265 lines
13 KiB
C++
265 lines
13 KiB
C++
#include "encode.h"
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constexpr int N = 174, K = 87, M = N-K; // Define the LDPC sizes
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constexpr uint16_t POLYNOMIAL = 0xC06; // CRC-12 polynomial without the leading (MSB) 1
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// Parity generator matrix for (174,87) LDPC code, stored in bitpacked format (MSB first)
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const uint8_t G[87][11] = {
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{ 0x23, 0xbb, 0xa8, 0x30, 0xe2, 0x3b, 0x6b, 0x6f, 0x50, 0x98, 0x2e },
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{ 0x1f, 0x8e, 0x55, 0xda, 0x21, 0x8c, 0x5d, 0xf3, 0x30, 0x90, 0x52 },
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{ 0xca, 0x7b, 0x32, 0x17, 0xcd, 0x92, 0xbd, 0x59, 0xa5, 0xae, 0x20 },
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{ 0x56, 0xf7, 0x83, 0x13, 0x53, 0x7d, 0x0f, 0x43, 0x82, 0x96, 0x4e },
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{ 0x29, 0xc2, 0x9d, 0xba, 0x9c, 0x54, 0x5e, 0x26, 0x77, 0x62, 0xfe },
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{ 0x6b, 0xe3, 0x96, 0xb5, 0xe2, 0xe8, 0x19, 0xe3, 0x73, 0x34, 0x0c },
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{ 0x29, 0x35, 0x48, 0xa1, 0x38, 0x85, 0x83, 0x28, 0xaf, 0x42, 0x10 },
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{ 0xcb, 0x6c, 0x6a, 0xfc, 0xdc, 0x28, 0xbb, 0x3f, 0x7c, 0x6e, 0x86 },
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{ 0x3f, 0x2a, 0x86, 0xf5, 0xc5, 0xbd, 0x22, 0x5c, 0x96, 0x11, 0x50 },
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{ 0x84, 0x9d, 0xd2, 0xd6, 0x36, 0x73, 0x48, 0x18, 0x60, 0xf6, 0x2c },
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{ 0x56, 0xcd, 0xae, 0xc6, 0xe7, 0xae, 0x14, 0xb4, 0x3f, 0xee, 0xee },
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{ 0x04, 0xef, 0x5c, 0xfa, 0x37, 0x66, 0xba, 0x77, 0x8f, 0x45, 0xa4 },
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{ 0xc5, 0x25, 0xae, 0x4b, 0xd4, 0xf6, 0x27, 0x32, 0x0a, 0x39, 0x74 },
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{ 0xfe, 0x37, 0x80, 0x29, 0x41, 0xd6, 0x6d, 0xde, 0x02, 0xb9, 0x9c },
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{ 0x41, 0xfd, 0x95, 0x20, 0xb2, 0xe4, 0xab, 0xeb, 0x2f, 0x98, 0x9c },
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{ 0x40, 0x90, 0x7b, 0x01, 0x28, 0x0f, 0x03, 0xc0, 0x32, 0x39, 0x46 },
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{ 0x7f, 0xb3, 0x6c, 0x24, 0x08, 0x5a, 0x34, 0xd8, 0xc1, 0xdb, 0xc4 },
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{ 0x40, 0xfc, 0x3e, 0x44, 0xbb, 0x7d, 0x2b, 0xb2, 0x75, 0x6e, 0x44 },
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{ 0xd3, 0x8a, 0xb0, 0xa1, 0xd2, 0xe5, 0x2a, 0x8e, 0xc3, 0xbc, 0x76 },
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{ 0x3d, 0x0f, 0x92, 0x9e, 0xf3, 0x94, 0x9b, 0xd8, 0x4d, 0x47, 0x34 },
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{ 0x45, 0xd3, 0x81, 0x4f, 0x50, 0x40, 0x64, 0xf8, 0x05, 0x49, 0xae },
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{ 0xf1, 0x4d, 0xbf, 0x26, 0x38, 0x25, 0xd0, 0xbd, 0x04, 0xb0, 0x5e },
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{ 0xf0, 0x8a, 0x91, 0xfb, 0x2e, 0x1f, 0x78, 0x29, 0x06, 0x19, 0xa8 },
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{ 0x7a, 0x8d, 0xec, 0x79, 0xa5, 0x1e, 0x8a, 0xc5, 0x38, 0x80, 0x22 },
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{ 0xca, 0x41, 0x86, 0xdd, 0x44, 0xc3, 0x12, 0x15, 0x65, 0xcf, 0x5c },
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{ 0xdb, 0x71, 0x4f, 0x8f, 0x64, 0xe8, 0xac, 0x7a, 0xf1, 0xa7, 0x6e },
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{ 0x8d, 0x02, 0x74, 0xde, 0x71, 0xe7, 0xc1, 0xa8, 0x05, 0x5e, 0xb0 },
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{ 0x51, 0xf8, 0x15, 0x73, 0xdd, 0x40, 0x49, 0xb0, 0x82, 0xde, 0x14 },
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{ 0xd0, 0x37, 0xdb, 0x82, 0x51, 0x75, 0xd8, 0x51, 0xf3, 0xaf, 0x00 },
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{ 0xd8, 0xf9, 0x37, 0xf3, 0x18, 0x22, 0xe5, 0x7c, 0x56, 0x23, 0x70 },
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{ 0x1b, 0xf1, 0x49, 0x06, 0x07, 0xc5, 0x40, 0x32, 0x66, 0x0e, 0xde },
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{ 0x16, 0x16, 0xd7, 0x80, 0x18, 0xd0, 0xb4, 0x74, 0x5c, 0xa0, 0xf2 },
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{ 0xa9, 0xfa, 0x8e, 0x50, 0xbc, 0xb0, 0x32, 0xc8, 0x5e, 0x33, 0x04 },
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{ 0x83, 0xf6, 0x40, 0xf1, 0xa4, 0x8a, 0x8e, 0xbc, 0x04, 0x43, 0xea },
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{ 0xec, 0xa9, 0xaf, 0xa0, 0xf6, 0xb0, 0x1d, 0x92, 0x30, 0x5e, 0xdc },
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{ 0x37, 0x76, 0xaf, 0x54, 0xcc, 0xfb, 0xae, 0x91, 0x6a, 0xfd, 0xe6 },
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{ 0x6a, 0xbb, 0x21, 0x2d, 0x97, 0x39, 0xdf, 0xc0, 0x25, 0x80, 0xf2 },
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{ 0x05, 0x20, 0x9a, 0x0a, 0xbb, 0x53, 0x0b, 0x9e, 0x7e, 0x34, 0xb0 },
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{ 0x61, 0x2f, 0x63, 0xac, 0xc0, 0x25, 0xb6, 0xab, 0x47, 0x6f, 0x7c },
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{ 0x0a, 0xf7, 0x72, 0x31, 0x61, 0xec, 0x22, 0x30, 0x80, 0xbe, 0x86 },
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{ 0xa8, 0xfc, 0x90, 0x69, 0x76, 0xc3, 0x56, 0x69, 0xe7, 0x9c, 0xe0 },
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{ 0x45, 0xb7, 0xab, 0x62, 0x42, 0xb7, 0x74, 0x74, 0xd9, 0xf1, 0x1a },
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{ 0xb2, 0x74, 0xdb, 0x8a, 0xbd, 0x3c, 0x6f, 0x39, 0x6e, 0xa3, 0x56 },
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{ 0x90, 0x59, 0xdf, 0xa2, 0xbb, 0x20, 0xef, 0x7e, 0xf7, 0x3a, 0xd4 },
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{ 0x3d, 0x18, 0x8e, 0xa4, 0x77, 0xf6, 0xfa, 0x41, 0x31, 0x7a, 0x4e },
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{ 0x8d, 0x90, 0x71, 0xb7, 0xe7, 0xa6, 0xa2, 0xee, 0xd6, 0x96, 0x5e },
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{ 0xa3, 0x77, 0x25, 0x37, 0x73, 0xea, 0x67, 0x83, 0x67, 0xc3, 0xf6 },
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{ 0xec, 0xbd, 0x7c, 0x73, 0xb9, 0xcd, 0x34, 0xc3, 0x72, 0x0c, 0x8a },
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{ 0xb6, 0x53, 0x7f, 0x41, 0x7e, 0x61, 0xd1, 0xa7, 0x08, 0x53, 0x36 },
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{ 0x6c, 0x28, 0x0d, 0x2a, 0x05, 0x23, 0xd9, 0xc4, 0xbc, 0x59, 0x46 },
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{ 0xd3, 0x6d, 0x66, 0x2a, 0x69, 0xae, 0x24, 0xb7, 0x4d, 0xcb, 0xd8 },
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{ 0xd7, 0x47, 0xbf, 0xc5, 0xfd, 0x65, 0xef, 0x70, 0xfb, 0xd9, 0xbc },
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{ 0xa9, 0xfa, 0x2e, 0xef, 0xa6, 0xf8, 0x79, 0x6a, 0x35, 0x57, 0x72 },
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{ 0xcc, 0x9d, 0xa5, 0x5f, 0xe0, 0x46, 0xd0, 0xcb, 0x3a, 0x77, 0x0c },
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{ 0xf6, 0xad, 0x48, 0x24, 0xb8, 0x7c, 0x80, 0xeb, 0xfc, 0xe4, 0x66 },
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{ 0xcc, 0x6d, 0xe5, 0x97, 0x55, 0x42, 0x09, 0x25, 0xf9, 0x0e, 0xd2 },
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{ 0x16, 0x4c, 0xc8, 0x61, 0xbd, 0xd8, 0x03, 0xc5, 0x47, 0xf2, 0xac },
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{ 0xc0, 0xfc, 0x3e, 0xc4, 0xfb, 0x7d, 0x2b, 0xb2, 0x75, 0x66, 0x44 },
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{ 0x0d, 0xbd, 0x81, 0x6f, 0xba, 0x15, 0x43, 0xf7, 0x21, 0xdc, 0x72 },
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{ 0xa0, 0xc0, 0x03, 0x3a, 0x52, 0xab, 0x62, 0x99, 0x80, 0x2f, 0xd2 },
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{ 0xbf, 0x4f, 0x56, 0xe0, 0x73, 0x27, 0x1f, 0x6a, 0xb4, 0xbf, 0x80 },
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{ 0x57, 0xda, 0x6d, 0x13, 0xcb, 0x96, 0xa7, 0x68, 0x9b, 0x27, 0x90 },
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{ 0x81, 0xcf, 0xc6, 0xf1, 0x8c, 0x35, 0xb1, 0xe1, 0xf1, 0x71, 0x14 },
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{ 0x48, 0x1a, 0x2a, 0x0d, 0xf8, 0xa2, 0x35, 0x83, 0xf8, 0x2d, 0x6c },
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{ 0x1a, 0xc4, 0x67, 0x2b, 0x54, 0x9c, 0xd6, 0xdb, 0xa7, 0x9b, 0xcc },
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{ 0xc8, 0x7a, 0xf9, 0xa5, 0xd5, 0x20, 0x6a, 0xbc, 0xa5, 0x32, 0xa8 },
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{ 0x97, 0xd4, 0x16, 0x9c, 0xb3, 0x3e, 0x74, 0x35, 0x71, 0x8d, 0x90 },
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{ 0xa6, 0x57, 0x3f, 0x3d, 0xc8, 0xb1, 0x6c, 0x9d, 0x19, 0xf7, 0x46 },
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{ 0x2c, 0x41, 0x42, 0xbf, 0x42, 0xb0, 0x1e, 0x71, 0x07, 0x6a, 0xcc },
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{ 0x08, 0x1c, 0x29, 0xa1, 0x0d, 0x46, 0x8c, 0xcd, 0xbc, 0xec, 0xb6 },
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{ 0x5b, 0x0f, 0x77, 0x42, 0xbc, 0xa8, 0x6b, 0x80, 0x12, 0x60, 0x9a },
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{ 0x01, 0x2d, 0xee, 0x21, 0x98, 0xeb, 0xa8, 0x2b, 0x19, 0xa1, 0xda },
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{ 0xf1, 0x62, 0x77, 0x01, 0xa2, 0xd6, 0x92, 0xfd, 0x94, 0x49, 0xe6 },
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{ 0x35, 0xad, 0x3f, 0xb0, 0xfa, 0xeb, 0x5f, 0x1b, 0x0c, 0x30, 0xdc },
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{ 0xb1, 0xca, 0x4e, 0xa2, 0xe3, 0xd1, 0x73, 0xba, 0xd4, 0x37, 0x9c },
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{ 0x37, 0xd8, 0xe0, 0xaf, 0x92, 0x58, 0xb9, 0xe8, 0xc5, 0xf9, 0xb2 },
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{ 0xcd, 0x92, 0x1f, 0xdf, 0x59, 0xe8, 0x82, 0x68, 0x37, 0x63, 0xf6 },
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{ 0x61, 0x14, 0xe0, 0x84, 0x83, 0x04, 0x3f, 0xd3, 0xf3, 0x8a, 0x8a },
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{ 0x2e, 0x54, 0x7d, 0xd7, 0xa0, 0x5f, 0x65, 0x97, 0xaa, 0xc5, 0x16 },
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{ 0x95, 0xe4, 0x5e, 0xcd, 0x01, 0x35, 0xac, 0xa9, 0xd6, 0xe6, 0xae },
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{ 0xb3, 0x3e, 0xc9, 0x7b, 0xe8, 0x3c, 0xe4, 0x13, 0xf9, 0xac, 0xc8 },
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{ 0xc8, 0xb5, 0xdf, 0xfc, 0x33, 0x50, 0x95, 0xdc, 0xdc, 0xaf, 0x2a },
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{ 0x3d, 0xd0, 0x1a, 0x59, 0xd8, 0x63, 0x10, 0x74, 0x3e, 0xc7, 0x52 },
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{ 0x14, 0xcd, 0x0f, 0x64, 0x2f, 0xc0, 0xc5, 0xfe, 0x3a, 0x65, 0xca },
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{ 0x3a, 0x0a, 0x1d, 0xfd, 0x7e, 0xee, 0x29, 0xc2, 0xe8, 0x27, 0xe0 },
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{ 0x8a, 0xbd, 0xb8, 0x89, 0xef, 0xbe, 0x39, 0xa5, 0x10, 0xa1, 0x18 },
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{ 0x3f, 0x23, 0x1f, 0x21, 0x20, 0x55, 0x37, 0x1c, 0xf3, 0xe2, 0xa2 }
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};
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// Column order (permutation) in which the bits in codeword are stored
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const uint8_t colorder[174] = {
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0, 1, 2, 3, 30, 4, 5, 6, 7, 8, 9, 10, 11, 32, 12, 40, 13, 14, 15, 16,
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17, 18, 37, 45, 29, 19, 20, 21, 41, 22, 42, 31, 33, 34, 44, 35, 47, 51, 50, 43,
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36, 52, 63, 46, 25, 55, 27, 24, 23, 53, 39, 49, 59, 38, 48, 61, 60, 57, 28, 62,
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56, 58, 65, 66, 26, 70, 64, 69, 68, 67, 74, 71, 54, 76, 72, 75, 78, 77, 80, 79,
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73, 83, 84, 81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,
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100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
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120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,
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140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,
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160,161,162,163,164,165,166,167,168,169,170,171,172,173
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};
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// Costas 7x7 tone pattern
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const uint8_t ICOS7[] = { 2,5,6,0,4,1,3 };
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// Returns 1 if an odd number of bits are set in x, zero otherwise
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uint8_t parity8(uint8_t x) {
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x ^= x >> 4; // a b c d ae bf cg dh
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x ^= x >> 2; // a b ac bd cae dbf aecg bfdh
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x ^= x >> 1; // a ab bac acbd bdcae caedbf aecgbfdh
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return (x) & 1;
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}
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// Encode an 87-bit message and return a 174-bit codeword.
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// The generator matrix has dimensions (87,87).
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// The code is a (174,87) regular ldpc code with column weight 3.
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// The code was generated using the PEG algorithm.
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// After creating the codeword, the columns are re-ordered according to
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// "colorder" to make the codeword compatible with the parity-check matrix
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// Arguments:
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// [IN] message - array of 87 bits stored as 11 bytes (MSB first)
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// [OUT] codeword - array of 174 bits stored as 22 bytes (MSB first)
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void encode174(const uint8_t *message, uint8_t *codeword) {
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// Here we don't generate the generator bit matrix as in WSJT-X implementation
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// Instead we access the generator bits straight from the binary representation in G
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// Also we don't use the itmp temporary buffer, instead filling codeword bit by bit
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// in the reordered order as we compute the result.
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// For reference:
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// itmp(1:M)=pchecks
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// itmp(M+1:N)=message(1:K)
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// codeword(colorder+1)=itmp(1:N)
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int colidx = 0; // track the current column in codeword
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// Fill the codeword with zeroes, as we will only update binary ones later
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for (int i = 0; i < (N + 7) / 8; i++) {
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codeword[i] = 0;
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}
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// Compute the first part of itmp (1:M) and store the result in codeword
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for (int i = 0; i < M; ++i) { // do i=1,M
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// Fast implementation of bitwise multiplication and parity checking
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// Normally nsum would contain the result of dot product between message and G[i],
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// but we only compute the sum modulo 2.
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uint8_t nsum = 0;
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for (int j = 0; j < 11; ++j) {
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uint8_t bits = message[j] & G[i][j]; // bitwise AND (bitwise multiplication)
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nsum ^= parity8(bits); // bitwise XOR (addition modulo 2)
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}
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// Check if we need to set a bit in codeword
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if (nsum % 2) { // pchecks(i)=mod(nsum,2)
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uint8_t col = colorder[colidx]; // Index of the bit to set
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codeword[col/8] |= (1 << (7 - col%8));
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}
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++colidx;
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}
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// Compute the second part of itmp (M+1:N) and store the result in codeword
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uint8_t mask = 0x80; // Rolling mask starting with the MSB
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for (int j = 0; j < K; ++j) {
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// Copy the j-th bit from message to codeword
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if (message[j/8] & mask) {
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uint8_t col = colorder[colidx]; // Index of the bit to set
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codeword[col/8] |= (1 << (7 - col%8));
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}
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++colidx;
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// Roll the bitmask to the right
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mask >>= 1;
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if (mask == 0) mask = 0x80;
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}
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}
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// Compute 12-bit CRC for a sequence of given number of bits
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// [IN] message - byte sequence (MSB first)
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// [IN] num_bits - number of bits in the sequence
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uint16_t ft8_crc(uint8_t *message, int num_bits) {
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// Adapted from https://barrgroup.com/Embedded-Systems/How-To/CRC-Calculation-C-Code
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constexpr int WIDTH = 12;
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constexpr uint16_t TOPBIT = (1 << (WIDTH - 1));
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uint16_t remainder = 0;
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int idx_byte = 0;
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// Perform modulo-2 division, a bit at a time.
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for (int idx_bit = 0; idx_bit < num_bits; ++idx_bit) {
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if (idx_bit % 8 == 0) {
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// Bring the next byte into the remainder.
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remainder ^= (message[idx_byte] << (WIDTH - 8));
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++idx_byte;
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}
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// Try to divide the current data bit.
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if (remainder & TOPBIT) {
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remainder = (remainder << 1) ^ POLYNOMIAL;
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}
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else {
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remainder = (remainder << 1);
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}
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}
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return remainder & ((1 << WIDTH) - 1);
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}
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// Generate FT8 tone sequence from payload data
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// [IN] payload - 9 byte array consisting of 72 bit payload (MSB first)
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// [IN] i3 - 3 bits containing message type (zero?)
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// [OUT] itone - array of NN (79) bytes to store the generated tones (encoded as 0..7)
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void genft8(const uint8_t *payload, uint8_t i3, uint8_t *itone) {
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uint8_t a87[11]; // Store 72 bits of payload + 3 bits i3 + 12 bits CRC
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for (int i = 0; i < 9; i++)
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a87[i] = payload[i];
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// Append 3 bits of i3 at the end of 72 bit payload
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a87[9] = ((i3 & 0x07) << 5);
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// Calculate CRC of 76 bits (yes, 72 + 3 + 1 zero bit), see WSJT-X code
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uint16_t checksum = ft8_crc(a87, 76);
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// Store the CRC at the end of 75 bit message (yes, 72 + 3)
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uint16_t tmp = (checksum << 1);
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a87[9] |= (uint8_t)(tmp >> 8);
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a87[10] = (uint8_t)tmp;
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// a87 contains 72 bits of payload + 3 bits of i3 + 12 bits of CRC
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uint8_t codeword[22];
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encode174(a87, codeword);
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// Message structure: S7 D29 S7 D29 S7
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for (int i = 0; i < 7; ++i) {
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itone[i] = ICOS7[i];
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itone[36 + i] = ICOS7[i];
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itone[72 + i] = ICOS7[i];
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}
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int k = 7; // Skip over the first set of Costas symbols
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for (int j = 0; j < ND; ++j) { // do j=1,ND
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if (j == 29) {
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k += 7; // Skip over the second set of Costas symbols
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}
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// Extract 3 bits from codeword at i-th position
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itone[k] = 0;
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int i = 3*j;
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|
if (codeword[i/8] & (1 << (7 - i%8))) itone[k] |= 4;
|
|
++i;
|
|
if (codeword[i/8] & (1 << (7 - i%8))) itone[k] |= 2;
|
|
++i;
|
|
if (codeword[i/8] & (1 << (7 - i%8))) itone[k] |= 1;
|
|
++k;
|
|
}
|
|
}
|