeword[col_idx] |= col_mask; } col_mask >>= 1; if (col_mask == 0) { col_mask = 0x80; ++col_idx; } } // printf("Result "); // for (int i = 0; i < (N + 7) / 8; ++i) { // printf("%02x ", codeword[i]); // } // printf("\n"); } // Compute 14-bit CRC for a sequence of given number of bits // [IN] message - byte sequence (MSB first) // [IN] num_bits - number of bits in the sequence uint16_t ft8_crc(uint8_t *message, int num_bits) { // Adapted from https://barrgroup.com/Embedded-Systems/How-To/CRC-Calculation-C-Code constexpr int WIDTH = 14; constexpr uint16_t TOPBIT = (1 << (WIDTH - 1)); // printf("CRC, %d bits: ", num_bits); // for (int i = 0; i < (num_bits + 7) / 8; ++i) { // printf("%02x ", message[i]); // } // printf("\n"); uint16_t remainder = 0; int idx_byte = 0; // Perform modulo-2 division, a bit at a time. for (int idx_bit = 0; idx_bit < num_bits; ++idx_bit) { if (idx_bit % 8 == 0) { // Bring the next byte into the remainder. remainder ^= (message[idx_byte] << (WIDTH - 8)); ++idx_byte; } // Try to divide the current data bit. if (remainder & TOPBIT) { remainder = (remainder << 1) ^ POLYNOMIAL; } else { remainder = (remainder << 1); } } // printf("CRC = %04xh\n", remainder & ((1 << WIDTH) - 1)); return remainder & ((1 << WIDTH) - 1); } // Generate FT8 tone sequence from payload data // [IN] payload - 10 byte array consisting of 77 bit payload (MSB first) // [OUT] itone - array of NN (79) bytes to store the generated tones (encoded as 0..7) void genft8(const uint8_t *payload, uint8_t *itone) { uint8_t a91[12]; // Store 77 bits of payload + 14 bits CRC // Copy 77 bits of payload data for (int i = 0; i < 10; i++) a91[i] = payload[i]; // Clear 3 bits after the payload to make 80 bits a91[9] &= 0xF8; a91[10] = 0; a91[11] = 0; // Calculate CRC of 12 bytes = 96 bits, see WSJT-X code uint16_t checksum = ft8_crc(a91, 96 - 14); // Store the CRC at the end of 77 bit message a91[9] |= (uint8_t)(checksum >> 11); a91[10] = (uint8_t)(checksum >> 3); a91[11] = (uint8_t)(checksum << 5); // a87 contains 77 bits of payload + 14 bits of CRC uint8_t codeword[22]; encode174(a91, codeword); // Message structure: S7 D29 S7 D29 S7 for (int i = 0; i < 7; ++i) { itone[i] = kCostas_map[i]; itone[36 + i] = kCostas_map[i]; itone[72 + i] = kCostas_map[i]; } int k = 7; // Skip over the first set of Costas symbols uint8_t mask = 0x80; int i_byte = 0; for (int j = 0; j < ND; ++j) { // do j=1,ND if (j == 29) { k += 7; // Skip over the second set of Costas symbols } // Extract 3 bits from codeword at i-th position uint8_t bits3 = 0; if (codeword[i_byte] & mask) bits3 |= 4; if (0 == (mask >>= 1)) { mask = 0x80; i_byte++; } if (codeword[i_byte] & mask) bits3 |= 2; if (0 == (mask >>= 1)) { mask = 0x80; i_byte++; } if (codeword[i_byte] & mask) bits3 |= 1; if (0 == (mask >>= 1)) { mask = 0x80; i_byte++; } itone[k] = kGray_map[bits3]; ++k; } } }; // ft8_v2