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revised modes to better amortize the preamble cost

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.. and to have a larger minimum size payload of 256 bytes
This commit is contained in:
Ahmet Inan 2024-01-04 11:48:08 +01:00
commit 390a11e5dc
5 changed files with 139 additions and 83 deletions
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24
README.md vendored
View file

@ -12,7 +12,7 @@ dd if=/dev/urandom of=uncoded.dat bs=1 count=256
Encode file ```uncoded.dat``` to ```encoded.wav``` [WAV](https://en.wikipedia.org/wiki/WAV) audio file with 8000 Hz sample rate, 16 bits and only 1 (real) channel:
```
./encode encoded.wav 8000 16 1 uncoded.dat 25
./encode encoded.wav 8000 16 1 uncoded.dat 23
```
Start recording to ```recorded.wav``` audio file and stop after 5 seconds:
@ -39,6 +39,26 @@ Compare original ```uncoded.dat``` with ```decoded.dat```:
diff -s uncoded.dat decoded.dat
```
### Supported Modes
Ping:
* Mode 0: DBPSK, 2/7-rate code, 1600 Hz bandwidth, 0.36 seconds and no payload
Rattlegram:
* Mode 14: DQPSK, 2/3-rate code, 1600 Hz bandwidth, 1.08 seconds and 170 bytes
* Mode 15: DQPSK, 1/2-rate code, 1600 Hz bandwidth, 1.08 seconds and 128 bytes
* Mode 16: DQPSK, 1/3-rate code, 1600 Hz bandwidth, 1.08 seconds and 85 bytes
Next:
* Mode 23: DQPSK, 1/2-rate code, 1600 Hz bandwidth, 1.80 seconds and 256 bytes
* Mode 24: DQPSK, 1/2-rate code, 1600 Hz bandwidth, 3.24 seconds and 512 bytes
* Mode 25: DQPSK, 1/2-rate code, 1600 Hz bandwidth, 6.12 seconds and 1024 bytes
* Mode 26: QAM16, 1/2-rate code, 1700 Hz bandwidth, 1.08 seconds and 256 bytes
* Mode 27: QAM16, 1/2-rate code, 1700 Hz bandwidth, 1.80 seconds and 512 bytes
* Mode 28: QAM16, 1/2-rate code, 1700 Hz bandwidth, 3.24 seconds and 1024 bytes
* Mode 29: QAM64, 1/2-rate code, 1900 Hz bandwidth, 1.26 seconds and 512 bytes
* Mode 30: QAM64, 1/2-rate code, 1900 Hz bandwidth, 2.16 seconds and 1024 bytes
### Simulating
Prerequisite: [disorders](https://github.com/aicodix/disorders)
@ -46,7 +66,7 @@ Prerequisite: [disorders](https://github.com/aicodix/disorders)
Encode ```uncoded.dat``` to [analytic](https://en.wikipedia.org/wiki/Analytic_signal) audio signal, add [multipath](https://en.wikipedia.org/wiki/Multipath_propagation), [CFO, SFO](https://en.wikipedia.org/wiki/Carrier_frequency_offset), [AWGN](https://en.wikipedia.org/wiki/Additive_white_Gaussian_noise), decode and compare:
```
./encode - 8000 16 2 uncoded.dat 25 | ../disorders/multipath - - ../disorders/multipath.txt 10 | ../disorders/cfo - - 234.567 | ../disorders/sfo - - 147 | ../disorders/awgn - - -30 | ./decode - - | diff -q -s uncoded.dat -
./encode - 8000 16 2 uncoded.dat 23 | ../disorders/multipath - - ../disorders/multipath.txt 10 | ../disorders/cfo - - 234.567 | ../disorders/sfo - - 147 | ../disorders/awgn - - -30 | ./decode - - | diff -q -s uncoded.dat -
```
### Reading

94
decode.cc
View file

@ -177,10 +177,10 @@ struct Decoder
static const int filter_len = (((21 * rate) / 8000) & ~3) | 1;
static const int guard_len = symbol_len / 8;
static const int extended_len = symbol_len + guard_len;
static const int code_max = 13;
static const int code_max = 14;
static const int bits_max = 1 << code_max;
static const int cols_max = 273 + 16;
static const int rows_max = 5;
static const int rows_max = 32;
static const int cons_max = cols_max * rows_max;
static const int mls0_len = 127;
static const int mls0_off = - mls0_len + 1;
@ -202,9 +202,9 @@ struct Decoder
CODE::OrderedStatisticsDecoder<255, 71, 4> osddec;
CODE::PolarEncoder<mesg_type> polarenc;
CODE::PolarListDecoder<mesg_type, code_max> polardec;
CODE::ReverseFisherYatesShuffle<2048> shuffle_2048;
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];
code_type code[bits_max];
@ -289,18 +289,16 @@ struct Decoder
}
void shuffle(code_type *c)
{
if (oper_mode < 25)
return;
switch (code_order) {
case 11:
shuffle_2048(c);
break;
case 12:
shuffle_4096(c);
break;
case 13:
shuffle_8192(c);
break;
case 14:
shuffle_16384(c);
break;
}
}
const cmplx *next_sample()
@ -370,7 +368,7 @@ struct Decoder
continue;
}
oper_mode = md & 255;
if (oper_mode && (oper_mode < 14 || (oper_mode > 16 && oper_mode < 23) || oper_mode > 28)) {
if (oper_mode && (oper_mode < 14 || (oper_mode > 16 && oper_mode < 23) || oper_mode > 30)) {
std::cerr << "operation mode " << oper_mode << " unsupported." << std::endl;
continue;
}
@ -424,23 +422,32 @@ struct Decoder
break;
case 23:
mod_bits = 2;
cons_rows = 4;
cons_rows = 8;
comb_cols = 0;
code_order = 11;
code_order = 12;
code_cols = 256;
data_bits = 1024;
frozen_bits = frozen_2048_1056;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
break;
case 24:
mod_bits = 2;
cons_rows = 4;
cons_rows = 16;
comb_cols = 0;
code_order = 11;
code_order = 13;
code_cols = 256;
data_bits = 1536;
frozen_bits = frozen_2048_1568;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 25:
mod_bits = 2;
cons_rows = 32;
comb_cols = 0;
code_order = 14;
code_cols = 256;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 26:
mod_bits = 4;
cons_rows = 4;
comb_cols = 8;
@ -449,32 +456,41 @@ struct Decoder
data_bits = 2048;
frozen_bits = frozen_4096_2080;
break;
case 26:
mod_bits = 4;
cons_rows = 4;
comb_cols = 8;
code_order = 12;
code_cols = 256;
data_bits = 3072;
frozen_bits = frozen_4096_3104;
break;
case 27:
mod_bits = 6;
cons_rows = 5;
comb_cols = 16;
mod_bits = 4;
cons_rows = 8;
comb_cols = 8;
code_order = 13;
code_cols = 273;
data_bits = 5440;
frozen_bits = frozen_8192_5472;
code_cols = 256;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 28:
mod_bits = 4;
cons_rows = 16;
comb_cols = 8;
code_order = 14;
code_cols = 256;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 29:
mod_bits = 6;
cons_rows = 5;
comb_cols = 16;
code_order = 13;
code_cols = 273;
data_bits = 6144;
frozen_bits = frozen_8192_6176;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 30:
mod_bits = 6;
cons_rows = 10;
comb_cols = 16;
code_order = 14;
code_cols = 273;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
default:
return;
@ -505,7 +521,7 @@ struct Decoder
fwd(fdom, tdom);
for (int i = 0; i < cons_cols; ++i)
cons[cons_cols*j+i] = demod_or_erase(fdom[bin(i+code_off)], prev[i]);
if (oper_mode > 24) {
if (oper_mode > 25) {
for (int i = 0; i < comb_cols; ++i)
cons[cons_cols*j+comb_dist*i+comb_off] *= nrz(seq0());
for (int i = 0; i < comb_cols; ++i) {
@ -538,7 +554,7 @@ struct Decoder
//std::cerr << "Theil-Sen yint = " << tse.yint() << std::endl;
for (int i = 0; i < cons_cols; ++i)
cons[cons_cols*j+i] *= DSP::polar<value>(1, -tse(i+code_off));
if (oper_mode > 24) {
if (oper_mode > 25) {
for (int i = 0; i < cons_cols; ++i)
if (i % comb_dist != comb_off)
prev[i] *= DSP::polar<value>(1, tse(i+code_off));
@ -552,7 +568,7 @@ struct Decoder
std::cerr << "Es/N0 (dB):";
value sp = 0, np = 0;
for (int j = 0, k = 0; j < cons_rows; ++j) {
if (oper_mode > 24) {
if (oper_mode > 25) {
for (int i = 0; i < comb_cols; ++i) {
cmplx hard(1, 0);
cmplx error = cons[cons_cols*j+comb_dist*i+comb_off] - hard;
@ -574,7 +590,7 @@ struct Decoder
value snr = DSP::decibel(precision);
std::cerr << " " << snr;
for (int i = 0; i < cons_cols; ++i) {
if (oper_mode > 24 && i % comb_dist == comb_off)
if (oper_mode > 25 && i % comb_dist == comb_off)
continue;
mod_soft(code+k, cons[cons_cols*j+i], precision);
k += mod_bits;
@ -649,7 +665,7 @@ int main(int argc, char **argv)
if (argc > 3)
skip_count = std::atoi(argv[3]);
const int data_max = 768;
const int data_max = 1024;
uint8_t *output_data = new uint8_t[data_max];
int data_len = 0;

118
encode.cc
View file

@ -31,7 +31,7 @@ struct Encoder
typedef int8_t code_type;
static const int symbol_len = (1280 * rate) / 8000;
static const int guard_len = symbol_len / 8;
static const int bits_max = 8192;
static const int bits_max = 16384;
static const int cols_max = 273 + 16;
static const int mls0_len = 127;
static const int mls0_poly = 0b10001001;
@ -45,9 +45,9 @@ struct Encoder
CODE::CRC<uint32_t> crc1;
CODE::BoseChaudhuriHocquenghemEncoder<255, 71> bchenc;
CODE::PolarSysEnc<code_type> polarenc;
CODE::FisherYatesShuffle<2048> shuffle_2048;
CODE::FisherYatesShuffle<4096> shuffle_4096;
CODE::FisherYatesShuffle<8192> shuffle_8192;
CODE::FisherYatesShuffle<16384> shuffle_16384;
code_type code[bits_max], mesg[bits_max];
cmplx fdom[symbol_len];
cmplx tdom[symbol_len];
@ -116,8 +116,8 @@ struct Encoder
bwd(tdom, fdom);
for (int i = 0; i < symbol_len; ++i)
tdom[i] /= std::sqrt(value(symbol_len*4));
clipping_and_filtering(oper_mode > 24 && papr_reduction);
if (oper_mode > 24 && papr_reduction)
clipping_and_filtering(oper_mode > 25 && papr_reduction);
if (oper_mode > 25 && papr_reduction)
tone_reservation();
for (int i = 0; i < symbol_len; ++i)
tdom[i] = cmplx(std::min(value(1), tdom[i].real()), std::min(value(1), tdom[i].imag()));
@ -191,7 +191,7 @@ struct Encoder
fdom[bin(i+mls1_off)] *= fdom[bin(i-1+mls1_off)];
for (int i = 0; i < mls1_len; ++i)
fdom[bin(i+mls1_off)] *= nrz(seq1());
if (oper_mode > 24) {
if (oper_mode > 25) {
for (int i = code_off; i < code_off + cons_cols; ++i) {
if (i == mls1_off-1)
i += mls1_len + 1;
@ -226,18 +226,16 @@ struct Encoder
}
void shuffle(code_type *c)
{
if (oper_mode < 25)
return;
switch (code_order) {
case 11:
shuffle_2048(c);
break;
case 12:
shuffle_4096(c);
break;
case 13:
shuffle_8192(c);
break;
case 14:
shuffle_16384(c);
break;
}
}
Encoder(DSP::WritePCM<value> *pcm, const uint8_t *inp, int freq_off, uint64_t call_sign, int oper_mode) :
@ -293,25 +291,35 @@ struct Encoder
break;
case 23:
mod_bits = 2;
cons_rows = 4;
cons_rows = 8;
comb_cols = 0;
code_order = 11;
code_order = 12;
code_cols = 256;
data_bits = 1024;
data_bits = 2048;
reserved_tones = 0;
frozen_bits = frozen_2048_1056;
frozen_bits = frozen_4096_2080;
break;
case 24:
mod_bits = 2;
cons_rows = 4;
cons_rows = 16;
comb_cols = 0;
code_order = 11;
code_order = 13;
code_cols = 256;
data_bits = 1536;
data_bits = 4096;
reserved_tones = 0;
frozen_bits = frozen_2048_1568;
frozen_bits = frozen_8192_4128;
break;
case 25:
mod_bits = 2;
cons_rows = 32;
comb_cols = 0;
code_order = 14;
code_cols = 256;
data_bits = 8192;
reserved_tones = 0;
frozen_bits = frozen_16384_8224;
break;
case 26:
mod_bits = 4;
cons_rows = 4;
comb_cols = 8;
@ -321,35 +329,45 @@ struct Encoder
reserved_tones = 8;
frozen_bits = frozen_4096_2080;
break;
case 26:
mod_bits = 4;
cons_rows = 4;
comb_cols = 8;
code_order = 12;
code_cols = 256;
data_bits = 3072;
reserved_tones = 8;
frozen_bits = frozen_4096_3104;
break;
case 27:
mod_bits = 6;
cons_rows = 5;
comb_cols = 16;
mod_bits = 4;
cons_rows = 8;
comb_cols = 8;
code_order = 13;
code_cols = 273;
data_bits = 5440;
reserved_tones = 15;
frozen_bits = frozen_8192_5472;
code_cols = 256;
data_bits = 4096;
reserved_tones = 8;
frozen_bits = frozen_8192_4128;
break;
case 28:
mod_bits = 4;
cons_rows = 16;
comb_cols = 8;
code_order = 14;
code_cols = 256;
data_bits = 8192;
reserved_tones = 8;
frozen_bits = frozen_16384_8224;
break;
case 29:
mod_bits = 6;
cons_rows = 5;
comb_cols = 16;
code_order = 13;
code_cols = 273;
data_bits = 6144;
data_bits = 4096;
reserved_tones = 15;
frozen_bits = frozen_8192_6176;
frozen_bits = frozen_8192_4128;
break;
case 30:
mod_bits = 6;
cons_rows = 10;
comb_cols = 16;
code_order = 14;
code_cols = 273;
data_bits = 8192;
reserved_tones = 15;
frozen_bits = frozen_16384_8224;
break;
default:
return;
@ -391,7 +409,7 @@ struct Encoder
CODE::MLS seq0(mls0_poly);
for (int j = 0, k = 0; j < cons_rows; ++j) {
for (int i = 0; i < cons_cols; ++i) {
if (oper_mode < 25) {
if (oper_mode < 26) {
prev[i] *= mod_map(code+k);
fdom[bin(i+code_off)] = prev[i];
k += mod_bits;
@ -481,22 +499,28 @@ int main(int argc, char **argv)
data_bits = 680;
break;
case 23:
data_bits = 1024;
break;
case 24:
data_bits = 1536;
break;
case 25:
data_bits = 2048;
break;
case 24:
data_bits = 4096;
break;
case 25:
data_bits = 8192;
break;
case 26:
data_bits = 3072;
data_bits = 2048;
break;
case 27:
data_bits = 5440;
data_bits = 4096;
break;
case 28:
data_bits = 6144;
data_bits = 8192;
break;
case 29:
data_bits = 4096;
break;
case 30:
data_bits = 8192;
break;
default:
std::cerr << "Unsupported operation mode." << std::endl;

6
freezer.cc
View file

@ -33,11 +33,9 @@ void code(int N, int K)
int main()
{
code<13>(8192, 6144+32);
code<13>(8192, 5440+32);
code<12>(4096, 3072+32);
code<14>(16384, 8192+32);
code<13>(8192, 4096+32);
code<12>(4096, 2048+32);
code<11>(2048, 1536+32);
code<11>(2048, 1360+32);
code<11>(2048, 1024+32);
code<11>(2048, 680+32);

6
polar_tables.hh
View file

@ -1,8 +1,6 @@
static const uint32_t frozen_8192_6176[256] = { 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, 0x117177f, 0x177f7fff, 0x1017f, 0x10117, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1077f, 0x7fffffff, 0x177f7fff, 0x11f7fff, 0x10117, 0x11717ff, 0x10117, 0x10117, 0x0, 0x7fffffff, 0x11717ff, 0x117177f, 0x10117, 0x17177f, 0x3, 0x1, 0x0, 0x1077f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0x7fffffff, 0x177f7fff, 0x7fffffff, 0x1173fff, 0x11717ff, 0x10117, 0x17ffffff, 0x117177f, 0x17177f, 0x3, 0x1077f, 0x1, 0x1, 0x0, 0x177f7fff, 0x3077f, 0x1013f, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x13f7fff, 0x10117, 0x10117, 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, 0xffffffff, 0x7fffffff, 0x17ffffff, 0x117177f, 0x177f7fff, 0x7177f, 0x1017f, 0x1, 0x37f7fff, 0x1011f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x1171fff, 0x10117, 0x10117, 0x1, 0x10117, 0x0, 0x0, 0x0, 0x17, 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, };
static const uint32_t frozen_8192_5472[256] = { 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, 0x11f7fff, 0x10117, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x11f7fff, 0x1fffffff, 0x117177f, 0x117177f, 0x17, 0xffffffff, 0x7fffffff, 0x17ffffff, 0x117177f, 0x177f7fff, 0x1077f, 0x1011f, 0x1, 0x13f7fff, 0x10117, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0xffffffff, 0x17ffffff, 0x177f7fff, 0x3177f, 0x37f7fff, 0x1011f, 0x10117, 0x1, 0x7fffffff, 0x77f7fff, 0x11f7fff, 0x10117, 0x11717ff, 0x10117, 0x10117, 0x0, 0x117177f, 0x17, 0x3, 0x0, 0x1, 0x0, 0x0, 0x0, 0x7fffffff, 0x11717ff, 0x117177f, 0x117, 0x17177f, 0x3, 0x1, 0x0, 0x1037f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1011f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0x177f7fff, 0x11f7fff, 0x10117, 0x7fffffff, 0x1171fff, 0x117177f, 0x10117, 0x117177f, 0x17, 0x3, 0x0, 0x17ffffff, 0x117177f, 0x7177f, 0x1, 0x1017f, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x177f7fff, 0x1037f, 0x1011f, 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, 0x11f7fff, 0x10117, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x17, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x3, 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_4096_3104[128] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x17ffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x1173fff, 0x11717ff, 0x10117, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x11717ff, 0x177fffff, 0x17177f, 0x1077f, 0x1, 0x177f7fff, 0x1017f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0x17ffffff, 0x177f7fff, 0x1037f, 0x13f7fff, 0x10117, 0x10117, 0x1, 0x11717ff, 0x10117, 0x10117, 0x0, 0x17, 0x0, 0x0, 0x0, 0x117177f, 0x17, 0x3, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x7fffffff, 0x13f7fff, 0x1171fff, 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_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_2048_1568[64] = { 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1017f, 0x7fffffff, 0x37f7fff, 0x1173fff, 0x10117, 0x11717ff, 0x17, 0x3, 0x0, 0x7fffffff, 0x11717ff, 0x17177f, 0x3, 0x1077f, 0x1, 0x1, 0x0, 0x1011f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x177fffff, 0x3077f, 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_2048_1392[64] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x11f7fff, 0xffffffff, 0x7fffffff, 0x17ffffff, 0x117177f, 0x177f7fff, 0x1037f, 0x1011f, 0x1, 0xffffffff, 0x177fffff, 0x77f7fff, 0x1011f, 0x1173fff, 0x10117, 0x10117, 0x0, 0x117177f, 0x17, 0x3, 0x0, 0x1, 0x0, 0x0, 0x0, 0x7fffffff, 0x11f7fff, 0x11717ff, 0x117, 0x17177f, 0x3, 0x1, 0x0, 0x1037f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1011f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_2048_1056[64] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1017f, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x13f7fff, 0x1171fff, 0x117, 0x3fffffff, 0x11717ff, 0x7177f, 0x1, 0x1017f, 0x1, 0x1, 0x0, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x1171fff, 0x17ffffff, 0x7177f, 0x1037f, 0x1, 0x77f7fff, 0x1013f, 0x10117, 0x1, 0x10117, 0x0, 0x0, 0x0, 0x1173fff, 0x10117, 0x117, 0x0, 0x7, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_2048_712[64] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x11f7fff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x17177f, 0x177fffff, 0x1037f, 0x1011f, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x1fffffff, 0x177fffff, 0x1077f, 0xffffffff, 0x177f7fff, 0x13f7fff, 0x10117, 0x1171fff, 0x117, 0x7, 0x0, 0x7fffffff, 0x1173fff, 0x11717ff, 0x7, 0x3077f, 0x1, 0x1, 0x0, 0x1013f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, };