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sys/ecc: add golay(24,12) ECC

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PeterKietzmann 2018-07-26 15:41:54 +02:00
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427
sys/ecc/golay2412.c Normal file
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/*
* Copyright (c) 2007 - 2015 Joseph Gaeddert
* Copyright (c) 2018 HAW Hamburg
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
/**
* @ingroup sys_ecc
* @{
*
* @file
* @brief Golay(24,12) half-rate forward error-correction code
*
* Code referring to Liquid-DSP
* https://github.com/jgaeddert/liquid-dsp/blob/master/src/fec/src/fec_golay2412.c
*
* @author Joseph Gaeddert
* @author Peter Kietzmann <peter.kietzmann@haw.hamburg.de>
*
* @}
*/
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <errno.h>
#include "bitarithm.h"
#include "ecc/golay2412.h"
#define ENABLE_DEBUG (0)
#include "debug.h"
#if ENABLE_DEBUG
#define DEBUG_FEC_GOLAY2412 (1)
#else
#define DEBUG_FEC_GOLAY2412 (0)
#endif
/* generator matrix transposed [24 x 12] */
static const uint32_t golay2412_Gt[24] = {
0x08ed, 0x01db, 0x03b5, 0x0769, 0x0ed1, 0x0da3, 0x0b47, 0x068f,
0x0d1d, 0x0a3b, 0x0477, 0x0ffe, 0x0800, 0x0400, 0x0200, 0x0100,
0x0080, 0x0040, 0x0020, 0x0010, 0x0008, 0x0004, 0x0002, 0x0001
};
/* P matrix [12 x 12] */
static const uint32_t golay2412_P[12] = {
0x08ed, 0x01db, 0x03b5, 0x0769,
0x0ed1, 0x0da3, 0x0b47, 0x068f,
0x0d1d, 0x0a3b, 0x0477, 0x0ffe
};
/* parity check matrix [12 x 24] */
static const uint32_t golay2412_H[12] = {
0x008008ed, 0x004001db, 0x002003b5, 0x00100769,
0x00080ed1, 0x00040da3, 0x00020b47, 0x0001068f,
0x00008d1d, 0x00004a3b, 0x00002477, 0x00001ffe
};
#if DEBUG_FEC_GOLAY2412
/* print string of bits to standard output */
static inline void liquid_print_bitstring(uint32_t _x,
uint32_t _n)
{
uint32_t i;
for (i = 0; i < _n; i++) {
printf("%" PRIu32, (_x >> (_n - i - 1)) & 1);
}
}
#endif
#ifndef NDEBUG
static uint32_t block_get_enc_msg_len(uint32_t _dec_msg_len,
uint32_t _m,
uint32_t _k)
{
assert((_m > 0) && (_k >= _m));
/* compute total number of bits in decoded message */
uint32_t num_bits_in = _dec_msg_len * 8;
/* compute total number of blocks: ceil(num_bits_in/_m) */
uint32_t num_blocks = num_bits_in / _m + ((num_bits_in % _m) ? 1 : 0);
/* compute total number of bits out */
uint32_t num_bits_out = num_blocks * _k;
/* compute total number of bytes out: ceil(num_bits_out/8) */
uint32_t num_bytes_out = num_bits_out / 8 + ((num_bits_out % 8) ? 1 : 0);
#if DEBUG_FEC_GOLAY2412
printf("block_get_enc_msg_len(%" PRIu32 ",%" PRIu32 ",%" PRIu32 ")\n", _dec_msg_len, _m, _k);
printf(" dec msg len : %" PRIu32 " bytes\n", _dec_msg_len);
printf(" m : %" PRIu32 " bits\n", _m);
printf(" k : %" PRIu32 " bits\n", _k);
printf(" num bits in : %" PRIu32 " bits\n", num_bits_in);
printf(" num blocks : %" PRIu32 "\n", num_blocks);
printf(" num bits out: %" PRIu32 " bits\n", num_bits_out);
printf(" enc msg len : %" PRIu32 " bytes\n", num_bytes_out);
#endif
return num_bytes_out;
}
#endif
/* multiply input vector with parity check matrix, H */
static uint32_t golay2412_matrix_mul(uint32_t _v,
const uint32_t *_A,
uint32_t _n)
{
uint32_t x = 0;
uint32_t i;
for (i = 0; i < _n; i++) {
x <<= 1;
/* same as above, but exploit the fact that vectors are at
* most 24 bits long */
uint32_t p = _A[i] & _v;
uint32_t c = 0;
c = bitarithm_bits_set_u32(p & 0x00ffffff);
/* mod 2 */
x |= c & 0x0001;
}
return x;
}
static uint32_t golay2412_encode_symbol(uint32_t _sym_dec, const uint32_t *_A)
{
/* validate input */
assert(_sym_dec > (1 << 12));
/* compute encoded/transmitted message: v = m*G */
return golay2412_matrix_mul(_sym_dec, _A, 24);
}
/* search for p[i] such that w(v+p[i]) <= 2, return -1 on fail */
static int8_t golay2412_parity_search(uint32_t _v, const uint32_t *_A)
{
assert(_v < (1 << 12));
uint8_t i;
for (i = 0; i < 12; i++) {
/* same as above but faster, exploiting fact that P has
* only 12 bits of resolution */
uint32_t p = _v ^ _A[i];
if (bitarithm_bits_set_u32(p & 0x00000fff) <= 2) {
return i;
}
}
/* could not find p[i] to satisfy criteria */
return -1;
}
static uint32_t golay2412_decode_symbol(uint32_t _sym_enc,
const uint32_t *_A,
const uint32_t *_B)
{
/* validate input */
assert((_sym_enc) < (1L << 24));
/* state variables */
uint32_t s = 0; /* syndrome vector */
uint32_t e_hat = 0; /* estimated error vector */
uint32_t v_hat = 0; /* estimated transmitted message */
uint32_t m_hat = 0; /* estimated original message */
/* compute syndrome vector, s = r*H^T = ( H*r^T )^T */
s = golay2412_matrix_mul(_sym_enc, _B, 12);
#if DEBUG_FEC_GOLAY2412
printf("s (syndrome vector): "); liquid_print_bitstring(s, 12); printf("\n");
#endif
/* compute weight of s (12 bits) */
uint8_t ws = bitarithm_bits_set_u32(s & 0x00000fff);
#if DEBUG_FEC_GOLAY2412
printf("w(s) = %u\n", ws);
#endif
/* step 2: */
e_hat = 0;
if (ws <= 3) {
#if DEBUG_FEC_GOLAY2412
printf(" w(s) <= 3: estimating error vector as [s, 0(12)]\n");
#endif
/* set e_hat = [s 0(12)] */
e_hat = (s << 12) & 0xfff000;
}
else {
/* step 3: search for p[i] s.t. w(s+p[i]) <= 2 */
#if DEBUG_FEC_GOLAY2412
printf(" searching for w(s + p_i) <= 2...\n");
#endif
int8_t s_index = golay2412_parity_search(s, _A);
if (s_index >= 0) {
/* vector found! */
#if DEBUG_FEC_GOLAY2412
printf(" w(s + p[%2i]) <= 2: estimating error vector as [s+p[%2i],"
"u[%2i]]\n", s_index, s_index, s_index);
#endif
/* NOTE : uj = 1 << (12-j-1) */
e_hat = ((s ^ _A[s_index]) << 12) | (1 << (11 - s_index));
}
else {
/* step 4: compute s*P */
uint32_t sP = golay2412_matrix_mul(s, _A, 12);
#if DEBUG_FEC_GOLAY2412
printf("s*P: "); liquid_print_bitstring(sP, 12); printf("\n");
#endif
/* compute weight of sP (12 bits) */
uint8_t wsP = bitarithm_bits_set_u32(sP & 0x00000fff);
#if DEBUG_FEC_GOLAY2412
printf("w(s*P) = %u\n", wsP);
#endif
if (wsP == 2 || wsP == 3) {
/* step 5: set e = [0, s*P] */
#if DEBUG_FEC_GOLAY2412
printf(" w(s*P) in [2,3]: estimating error vector as [0(12), s*P]\n");
#endif
e_hat = sP;
}
else {
/* step 6: search for p[i] s.t. w(s*P + p[i]) == 2... */
#if DEBUG_FEC_GOLAY2412
printf(" searching for w(s*P + p_i) == 2...\n");
#endif
int8_t sP_index = golay2412_parity_search(sP, _A);
if (sP_index >= 0) {
/* vector found! */
#if DEBUG_FEC_GOLAY2412
printf(" w(s*P + p[%2i]) == 2: estimating error vector as [u[%2i],"
"s*P+p[%2i]]\n", sP_index, sP_index, sP_index);
#endif
/* NOTE : uj = 1 << (12-j-1)
* [ uj << 1 2 ] [ sP + p[j] ] */
e_hat = (1L << (23 - sP_index)) | (sP ^ _A[sP_index]);
}
else {
/* step 7: decoding error */
#if DEBUG_FEC_GOLAY2412
printf(" **** decoding error\n");
#endif
}
}
}
}
/* step 8: compute estimated transmitted message: v_hat = r + e_hat */
v_hat = _sym_enc ^ e_hat;
#if DEBUG_FEC_GOLAY2412
printf("r (recevied vector): ");
liquid_print_bitstring(_sym_enc, 24); printf("\n");
printf("e-hat (estimated error vector): ");
liquid_print_bitstring(e_hat, 24); printf("\n");
printf("v-hat (estimated tx vector): ");
liquid_print_bitstring(v_hat, 24); printf("\n");
#endif
/* compute estimated original message: (last 12 bits of encoded message) */
m_hat = v_hat & 0x0fff;
return m_hat;
}
void golay2412_encode(uint32_t _dec_msg_len,
unsigned char *_msg_dec,
unsigned char *_msg_enc)
{
uint32_t i = 0; /* decoded byte counter */
uint32_t j = 0; /* encoded byte counter */
uint32_t m0; /* first 12-bit symbol (uncoded) */
uint32_t v0; /* first 24-bit symbol (encoded) */
unsigned char s0; /* first 8-bit symbol */
/* determine remainder of input length / 3 */
uint32_t r = _dec_msg_len % 3;
for (i = 0; i < _dec_msg_len - r; i += 3) {
uint32_t m1; /* second 12-bit symbol (uncoded) */
uint32_t v1; /* second 24-bit symbol (encoded) */
unsigned char s1, s2; /* second and third 8-bit symbols */
/* strip three input bytes (two uncoded symbols) */
s0 = _msg_dec[i + 0];
s1 = _msg_dec[i + 1];
s2 = _msg_dec[i + 2];
/* pack into two 12-bit symbols */
m0 = ((s0 << 4) & 0x0ff0) | ((s1 >> 4) & 0x000f);
m1 = ((s1 << 8) & 0x0f00) | ((s2) & 0x00ff);
/* encode each 12-bit symbol into a 24-bit symbol */
v0 = golay2412_encode_symbol(m0, golay2412_Gt);
v1 = golay2412_encode_symbol(m1, golay2412_Gt);
/* unpack two 24-bit symbols into six 8-bit bytes
* retaining order of bits in output */
_msg_enc[j + 0] = (v0 >> 16) & 0xff;
_msg_enc[j + 1] = (v0 >> 8) & 0xff;
_msg_enc[j + 2] = (v0) & 0xff;
_msg_enc[j + 3] = (v1 >> 16) & 0xff;
_msg_enc[j + 4] = (v1 >> 8) & 0xff;
_msg_enc[j + 5] = (v1) & 0xff;
j += 6;
}
/* if input length isn't divisible by 3, encode last 1 or two bytes */
for (i = _dec_msg_len - r; i < _dec_msg_len; i++) {
/* strip last input symbol */
s0 = _msg_dec[i];
/* extend as 12-bit symbol */
m0 = s0;
/* encode into 24-bit symbol */
v0 = golay2412_encode_symbol(m0, golay2412_Gt);
/* unpack one 24-bit symbol into three 8-bit bytes, and
* append to output array */
_msg_enc[j + 0] = (v0 >> 16) & 0xff;
_msg_enc[j + 1] = (v0 >> 8) & 0xff;
_msg_enc[j + 2] = (v0) & 0xff;
j += 3;
}
assert( j == block_get_enc_msg_len(_dec_msg_len, 12, 24));
assert( i == _dec_msg_len);
}
void golay2412_decode(uint32_t _dec_msg_len,
unsigned char *_msg_enc,
unsigned char *_msg_dec)
{
uint32_t i = 0; /* decoded byte counter */
uint32_t j = 0; /* encoded byte counter */
uint32_t v0; /* first 24-bit encoded symbol */
uint32_t m0_hat; /* first 12-bit decoded symbol */
unsigned char r0, r1, r2; /* first three 8-bit bytes */
/* determine remainder of input length / 3 */
uint32_t r = _dec_msg_len % 3;
for (i = 0; i < _dec_msg_len - r; i += 3) {
uint32_t v1; /* second 24-bit encoded symbol */
uint32_t m1_hat; /* second 12-bit decoded symbol */
unsigned char r3, r4, r5; /* last three 8-bit bytes */
/* strip six input bytes (two encoded symbols) */
r0 = _msg_enc[j + 0];
r1 = _msg_enc[j + 1];
r2 = _msg_enc[j + 2];
r3 = _msg_enc[j + 3];
r4 = _msg_enc[j + 4];
r5 = _msg_enc[j + 5];
/* pack six 8-bit symbols into two 24-bit symbols */
v0 = (((uint32_t)r0 << 16) & 0xff0000)
| (((uint32_t)r1 << 8) & 0x00ff00)
| (((uint32_t)r2 << 0) & 0x0000ff);
v1 = (((uint32_t)r3 << 16) & 0xff0000)
| (((uint32_t)r4 << 8) & 0x00ff00)
| (((uint32_t)r5 << 0) & 0x0000ff);
/* decode each symbol into a 12-bit symbol */
m0_hat = golay2412_decode_symbol(v0, golay2412_P, golay2412_H);
m1_hat = golay2412_decode_symbol(v1, golay2412_P, golay2412_H);
/* unpack two 12-bit symbols into three 8-bit bytes */
_msg_dec[i + 0] = ((m0_hat >> 4) & 0xff);
_msg_dec[i + 1] = ((m0_hat << 4) & 0xf0) | ((m1_hat >> 8) & 0x0f);
_msg_dec[i + 2] = ((m1_hat) & 0xff);
j += 6;
}
/* if input length isn't divisible by 3, decode last 1 or two bytes */
for (i = _dec_msg_len - r; i < _dec_msg_len; i++) {
/* strip last input symbol (three bytes) */
r0 = _msg_enc[j + 0];
r1 = _msg_enc[j + 1];
r2 = _msg_enc[j + 2];
/* pack three 8-bit symbols into one 24-bit symbol */
v0 = (((uint32_t)r0 << 16) & 0xff0000)
| (((uint32_t)r1 << 8) & 0x00ff00)
| (((uint32_t)r2 << 0) & 0x0000ff);
/* decode into a 12-bit symbol */
m0_hat = golay2412_decode_symbol(v0, golay2412_P, golay2412_H);
/* retain last 8 bits of 12-bit symbol */
_msg_dec[i] = m0_hat & 0xff;
j += 3;
}
assert( j == block_get_enc_msg_len(_dec_msg_len, 12, 24));
assert( i == _dec_msg_len);
}

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sys/include/ecc/golay2412.h Normal file
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/*
* Copyright (c) 2007 - 2015 Joseph Gaeddert
* Copyright (c) 2018 HAW Hamburg
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
/**
* @ingroup sys_ecc
* @{
*
* @file
* @brief Golay(24,12) half-rate forward error-correction code
*
* References:
* [Lin:2004] Lin, Shu and Costello, Daniel L. Jr., "Error Control
* Coding," Prentice Hall, New Jersey, 2nd edition, 2004.
*
* @author Joseph Gaeddert
* @author Peter Kietzmann <peter.kietzmann@haw.hamburg.de>
*
* @}
*/
#ifndef ECC_GOLAY2412_H
#define ECC_GOLAY2412_H
#ifdef __cplusplus
extern "C" {
#endif
/**
* @brief encode block of data using Golay(24,12) encoder
*
* @pre _dec_msg_len and sizeof(_msg_dec) accordingly have to be multiples of 3
*
* @param[in] _dec_msg_len decoded message length (number of bytes)
* @param[in] _msg_dec decoded message [size: 1 x _dec_msg_len]
* @param[in] _msg_enc encoded message [size: 1 x 2*_dec_msg_len]
*/
void golay2412_encode(uint32_t _dec_msg_len,
unsigned char *_msg_dec,
unsigned char *_msg_enc);
/**
* @brief decode block of data using Golay(24,12) decoder
*
* @param[in] _dec_msg_len decoded message length (number of bytes)
* @param[in] _msg_dec encoded message [size: 1 x 2*_dec_msg_len]
* @param[in] _msg_enc decoded message [size: 1 x _dec_msg_len]
*/
void golay2412_decode(uint32_t _dec_msg_len,
unsigned char *_msg_enc,
unsigned char *_msg_dec);
#ifdef __cplusplus
}
#endif
#endif /* ECC_GOLAY2412_H */
/** @} */

1
tests/unittests/tests-ecc/Makefile.include
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@ -1 +1,2 @@
USEMODULE += ecc_golay2412
USEMODULE += ecc_hamming256

57
tests/unittests/tests-ecc/tests-ecc.c
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@ -20,6 +20,18 @@
#include "embUnit.h"
#include "ecc/hamming256.h"
#include "ecc/golay2412.h"
/* source for random bytes: https://www.random.org/bytes */
unsigned char data_in[] = { 201, 240, 154, 5, 227, 60, 116, 192, 214 };
/* encoded sequence */
unsigned char msg_enc[] = { 220, 124, 159, 19, 64, 154, 135, 208, 94,
227, 35, 60, 248, 39, 76, 187, 16, 214 };
/* Added errors. golay(24, 12) can correct up to 3 errors in one 24-bit
* symbol (= 3 bytes). Positions for bitflips generated at
* https://www.random.org/bytes */
unsigned char msg_enc_3_err_per_symbol[] = { 252, 60, 191, 18, 64, 190, 135, 209, 22,
227, 43, 188, 252, 33, 76, 57, 16, 212 };
static void test_hamming256_single(void)
{
@ -75,11 +87,56 @@ static void test_hamming256_padding(void)
TEST_ASSERT_EQUAL_INT(Hamming_ERROR_ECC, result);
}
static void test_golay2412_message_encode(void)
{
unsigned char encoded[2 * sizeof(data_in)];
golay2412_encode(sizeof(data_in), &data_in[0], &encoded[0]);
TEST_ASSERT_EQUAL_INT(0, memcmp(&msg_enc, &encoded, sizeof(encoded)));
}
static void test_golay2412_message_noerr(void)
{
unsigned char result[sizeof(data_in)];
unsigned char encoded[2 * sizeof(data_in)];
golay2412_encode(sizeof(data_in), &data_in[0], &encoded[0]);
golay2412_decode(sizeof(result), &encoded[0], &result[0]);
TEST_ASSERT_EQUAL_INT(0, memcmp(&data_in, &result, sizeof(data_in)));
}
static void test_golay2412_message_decode_success(void)
{
unsigned char result[sizeof(data_in)];
golay2412_decode(sizeof(result), &msg_enc_3_err_per_symbol[0], &result[0]);
TEST_ASSERT_EQUAL_INT(0, memcmp(&data_in, &result, sizeof(data_in)));
}
static void test_golay2412_message_decode_fail(void)
{
unsigned char result[sizeof(data_in)];
/* adding a 4th error to the first symbol leads to an
uncorrectable sequence */
msg_enc_3_err_per_symbol[0] ^= (1L << 6);
golay2412_decode(sizeof(result), &msg_enc_3_err_per_symbol[0], &result[0]);
TEST_ASSERT(memcmp(&data_in, &result, sizeof(data_in)));
}
TestRef test_all(void)
{
EMB_UNIT_TESTFIXTURES(fixtures) {
new_TestFixture(test_hamming256_single),
new_TestFixture(test_hamming256_padding),
new_TestFixture(test_golay2412_message_encode),
new_TestFixture(test_golay2412_message_noerr),
new_TestFixture(test_golay2412_message_decode_success),
new_TestFixture(test_golay2412_message_decode_fail),
};
EMB_UNIT_TESTCALLER(EccTest, NULL, NULL, fixtures);