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added parity check aided SCL decoding
This commit is contained in:
Ahmet Inan
parent
37ba4b64ef
commit
0bb0eaf5a9
2 changed files with 402 additions and 2 deletions
386
polar_parity_aided.hh
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386
polar_parity_aided.hh
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/*
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Parity aided successive cancellation list decoding of polar codes
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Copyright 2023 Ahmet Inan <inan@aicodix.de>
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*/
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#pragma once
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#include <algorithm>
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#include "polar_helper.hh"
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namespace CODE {
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template <typename TYPE>
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class PolarParityEncoder
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{
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typedef PolarHelper<TYPE> PH;
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static bool get(const uint32_t *bits, int idx)
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{
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return (bits[idx/32] >> (idx%32)) & 1;
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}
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public:
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void operator()(TYPE *codeword, const TYPE *message, const uint32_t *frozen, int level, int stride)
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{
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int length = 1 << level;
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int count = stride;
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TYPE parity = PH::one();
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for (int i = 0; i < length; i += 2) {
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TYPE msg0, msg1;
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if (get(frozen, i)) {
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msg0 = PH::one();
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} else if (count) {
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msg0 = *message++;
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parity = PH::qmul(parity, msg0);
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--count;
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} else {
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msg0 = parity;
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parity = PH::one();
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count = stride;
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}
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if (get(frozen, i + 1)) {
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msg1 = PH::one();
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} else if (count) {
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msg1 = *message++;
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parity = PH::qmul(parity, msg1);
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--count;
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} else {
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msg1 = parity;
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parity = PH::one();
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count = stride;
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}
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codeword[i] = PH::qmul(msg0, msg1);
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codeword[i+1] = msg1;
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}
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for (int h = 2; h < length; h *= 2)
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for (int i = 0; i < length; i += 2 * h)
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for (int j = i; j < i + h; ++j)
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codeword[j] = PH::qmul(codeword[j], codeword[j+h]);
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}
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};
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template <typename TYPE, int M>
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struct PolarParityNode
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int N = 1 << M;
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static MAP rate0(PATH *metric, TYPE *hard, TYPE *soft)
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{
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for (int i = 0; i < N; ++i)
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hard[i] = PH::one();
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for (int i = 0; i < N; ++i)
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for (int k = 0; k < TYPE::SIZE; ++k)
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if (soft[i+N].v[k] < 0)
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metric[k] -= soft[i+N].v[k];
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MAP map;
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for (int k = 0; k < TYPE::SIZE; ++k)
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map.v[k] = k;
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return map;
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}
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};
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template <typename TYPE>
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struct PolarParityNode<TYPE, 0>
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static MAP rate0(PATH *metric, TYPE *hard, TYPE *soft)
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{
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*hard = PH::one();
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for (int k = 0; k < TYPE::SIZE; ++k)
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if (soft[1].v[k] < 0)
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metric[k] -= soft[1].v[k];
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MAP map;
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for (int k = 0; k < TYPE::SIZE; ++k)
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map.v[k] = k;
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return map;
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}
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static MAP rate1(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, TYPE *parity, int *count, int stride)
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{
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TYPE sft = soft[1];
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PATH fork[2*TYPE::SIZE];
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for (int k = 0; k < TYPE::SIZE; ++k)
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fork[k] = fork[k+TYPE::SIZE] = metric[k];
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for (int k = 0; k < TYPE::SIZE; ++k)
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if (sft.v[k] < 0)
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fork[k] -= sft.v[k];
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else
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fork[k+TYPE::SIZE] += sft.v[k];
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int perm[2*TYPE::SIZE];
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for (int k = 0; k < 2*TYPE::SIZE; ++k)
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perm[k] = k;
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std::nth_element(perm, perm+TYPE::SIZE, perm+2*TYPE::SIZE, [fork](int a, int b){ return fork[a] < fork[b]; });
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for (int k = 0; k < TYPE::SIZE; ++k)
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metric[k] = fork[perm[k]];
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MAP map;
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for (int k = 0; k < TYPE::SIZE; ++k)
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map.v[k] = perm[k] % TYPE::SIZE;
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TYPE hrd;
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for (int k = 0; k < TYPE::SIZE; ++k)
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hrd.v[k] = perm[k] < TYPE::SIZE ? 1 : -1;
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if (*count) {
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message[*index] = hrd;
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*parity = PH::qmul(vshuf(*parity, map), hrd);
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maps[*index] = map;
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++*index;
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--*count;
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} else {
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message[*index-1] = vshuf(message[*index-1], map);
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maps[*index-1] = vshuf(maps[*index-1], map);
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TYPE chk = vshuf(*parity, map);
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for (int k = 0; k < TYPE::SIZE; ++k)
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if (chk.v[k] != hrd.v[k])
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metric[k] = 1000;
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*parity = PH::one();
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*count = stride;
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}
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*hard = hrd;
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return map;
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}
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};
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template <typename TYPE, int M>
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struct PolarParityTree
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int N = 1 << M;
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static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, const uint32_t *frozen, TYPE *parity, int *count, int stride)
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{
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
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MAP lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen, parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
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MAP rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen+N/2/32, parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
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return vshuf(lmap, rmap);
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}
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};
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template <typename TYPE>
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struct PolarParityTree<TYPE, 6>
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int M = 6;
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static const int N = 1 << M;
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static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, const uint32_t *frozen, TYPE *parity, int *count, int stride)
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{
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
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MAP lmap, rmap;
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if (frozen[0] == 0xffffffff)
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lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
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else
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lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen[0], parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
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if (frozen[1] == 0xffffffff)
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rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
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else
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rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen[1], parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
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return vshuf(lmap, rmap);
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}
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};
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template <typename TYPE>
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struct PolarParityTree<TYPE, 5>
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int M = 5;
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static const int N = 1 << M;
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static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
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{
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
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MAP lmap, rmap;
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if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
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lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
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else
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lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
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if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
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rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
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else
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rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
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return vshuf(lmap, rmap);
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}
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};
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template <typename TYPE>
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struct PolarParityTree<TYPE, 4>
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int M = 4;
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static const int N = 1 << M;
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static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
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{
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
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MAP lmap, rmap;
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if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
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lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
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else
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lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
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if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
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rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
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else
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rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
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return vshuf(lmap, rmap);
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}
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};
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template <typename TYPE>
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struct PolarParityTree<TYPE, 3>
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int M = 3;
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static const int N = 1 << M;
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static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
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{
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
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MAP lmap, rmap;
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if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
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lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
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else
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lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
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if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
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rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
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else
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rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
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return vshuf(lmap, rmap);
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}
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};
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template <typename TYPE>
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struct PolarParityTree<TYPE, 2>
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int M = 2;
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static const int N = 1 << M;
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static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
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{
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
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MAP lmap, rmap;
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if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
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lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
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else
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lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
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if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
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rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
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else
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rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
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for (int i = 0; i < N/2; ++i)
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hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
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return vshuf(lmap, rmap);
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}
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};
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template <typename TYPE>
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struct PolarParityTree<TYPE, 1>
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{
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typedef PolarHelper<TYPE> PH;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
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{
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soft[1] = PH::prod(soft[2], soft[3]);
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MAP lmap, rmap;
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if (frozen & 1)
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lmap = PolarParityNode<TYPE, 0>::rate0(metric, hard, soft);
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else
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lmap = PolarParityNode<TYPE, 0>::rate1(metric, message, maps, index, hard, soft, parity, count, stride);
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soft[1] = PH::madd(hard[0], vshuf(soft[2], lmap), vshuf(soft[3], lmap));
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if (frozen >> 1)
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rmap = PolarParityNode<TYPE, 0>::rate0(metric, hard+1, soft);
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else
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rmap = PolarParityNode<TYPE, 0>::rate1(metric, message, maps, index, hard+1, soft, parity, count, stride);
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hard[0] = PH::qmul(vshuf(hard[0], rmap), hard[1]);
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return vshuf(lmap, rmap);
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}
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};
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template <typename TYPE, int MAX_M>
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class PolarParityDecoder
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{
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static_assert(MAX_M >= 5 && MAX_M <= 16);
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typedef PolarHelper<TYPE> PH;
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typedef typename TYPE::value_type VALUE;
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typedef typename PH::PATH PATH;
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typedef typename PH::MAP MAP;
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static const int MAX_N = 1 << MAX_M;
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TYPE soft[2*MAX_N];
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TYPE hard[MAX_N];
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MAP maps[MAX_N];
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public:
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void operator()(PATH *metric, TYPE *message, const VALUE *codeword, const uint32_t *frozen, int level, int stride)
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{
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assert(level <= MAX_M);
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int index = 0;
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metric[0] = 0;
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for (int k = 1; k < TYPE::SIZE; ++k)
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metric[k] = 1000;
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int length = 1 << level;
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for (int i = 0; i < length; ++i)
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soft[length+i] = vdup<TYPE>(codeword[i]);
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TYPE parity = PH::one();
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int count = stride;
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switch (level) {
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case 5: PolarParityTree<TYPE, 5>::decode(metric, message, maps, &index, hard, soft, *frozen, &parity, &count, stride); break;
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case 6: PolarParityTree<TYPE, 6>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
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case 7: PolarParityTree<TYPE, 7>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
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case 8: PolarParityTree<TYPE, 8>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
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case 9: PolarParityTree<TYPE, 9>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
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case 10: PolarParityTree<TYPE, 10>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
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case 11: PolarParityTree<TYPE, 11>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
||||
case 12: PolarParityTree<TYPE, 12>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
||||
case 13: PolarParityTree<TYPE, 13>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
||||
case 14: PolarParityTree<TYPE, 14>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
||||
case 15: PolarParityTree<TYPE, 15>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
||||
case 16: PolarParityTree<TYPE, 16>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
||||
default: assert(false);
|
||||
}
|
||||
|
||||
MAP acc = maps[index-1];
|
||||
for (int i = index-2; i >= 0; --i) {
|
||||
message[i] = vshuf(message[i], acc);
|
||||
acc = vshuf(maps[i], acc);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
Loading…
Add table
Add a link
Reference in a new issue