mirror of
https://github.com/aicodix/code.git
synced 2026-04-27 14:30:36 +00:00
392 lines
14 KiB
C++
392 lines
14 KiB
C++
/*
|
|
Parity aided successive cancellation list decoding of polar codes
|
|
|
|
Copyright 2023 Ahmet Inan <inan@aicodix.de>
|
|
*/
|
|
|
|
#pragma once
|
|
|
|
#include "polar_helper.hh"
|
|
|
|
namespace CODE {
|
|
|
|
template <typename TYPE>
|
|
class PolarParityEncoder
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
static bool get(const uint32_t *bits, int idx)
|
|
{
|
|
return (bits[idx/32] >> (idx%32)) & 1;
|
|
}
|
|
public:
|
|
void operator()(TYPE *codeword, const TYPE *message, const uint32_t *frozen, int level, int stride, int first)
|
|
{
|
|
int length = 1 << level;
|
|
int count = first;
|
|
TYPE parity = PH::one();
|
|
for (int i = 0; i < length; i += 2) {
|
|
TYPE msg0, msg1;
|
|
if (get(frozen, i)) {
|
|
msg0 = PH::one();
|
|
} else if (count) {
|
|
msg0 = *message++;
|
|
parity = PH::qmul(parity, msg0);
|
|
--count;
|
|
} else {
|
|
msg0 = parity;
|
|
parity = PH::one();
|
|
count = stride;
|
|
}
|
|
if (get(frozen, i + 1)) {
|
|
msg1 = PH::one();
|
|
} else if (count) {
|
|
msg1 = *message++;
|
|
parity = PH::qmul(parity, msg1);
|
|
--count;
|
|
} else {
|
|
msg1 = parity;
|
|
parity = PH::one();
|
|
count = stride;
|
|
}
|
|
codeword[i] = PH::qmul(msg0, msg1);
|
|
codeword[i+1] = msg1;
|
|
}
|
|
for (int h = 2; h < length; h *= 2)
|
|
for (int i = 0; i < length; i += 2 * h)
|
|
for (int j = i; j < i + h; ++j)
|
|
codeword[j] = PH::qmul(codeword[j], codeword[j+h]);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE, int M>
|
|
struct PolarParityNode
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int N = 1 << M;
|
|
static MAP rate0(PATH *metric, TYPE *hard, TYPE *soft)
|
|
{
|
|
for (int i = 0; i < N; ++i)
|
|
hard[i] = PH::one();
|
|
for (int i = 0; i < N; ++i)
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
if (soft[i+N].v[k] < 0)
|
|
metric[k] -= soft[i+N].v[k];
|
|
MAP map;
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
map.v[k] = k;
|
|
return map;
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct PolarParityNode<TYPE, 0>
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static MAP rate0(PATH *metric, TYPE *hard, TYPE *soft)
|
|
{
|
|
*hard = PH::one();
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
if (soft[1].v[k] < 0)
|
|
metric[k] -= soft[1].v[k];
|
|
MAP map;
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
map.v[k] = k;
|
|
return map;
|
|
}
|
|
static MAP rate1(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, TYPE *parity, int *count, int stride)
|
|
{
|
|
TYPE sft = soft[1];
|
|
SIMD<PATH, 2*TYPE::SIZE> fork;
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
fork.v[2*k] = fork.v[2*k+1] = metric[k];
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
if (sft.v[k] < 0)
|
|
fork.v[2*k] -= sft.v[k];
|
|
else
|
|
fork.v[2*k+1] += sft.v[k];
|
|
if (*count == 0) {
|
|
TYPE chk = *parity;
|
|
*parity = PH::one();
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
if (chk.v[k] < 0)
|
|
fork.v[2*k] = 1000000;
|
|
else
|
|
fork.v[2*k+1] = 1000000;
|
|
}
|
|
auto perm = vorder(fork);
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
metric[k] = fork.v[perm.v[k]];
|
|
MAP map;
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
map.v[k] = perm.v[k] >> 1;
|
|
TYPE hrd;
|
|
for (int k = 0; k < TYPE::SIZE; ++k)
|
|
hrd.v[k] = 1 - 2 * (perm.v[k] & 1);
|
|
if (*count) {
|
|
message[*index] = hrd;
|
|
*parity = PH::qmul(vshuf(*parity, map), hrd);
|
|
maps[*index] = map;
|
|
++*index;
|
|
--*count;
|
|
} else {
|
|
message[*index-1] = vshuf(message[*index-1], map);
|
|
maps[*index-1] = vshuf(maps[*index-1], map);
|
|
*count = stride;
|
|
}
|
|
*hard = hrd;
|
|
return map;
|
|
}
|
|
};
|
|
|
|
template <typename TYPE, int M>
|
|
struct PolarParityTree
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int N = 1 << M;
|
|
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)
|
|
{
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
|
|
MAP lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen, parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
|
|
MAP rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen+N/2/32, parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
|
|
return vshuf(lmap, rmap);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct PolarParityTree<TYPE, 6>
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int M = 6;
|
|
static const int N = 1 << M;
|
|
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)
|
|
{
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
|
|
MAP lmap, rmap;
|
|
if (frozen[0] == 0xffffffff)
|
|
lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
|
|
else
|
|
lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen[0], parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
|
|
if (frozen[1] == 0xffffffff)
|
|
rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
|
|
else
|
|
rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen[1], parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
|
|
return vshuf(lmap, rmap);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct PolarParityTree<TYPE, 5>
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int M = 5;
|
|
static const int N = 1 << M;
|
|
static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
|
|
{
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
|
|
MAP lmap, rmap;
|
|
if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
|
|
lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
|
|
else
|
|
lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
|
|
if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
|
|
rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
|
|
else
|
|
rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
|
|
return vshuf(lmap, rmap);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct PolarParityTree<TYPE, 4>
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int M = 4;
|
|
static const int N = 1 << M;
|
|
static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
|
|
{
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
|
|
MAP lmap, rmap;
|
|
if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
|
|
lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
|
|
else
|
|
lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
|
|
if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
|
|
rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
|
|
else
|
|
rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
|
|
return vshuf(lmap, rmap);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct PolarParityTree<TYPE, 3>
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int M = 3;
|
|
static const int N = 1 << M;
|
|
static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
|
|
{
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
|
|
MAP lmap, rmap;
|
|
if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
|
|
lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
|
|
else
|
|
lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
|
|
if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
|
|
rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
|
|
else
|
|
rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
|
|
return vshuf(lmap, rmap);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct PolarParityTree<TYPE, 2>
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int M = 2;
|
|
static const int N = 1 << M;
|
|
static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
|
|
{
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
|
|
MAP lmap, rmap;
|
|
if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
|
|
lmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard, soft);
|
|
else
|
|
lmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard, soft, frozen & ((1<<(1<<(M-1)))-1), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
|
|
if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
|
|
rmap = PolarParityNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
|
|
else
|
|
rmap = PolarParityTree<TYPE, M-1>::decode(metric, message, maps, index, hard+N/2, soft, frozen >> (N/2), parity, count, stride);
|
|
for (int i = 0; i < N/2; ++i)
|
|
hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
|
|
return vshuf(lmap, rmap);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct PolarParityTree<TYPE, 1>
|
|
{
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *index, TYPE *hard, TYPE *soft, uint32_t frozen, TYPE *parity, int *count, int stride)
|
|
{
|
|
soft[1] = PH::prod(soft[2], soft[3]);
|
|
MAP lmap, rmap;
|
|
if (frozen & 1)
|
|
lmap = PolarParityNode<TYPE, 0>::rate0(metric, hard, soft);
|
|
else
|
|
lmap = PolarParityNode<TYPE, 0>::rate1(metric, message, maps, index, hard, soft, parity, count, stride);
|
|
soft[1] = PH::madd(hard[0], vshuf(soft[2], lmap), vshuf(soft[3], lmap));
|
|
if (frozen >> 1)
|
|
rmap = PolarParityNode<TYPE, 0>::rate0(metric, hard+1, soft);
|
|
else
|
|
rmap = PolarParityNode<TYPE, 0>::rate1(metric, message, maps, index, hard+1, soft, parity, count, stride);
|
|
hard[0] = PH::qmul(vshuf(hard[0], rmap), hard[1]);
|
|
return vshuf(lmap, rmap);
|
|
}
|
|
};
|
|
|
|
template <typename TYPE, int MAX_M>
|
|
class PolarParityDecoder
|
|
{
|
|
static_assert(MAX_M >= 5 && MAX_M <= 16);
|
|
typedef PolarHelper<TYPE> PH;
|
|
typedef typename TYPE::value_type VALUE;
|
|
typedef typename PH::PATH PATH;
|
|
typedef typename PH::MAP MAP;
|
|
static const int MAX_N = 1 << MAX_M;
|
|
TYPE soft[2*MAX_N];
|
|
TYPE hard[MAX_N];
|
|
MAP maps[MAX_N];
|
|
public:
|
|
void operator()(int *rank, TYPE *message, const VALUE *codeword, const uint32_t *frozen, int level, int stride, int first)
|
|
{
|
|
assert(level <= MAX_M);
|
|
int index = 0;
|
|
PATH metric[TYPE::SIZE];
|
|
metric[0] = 0;
|
|
for (int k = 1; k < TYPE::SIZE; ++k)
|
|
metric[k] = 1000000;
|
|
int length = 1 << level;
|
|
for (int i = 0; i < length; ++i)
|
|
soft[length+i] = vdup<TYPE>(codeword[i]);
|
|
TYPE parity = PH::one();
|
|
int count = first;
|
|
|
|
switch (level) {
|
|
case 5: PolarParityTree<TYPE, 5>::decode(metric, message, maps, &index, hard, soft, *frozen, &parity, &count, stride); break;
|
|
case 6: PolarParityTree<TYPE, 6>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
|
case 7: PolarParityTree<TYPE, 7>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
|
case 8: PolarParityTree<TYPE, 8>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
|
case 9: PolarParityTree<TYPE, 9>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
|
case 10: PolarParityTree<TYPE, 10>::decode(metric, message, maps, &index, hard, soft, frozen, &parity, &count, stride); break;
|
|
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);
|
|
}
|
|
|
|
for (int i = 0, r = 0; rank != nullptr && i < TYPE::SIZE; ++i) {
|
|
if (i > 0 && metric[i-1] != metric[i])
|
|
++r;
|
|
rank[i] = r;
|
|
}
|
|
MAP acc = maps[index-1];
|
|
for (int i = index-2; i >= 0; --i) {
|
|
message[i] = vshuf(message[i], acc);
|
|
acc = vshuf(maps[i], acc);
|
|
}
|
|
}
|
|
};
|
|
|
|
}
|
|
|