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added Artin Schreier's imap acceleration

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This commit is contained in:
Ahmet Inan 2018-09-20 20:50:06 +02:00
commit 61b7c19e68
3 changed files with 31 additions and 11 deletions
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4
bose_chaudhuri_hocquenghem_decoder.hh
View file

@ -19,7 +19,7 @@ public:
typedef typename GF::ValueType ValueType; typedef typename GF::ValueType ValueType;
typedef typename GF::IndexType IndexType; typedef typename GF::IndexType IndexType;
static const int N = GF::N, NP = N - K; static const int N = GF::N, NP = N - K;
BoseChaudhuriHocquenghemDecoder() {} ReedSolomonErrorCorrection<NR, FCR, GF> algorithm;
int compute_syndromes(ValueType *code, ValueType *syndromes) int compute_syndromes(ValueType *code, ValueType *syndromes)
{ {
// $syndromes_i = code(pe^{FCR+i})$ // $syndromes_i = code(pe^{FCR+i})$
@ -49,7 +49,7 @@ public:
return 0; return 0;
IndexType locations[NR]; IndexType locations[NR];
ValueType magnitudes[NR]; ValueType magnitudes[NR];
int count = ReedSolomonErrorCorrection<NR, FCR, GF>::algorithm(syndromes, locations, magnitudes, erasures, erasures_count); int count = algorithm(syndromes, locations, magnitudes, erasures, erasures_count);
if (count <= 0) if (count <= 0)
return count; return count;
for (int i = 0; i < count; ++i) for (int i = 0; i < count; ++i)

4
reed_solomon_decoder.hh
View file

@ -19,7 +19,7 @@ public:
typedef typename GF::ValueType ValueType; typedef typename GF::ValueType ValueType;
typedef typename GF::IndexType IndexType; typedef typename GF::IndexType IndexType;
static const int N = GF::N, K = N - NR; static const int N = GF::N, K = N - NR;
ReedSolomonDecoder() {} ReedSolomonErrorCorrection<NR, FCR, GF> algorithm;
int compute_syndromes(ValueType *code, ValueType *syndromes) int compute_syndromes(ValueType *code, ValueType *syndromes)
{ {
// $syndromes_i = code(pe^{FCR+i})$ // $syndromes_i = code(pe^{FCR+i})$
@ -49,7 +49,7 @@ public:
return 0; return 0;
IndexType locations[NR]; IndexType locations[NR];
ValueType magnitudes[NR]; ValueType magnitudes[NR];
int count = ReedSolomonErrorCorrection<NR, FCR, GF>::algorithm(syndromes, locations, magnitudes, erasures, erasures_count); int count = algorithm(syndromes, locations, magnitudes, erasures, erasures_count);
if (count <= 0) if (count <= 0)
return count; return count;
for (int i = 0; i < count; ++i) for (int i = 0; i < count; ++i)

34
reed_solomon_error_correction.hh
View file

@ -35,30 +35,49 @@ struct Chien
}; };
template <int NR, typename GF> template <int NR, typename GF>
struct FindLocations struct LocationFinder
{ {
typedef typename GF::value_type value_type; typedef typename GF::value_type value_type;
typedef typename GF::ValueType ValueType; typedef typename GF::ValueType ValueType;
typedef typename GF::IndexType IndexType; typedef typename GF::IndexType IndexType;
static int search(ValueType *locator, int locator_degree, IndexType *locations) static const int Q = GF::Q, N = GF::N;
ValueType Artin_Schreier_imap[Q];
LocationFinder()
{
for (int i = 0; i < Q; ++i)
Artin_Schreier_imap[i] = ValueType(0);
for (int i = 2; i < N; i += 2) {
ValueType x(i);
ValueType xxx = x * x + x;
if (xxx == ValueType(N))
continue;
assert(xxx.v);
assert(!Artin_Schreier_imap[xxx.v].v);
Artin_Schreier_imap[xxx.v] = x;
}
}
ValueType imap(ValueType a) {
assert(a.v <= a.N);
assert(a.v);
return Artin_Schreier_imap[a.v];
}
int operator()(ValueType *locator, int locator_degree, IndexType *locations)
{ {
if (locator_degree == 1) { if (locator_degree == 1) {
locations[0] = (index(locator[0]) / index(locator[1])) / IndexType(1); locations[0] = (index(locator[0]) / index(locator[1])) / IndexType(1);
return 1; return 1;
} }
#if 0
if (locator_degree == 2) { if (locator_degree == 2) {
if (!locator[1] || !locator[0]) if (!locator[1] || !locator[0])
return 0; return 0;
ValueType a(locator[2]), b(locator[1]), c(locator[0]); ValueType a(locator[2]), b(locator[1]), c(locator[0]);
ValueType ba(b/a), R(Artin_Schreier_imap(a*c/(b*b))); ValueType ba(b/a), R(imap(a*c/(b*b)));
if (!R) if (!R)
return 0; return 0;
locations[0] = index(ba * R) / IndexType(1); locations[0] = index(ba * R) / IndexType(1);
locations[1] = index(ba * R + ba) / IndexType(1); locations[1] = index(ba * R + ba) / IndexType(1);
return 2; return 2;
} }
#endif
return Chien<NR, GF>::search(locator, locator_degree, locations); return Chien<NR, GF>::search(locator, locator_degree, locations);
} }
}; };
@ -171,7 +190,8 @@ struct ReedSolomonErrorCorrection
typedef typename GF::ValueType ValueType; typedef typename GF::ValueType ValueType;
typedef typename GF::IndexType IndexType; typedef typename GF::IndexType IndexType;
static const int N = GF::N, K = N - NR; static const int N = GF::N, K = N - NR;
static int algorithm(ValueType *syndromes, IndexType *locations, ValueType *magnitudes, IndexType *erasures = 0, int erasures_count = 0) RS::LocationFinder<NR, GF> search;
int operator()(ValueType *syndromes, IndexType *locations, ValueType *magnitudes, IndexType *erasures = 0, int erasures_count = 0)
{ {
assert(0 <= erasures_count && erasures_count <= NR); assert(0 <= erasures_count && erasures_count <= NR);
ValueType locator[NR+1]; ValueType locator[NR+1];
@ -193,7 +213,7 @@ struct ReedSolomonErrorCorrection
while (!locator[locator_degree]) while (!locator[locator_degree])
if (--locator_degree < 0) if (--locator_degree < 0)
return -1; return -1;
int count = RS::FindLocations<NR, GF>::search(locator, locator_degree, locations); int count = search(locator, locator_degree, locations);
if (count < locator_degree) if (count < locator_degree)
return -1; return -1;
ValueType evaluator[NR]; ValueType evaluator[NR];