use parity aided polar codes

This commit is contained in:
Ahmet Inan 2024-01-20 22:15:43 +01:00
commit d69dd7aa03
4 changed files with 34 additions and 52 deletions

View file

@ -7,6 +7,7 @@ Copyright 2021 Ahmet Inan <inan@aicodix.de>
#include <algorithm>
#include <iostream>
#include <cassert>
#include <cstdint>
#include <cmath>
namespace DSP { using std::abs; using std::min; using std::cos; using std::sin; }
#include "bip_buffer.hh"
@ -31,9 +32,7 @@ namespace DSP { using std::abs; using std::min; using std::cos; using std::sin;
#include "psk.hh"
#include "qam.hh"
#include "polar_tables.hh"
#include "polar_helper.hh"
#include "polar_encoder.hh"
#include "polar_list_decoder.hh"
#include "polar_parity_aided.hh"
template <typename value, typename cmplx, int search_pos, int symbol_len, int guard_len>
struct SchmidlCox
@ -200,13 +199,12 @@ struct Decoder
CODE::CRC<uint16_t> crc0;
CODE::CRC<uint32_t> crc1;
CODE::OrderedStatisticsDecoder<255, 71, 4> osddec;
CODE::PolarEncoder<mesg_type> polarenc;
CODE::PolarListDecoder<mesg_type, code_max> polardec;
CODE::PolarParityDecoder<mesg_type, code_max> polardec;
CODE::ReverseFisherYatesShuffle<4096> shuffle_4096;
CODE::ReverseFisherYatesShuffle<8192> shuffle_8192;
CODE::ReverseFisherYatesShuffle<16384> shuffle_16384;
int8_t genmat[255*71];
mesg_type mesg[bits_max], mess[bits_max];
mesg_type mesg[bits_max];
code_type code[bits_max];
cmplx cons[cons_max], prev[cols_max];
cmplx fdom[symbol_len], tdom[symbol_len];
@ -245,14 +243,6 @@ struct Decoder
fdom[(i+mls0_off/2+symbol_len/2)%(symbol_len/2)] = nrz(seq0());
return fdom;
}
void systematic()
{
polarenc(mess, mesg, frozen_bits, code_order);
int code_bits = 1 << code_order;
for (int i = 0, j = 0; i < code_bits && j < crc_bits; ++i)
if (!((frozen_bits[i/32] >> (i%32)) & 1))
mesg[j++] = mess[i];
}
cmplx mod_map(code_type *b)
{
switch (mod_bits) {
@ -400,7 +390,7 @@ struct Decoder
code_order = 12;
code_cols = 256;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
frozen_bits = frozen_4096_2147;
break;
case 24:
mod_bits = 2;
@ -409,7 +399,7 @@ struct Decoder
code_order = 13;
code_cols = 256;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
frozen_bits = frozen_8192_4261;
break;
case 25:
mod_bits = 2;
@ -418,7 +408,7 @@ struct Decoder
code_order = 14;
code_cols = 256;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
frozen_bits = frozen_16384_8489;
break;
case 26:
mod_bits = 4;
@ -427,7 +417,7 @@ struct Decoder
code_order = 12;
code_cols = 256;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
frozen_bits = frozen_4096_2147;
break;
case 27:
mod_bits = 4;
@ -436,7 +426,7 @@ struct Decoder
code_order = 13;
code_cols = 256;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
frozen_bits = frozen_8192_4261;
break;
case 28:
mod_bits = 4;
@ -445,7 +435,7 @@ struct Decoder
code_order = 14;
code_cols = 256;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
frozen_bits = frozen_16384_8489;
break;
case 29:
mod_bits = 6;
@ -454,7 +444,7 @@ struct Decoder
code_order = 13;
code_cols = 273;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
frozen_bits = frozen_8192_4261;
break;
case 30:
mod_bits = 6;
@ -463,7 +453,7 @@ struct Decoder
code_order = 14;
code_cols = 273;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
frozen_bits = frozen_16384_8489;
break;
default:
return;
@ -576,8 +566,7 @@ struct Decoder
for (int i = code_cols * cons_rows * mod_bits; i < bits_max; ++i)
code[i] = 0;
shuffle(code);
polardec(metric, mesg, code, frozen_bits, code_order);
systematic();
polardec(metric, mesg, code, frozen_bits, code_order, 31);
int order[mesg_type::SIZE];
for (int k = 0; k < mesg_type::SIZE; ++k)
order[k] = k;
@ -597,16 +586,8 @@ struct Decoder
*len = 0;
return;
}
int flips = 0;
for (int i = 0, j = 0; i < data_bits; ++i, ++j) {
while ((frozen_bits[j / 32] >> (j % 32)) & 1)
++j;
bool received = code[j] < 0;
bool decoded = mesg[i].v[best] < 0;
flips += received != decoded;
CODE::set_le_bit(out, i, decoded);
}
std::cerr << "bit flips: " << flips << std::endl;
for (int i = 0; i < data_bits; ++i)
CODE::set_le_bit(out, i, mesg[i].v[best] < 0);
}
};

View file

@ -6,6 +6,7 @@ Copyright 2021 Ahmet Inan <inan@aicodix.de>
#include <iostream>
#include <cassert>
#include <cstdint>
#include <cmath>
#include "xorshift.hh"
#include "complex.hh"
@ -21,8 +22,7 @@ Copyright 2021 Ahmet Inan <inan@aicodix.de>
#include "psk.hh"
#include "qam.hh"
#include "polar_tables.hh"
#include "polar_helper.hh"
#include "polar_encoder.hh"
#include "polar_parity_aided.hh"
#include "bose_chaudhuri_hocquenghem_encoder.hh"
template <typename value, typename cmplx, int rate>
@ -44,7 +44,7 @@ struct Encoder
CODE::CRC<uint16_t> crc0;
CODE::CRC<uint32_t> crc1;
CODE::BoseChaudhuriHocquenghemEncoder<255, 71> bchenc;
CODE::PolarSysEnc<code_type> polarenc;
CODE::PolarParityEncoder<code_type> polarenc;
CODE::FisherYatesShuffle<4096> shuffle_4096;
CODE::FisherYatesShuffle<8192> shuffle_8192;
CODE::FisherYatesShuffle<16384> shuffle_16384;
@ -267,7 +267,7 @@ struct Encoder
code_cols = 256;
data_bits = 2048;
reserved_tones = 0;
frozen_bits = frozen_4096_2080;
frozen_bits = frozen_4096_2147;
break;
case 24:
mod_bits = 2;
@ -277,7 +277,7 @@ struct Encoder
code_cols = 256;
data_bits = 4096;
reserved_tones = 0;
frozen_bits = frozen_8192_4128;
frozen_bits = frozen_8192_4261;
break;
case 25:
mod_bits = 2;
@ -287,7 +287,7 @@ struct Encoder
code_cols = 256;
data_bits = 8192;
reserved_tones = 0;
frozen_bits = frozen_16384_8224;
frozen_bits = frozen_16384_8489;
break;
case 26:
mod_bits = 4;
@ -297,7 +297,7 @@ struct Encoder
code_cols = 256;
data_bits = 2048;
reserved_tones = 8;
frozen_bits = frozen_4096_2080;
frozen_bits = frozen_4096_2147;
break;
case 27:
mod_bits = 4;
@ -307,7 +307,7 @@ struct Encoder
code_cols = 256;
data_bits = 4096;
reserved_tones = 8;
frozen_bits = frozen_8192_4128;
frozen_bits = frozen_8192_4261;
break;
case 28:
mod_bits = 4;
@ -317,7 +317,7 @@ struct Encoder
code_cols = 256;
data_bits = 8192;
reserved_tones = 8;
frozen_bits = frozen_16384_8224;
frozen_bits = frozen_16384_8489;
break;
case 29:
mod_bits = 6;
@ -327,7 +327,7 @@ struct Encoder
code_cols = 273;
data_bits = 4096;
reserved_tones = 15;
frozen_bits = frozen_8192_4128;
frozen_bits = frozen_8192_4261;
break;
case 30:
mod_bits = 6;
@ -337,7 +337,7 @@ struct Encoder
code_cols = 273;
data_bits = 8192;
reserved_tones = 15;
frozen_bits = frozen_16384_8224;
frozen_bits = frozen_16384_8489;
break;
default:
return;
@ -372,7 +372,7 @@ struct Encoder
crc1(inp[i]);
for (int i = 0; i < 32; ++i)
mesg[i+data_bits] = nrz((crc1()>>i)&1);
polarenc(code, mesg, frozen_bits, code_order);
polarenc(code, mesg, frozen_bits, code_order, 31);
shuffle(code);
for (int i = 0; i < cons_cols; ++i)
prev[i] = fdom[bin(i+code_off)];

View file

@ -25,6 +25,7 @@ void code(int N, int K)
(*freeze)(frozen, M, K+(1<<M)-N, better_probability);
delete freeze;
std::cerr << "Polar(" << N << ", " << K << ")" << std::endl;
std::cout << "static const uint32_t frozen_" << std::dec << N << "_" << K << "[" << (1<<(M-5)) << "] = { " << std::hex;
for (int i = 0; i < 1<<(M-5); ++i)
std::cout << "0x" << frozen[i] << ", ";
@ -33,8 +34,8 @@ void code(int N, int K)
int main()
{
code<14>(16384, 8192+32);
code<13>(8192, 4096+32);
code<12>(4096, 2048+32);
code<12>(4096, 2048+32+67);
code<13>(8192, 4096+32+133);
code<14>(16384, 8192+32+265);
return 0;
}

View file

@ -1,3 +1,3 @@
static const uint32_t frozen_16384_8224[512] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x11717ff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x177fffff, 0x177f7fff, 0x3177f, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x37f7fff, 0x1171fff, 0x10117, 0x7fffffff, 0x11717ff, 0x117177f, 0x10117, 0x117177f, 0x7, 0x1, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0x177f7fff, 0x13f7fff, 0x10117, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x11f7fff, 0x3fffffff, 0x117177f, 0x117177f, 0x117, 0xffffffff, 0x7fffffff, 0x17ffffff, 0x117177f, 0x177f7fff, 0x3177f, 0x1017f, 0x1, 0x17f7fff, 0x1011f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0xffffffff, 0x17ffffff, 0x177f7fff, 0x7177f, 0x77f7fff, 0x1011f, 0x10117, 0x1, 0x7fffffff, 0x177f7fff, 0x11f7fff, 0x10117, 0x11717ff, 0x10117, 0x10117, 0x1, 0x117177f, 0x10117, 0x17, 0x0, 0x3, 0x0, 0x0, 0x0, 0x7fffffff, 0x11717ff, 0x117177f, 0x10117, 0x117177f, 0x7, 0x1, 0x0, 0x3177f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1013f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x1173fff, 0xffffffff, 0x7fffffff, 0x177fffff, 0x117177f, 0x177f7fff, 0x3177f, 0x1013f, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x17ffffff, 0x177f7fff, 0x7177f, 0xffffffff, 0x177f7fff, 0x13f7fff, 0x10117, 0x1171fff, 0x10117, 0x10117, 0x1, 0x7fffffff, 0x1173fff, 0x117177f, 0x10117, 0x117177f, 0x117, 0x7, 0x0, 0x7177f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x11f7fff, 0x11717ff, 0x10117, 0x1fffffff, 0x117177f, 0x117177f, 0x117, 0x7177f, 0x1, 0x1, 0x0, 0x177f7fff, 0x17177f, 0x1037f, 0x1, 0x1011f, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x77f7fff, 0x1011f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x10117, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0x177fffff, 0x117177f, 0x1077f, 0x1, 0x177f7fff, 0x1017f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x1177fff, 0x10117, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x117177f, 0x10117, 0x10117, 0x1, 0x117, 0x0, 0x0, 0x0, 0x7, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x117177f, 0x117, 0x7, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_8192_4128[256] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x1fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x11717ff, 0xffffffff, 0x1fffffff, 0x177fffff, 0x17177f, 0x177f7fff, 0x1013f, 0x10117, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x7fffffff, 0x17ffffff, 0x117177f, 0xffffffff, 0xffffffff, 0xffffffff, 0x1fffffff, 0xffffffff, 0x177f7fff, 0x77f7fff, 0x1011f, 0x7fffffff, 0x13f7fff, 0x1171fff, 0x10117, 0x117177f, 0x117, 0x7, 0x0, 0xffffffff, 0xffffffff, 0x7fffffff, 0x77f7fff, 0x7fffffff, 0x1171fff, 0x117177f, 0x10117, 0x17ffffff, 0x117177f, 0x3177f, 0x1, 0x1013f, 0x1, 0x1, 0x0, 0x177f7fff, 0x1017f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x1fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x11f7fff, 0x11717ff, 0x10117, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x1171fff, 0x17ffffff, 0x117177f, 0x7177f, 0x1, 0x177f7fff, 0x1077f, 0x1011f, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0x17ffffff, 0x177fffff, 0x3177f, 0x37f7fff, 0x1011f, 0x10117, 0x1, 0x1171fff, 0x10117, 0x10117, 0x1, 0x117, 0x0, 0x0, 0x0, 0x117177f, 0x117, 0x17, 0x0, 0x3, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x7fffffff, 0x37f7fff, 0x1173fff, 0x10117, 0x11717ff, 0x10117, 0x17, 0x0, 0x117177f, 0x7, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1077f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1011f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_4096_2080[128] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x17ffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x77f7fff, 0x7fffffff, 0x1173fff, 0x11717ff, 0x117, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x11f7fff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0x177fffff, 0x1077f, 0x1013f, 0x1, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1013f, 0x11f7fff, 0x10117, 0x10117, 0x1, 0x11717ff, 0x117, 0x7, 0x0, 0x1, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x17ffffff, 0x177fffff, 0x1077f, 0xffffffff, 0x177f7fff, 0x11f7fff, 0x10117, 0x11717ff, 0x10117, 0x17, 0x0, 0x7fffffff, 0x1171fff, 0x117177f, 0x17, 0x3177f, 0x1, 0x1, 0x0, 0x1017f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x177fffff, 0x7177f, 0x1037f, 0x1, 0x1011f, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x10117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_4096_2147[128] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x13f7fff, 0x7fffffff, 0x11717ff, 0x117177f, 0x7, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x1171fff, 0xffffffff, 0x7fffffff, 0x17ffffff, 0x17177f, 0x177f7fff, 0x1017f, 0x10117, 0x1, 0xffffffff, 0x177f7fff, 0x17f7fff, 0x1011f, 0x1171fff, 0x10117, 0x117, 0x0, 0x117177f, 0x17, 0x3, 0x0, 0x1, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x3fffffff, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1017f, 0x7fffffff, 0x17f7fff, 0x1173fff, 0x10117, 0x117177f, 0x17, 0x3, 0x0, 0x3fffffff, 0x11717ff, 0x17177f, 0x3, 0x1077f, 0x1, 0x1, 0x0, 0x1011f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x177fffff, 0x1077f, 0x1013f, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_8192_4261[256] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x17f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1077f, 0x13f7fff, 0x10117, 0x10117, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x1fffffff, 0x177fffff, 0x7177f, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0x177f7fff, 0x11f7fff, 0x10117, 0x7fffffff, 0x1171fff, 0x117177f, 0x10117, 0x17177f, 0x3, 0x1, 0x0, 0xffffffff, 0xffffffff, 0x7fffffff, 0x11f7fff, 0x1fffffff, 0x117177f, 0x117177f, 0x7, 0x177fffff, 0x7177f, 0x1017f, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x37f7fff, 0x1011f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x37f7fff, 0x7fffffff, 0x1171fff, 0x117177f, 0x10117, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0x177fffff, 0x7177f, 0x1037f, 0x1, 0x77f7fff, 0x1011f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1017f, 0x11f7fff, 0x10117, 0x10117, 0x1, 0x11717ff, 0x10117, 0x117, 0x0, 0x7, 0x0, 0x0, 0x0, 0x117177f, 0x17, 0x3, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x7fffffff, 0x11f7fff, 0x11717ff, 0x10117, 0x117177f, 0x117, 0x7, 0x0, 0x7177f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1017f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_16384_8489[512] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x77f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x7fffffff, 0x17ffffff, 0x117177f, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x17ffffff, 0xffffffff, 0x177f7fff, 0x37f7fff, 0x1011f, 0xffffffff, 0xffffffff, 0x7fffffff, 0x177f7fff, 0x7fffffff, 0x1171fff, 0x117177f, 0x10117, 0x17ffffff, 0x117177f, 0x117177f, 0x7, 0x1077f, 0x1, 0x1, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x1fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x13f7fff, 0x1171fff, 0x10117, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x77f7fff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x11717ff, 0x177fffff, 0x117177f, 0x7177f, 0x1, 0xffffffff, 0x17ffffff, 0x177f7fff, 0x17177f, 0x77f7fff, 0x1013f, 0x10117, 0x1, 0x1173fff, 0x10117, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x3fffffff, 0x177fffff, 0x117177f, 0xffffffff, 0x177f7fff, 0x177f7fff, 0x1013f, 0x11f7fff, 0x10117, 0x10117, 0x1, 0x7fffffff, 0x13f7fff, 0x11717ff, 0x10117, 0x117177f, 0x10117, 0x117, 0x0, 0x117177f, 0x7, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1fffffff, 0x117177f, 0x117177f, 0x17, 0x3177f, 0x1, 0x1, 0x0, 0x1017f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x77f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0xffffffff, 0x17ffffff, 0x177f7fff, 0x7177f, 0x77f7fff, 0x1011f, 0x10117, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0x1fffffff, 0xffffffff, 0x177f7fff, 0x177f7fff, 0x1017f, 0x7fffffff, 0x17f7fff, 0x1171fff, 0x10117, 0x117177f, 0x10117, 0x10117, 0x0, 0x3fffffff, 0x117177f, 0x117177f, 0x117, 0x17177f, 0x3, 0x1, 0x0, 0x1037f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0x7fffffff, 0x37f7fff, 0x7fffffff, 0x11717ff, 0x117177f, 0x10117, 0x177fffff, 0x117177f, 0x7177f, 0x1, 0x1037f, 0x1, 0x1, 0x0, 0x177f7fff, 0x1037f, 0x1011f, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x11f7fff, 0x10117, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x10117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0x7fffffff, 0x177fffff, 0x117177f, 0x177f7fff, 0x3177f, 0x1013f, 0x1, 0x17f7fff, 0x10117, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x11717ff, 0x10117, 0x10117, 0x1, 0x10117, 0x1, 0x0, 0x0, 0x117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x117177f, 0x10117, 0x117, 0x0, 0x7, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x117177f, 0x7, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };