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kgoba-ft8_lib/utils/ldpc.py

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9.4 KiB
Python
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import numpy as np
FTX_LDPC_N = 174
FTX_LDPC_M = 83
def ldpc_check(codeword):
errors = 0
for m in range(FTX_LDPC_M):
x = False
for i in range(kFTX_LDPC_Num_rows[m]):
x ^= (codeword[kFTX_LDPC_Nm[m][i] - 1] > 0)
if x:
errors += 1
return errors
def bp_solve(codeword, max_iters=25, max_no_improvement=5):
tov = np.zeros((FTX_LDPC_N, 3))
toc = np.zeros((FTX_LDPC_M, 7))
# int min_errors = FTX_LDPC_M;
min_errors = FTX_LDPC_M
last_errors = FTX_LDPC_M
plain = None
no_improvement = 1
for iter in range(max_iters):
# Do a hard decision guess (tov=0 in iter 0)
plain = np.where((codeword + tov[:, 0] + tov[:, 1] + tov[:, 2]) > 0, 1, 0)
if np.sum(plain) == 0:
# Message converged to all-zeros, which is prohibited
break
# Check to see if we have a codeword (check before we do any iter)
errors = ldpc_check(plain)
print(f'iter {iter}, errors {errors}')
if errors < last_errors:
no_improvement = 1
last_errors = errors
else:
no_improvement += 1
if no_improvement >= max_no_improvement:
break
if errors < min_errors:
# We have a better guess - update the result
min_errors = errors
if errors == 0:
# Found a perfect answer
break
# Send messages from bits to check nodes
for m in range(FTX_LDPC_M):
for n_idx in range(kFTX_LDPC_Num_rows[m]):
n = kFTX_LDPC_Nm[m][n_idx] - 1
# for each (n, m)
Tnm = codeword[n]
for m_idx in range(3):
if (kFTX_LDPC_Mn[n][m_idx] - 1) != m:
Tnm += tov[n][m_idx]
toc[m][n_idx] = np.tanh(-Tnm / 2)
# Send messages from check nodes to variable nodes
for n in range(FTX_LDPC_N):
for m_idx in range(3):
m = kFTX_LDPC_Mn[n][m_idx] - 1
# for each (n, m)
Tmn = 1.0
for n_idx in range(kFTX_LDPC_Num_rows[m]):
if (kFTX_LDPC_Nm[m][n_idx] - 1) != n:
Tmn *= toc[m][n_idx]
tov[n][m_idx] = -2 * np.arctanh(Tmn)
return (min_errors, plain)
# Each row describes one LDPC parity check.
# Each number is an index into the codeword (1-origin).
# The codeword bits mentioned in each row must XOR to zero.
kFTX_LDPC_Nm = [
[ 4, 31, 59, 91, 92, 96, 153 ],
[ 5, 32, 60, 93, 115, 146, 0 ],
[ 6, 24, 61, 94, 122, 151, 0 ],
[ 7, 33, 62, 95, 96, 143, 0 ],
[ 8, 25, 63, 83, 93, 96, 148 ],
[ 6, 32, 64, 97, 126, 138, 0 ],
[ 5, 34, 65, 78, 98, 107, 154 ],
[ 9, 35, 66, 99, 139, 146, 0 ],
[ 10, 36, 67, 100, 107, 126, 0 ],
[ 11, 37, 67, 87, 101, 139, 158 ],
[ 12, 38, 68, 102, 105, 155, 0 ],
[ 13, 39, 69, 103, 149, 162, 0 ],
[ 8, 40, 70, 82, 104, 114, 145 ],
[ 14, 41, 71, 88, 102, 123, 156 ],
[ 15, 42, 59, 106, 123, 159, 0 ],
[ 1, 33, 72, 106, 107, 157, 0 ],
[ 16, 43, 73, 108, 141, 160, 0 ],
[ 17, 37, 74, 81, 109, 131, 154 ],
[ 11, 44, 75, 110, 121, 166, 0 ],
[ 45, 55, 64, 111, 130, 161, 173 ],
[ 8, 46, 71, 112, 119, 166, 0 ],
[ 18, 36, 76, 89, 113, 114, 143 ],
[ 19, 38, 77, 104, 116, 163, 0 ],
[ 20, 47, 70, 92, 138, 165, 0 ],
[ 2, 48, 74, 113, 128, 160, 0 ],
[ 21, 45, 78, 83, 117, 121, 151 ],
[ 22, 47, 58, 118, 127, 164, 0 ],
[ 16, 39, 62, 112, 134, 158, 0 ],
[ 23, 43, 79, 120, 131, 145, 0 ],
[ 19, 35, 59, 73, 110, 125, 161 ],
[ 20, 36, 63, 94, 136, 161, 0 ],
[ 14, 31, 79, 98, 132, 164, 0 ],
[ 3, 44, 80, 124, 127, 169, 0 ],
[ 19, 46, 81, 117, 135, 167, 0 ],
[ 7, 49, 58, 90, 100, 105, 168 ],
[ 12, 50, 61, 118, 119, 144, 0 ],
[ 13, 51, 64, 114, 118, 157, 0 ],
[ 24, 52, 76, 129, 148, 149, 0 ],
[ 25, 53, 69, 90, 101, 130, 156 ],
[ 20, 46, 65, 80, 120, 140, 170 ],
[ 21, 54, 77, 100, 140, 171, 0 ],
[ 35, 82, 133, 142, 171, 174, 0 ],
[ 14, 30, 83, 113, 125, 170, 0 ],
[ 4, 29, 68, 120, 134, 173, 0 ],
[ 1, 4, 52, 57, 86, 136, 152 ],
[ 26, 51, 56, 91, 122, 137, 168 ],
[ 52, 84, 110, 115, 145, 168, 0 ],
[ 7, 50, 81, 99, 132, 173, 0 ],
[ 23, 55, 67, 95, 172, 174, 0 ],
[ 26, 41, 77, 109, 141, 148, 0 ],
[ 2, 27, 41, 61, 62, 115, 133 ],
[ 27, 40, 56, 124, 125, 126, 0 ],
[ 18, 49, 55, 124, 141, 167, 0 ],
[ 6, 33, 85, 108, 116, 156, 0 ],
[ 28, 48, 70, 85, 105, 129, 158 ],
[ 9, 54, 63, 131, 147, 155, 0 ],
[ 22, 53, 68, 109, 121, 174, 0 ],
[ 3, 13, 48, 78, 95, 123, 0 ],
[ 31, 69, 133, 150, 155, 169, 0 ],
[ 12, 43, 66, 89, 97, 135, 159 ],
[ 5, 39, 75, 102, 136, 167, 0 ],
[ 2, 54, 86, 101, 135, 164, 0 ],
[ 15, 56, 87, 108, 119, 171, 0 ],
[ 10, 44, 82, 91, 111, 144, 149 ],
[ 23, 34, 71, 94, 127, 153, 0 ],
[ 11, 49, 88, 92, 142, 157, 0 ],
[ 29, 34, 87, 97, 147, 162, 0 ],
[ 30, 50, 60, 86, 137, 142, 162 ],
[ 10, 53, 66, 84, 112, 128, 165 ],
[ 22, 57, 85, 93, 140, 159, 0 ],
[ 28, 32, 72, 103, 132, 166, 0 ],
[ 28, 29, 84, 88, 117, 143, 150 ],
[ 1, 26, 45, 80, 128, 147, 0 ],
[ 17, 27, 89, 103, 116, 153, 0 ],
[ 51, 57, 98, 163, 165, 172, 0 ],
[ 21, 37, 73, 138, 152, 169, 0 ],
[ 16, 47, 76, 130, 137, 154, 0 ],
[ 3, 24, 30, 72, 104, 139, 0 ],
[ 9, 40, 90, 106, 134, 151, 0 ],
[ 15, 58, 60, 74, 111, 150, 163 ],
[ 18, 42, 79, 144, 146, 152, 0 ],
[ 25, 38, 65, 99, 122, 160, 0 ],
[ 17, 42, 75, 129, 170, 172, 0 ]
]
# Each row corresponds to a codeword bit.
# The numbers indicate which three LDPC parity checks (rows in Nm) refer to the codeword bit.
# 1-origin.
kFTX_LDPC_Mn = [
[ 16, 45, 73 ],
[ 25, 51, 62 ],
[ 33, 58, 78 ],
[ 1, 44, 45 ],
[ 2, 7, 61 ],
[ 3, 6, 54 ],
[ 4, 35, 48 ],
[ 5, 13, 21 ],
[ 8, 56, 79 ],
[ 9, 64, 69 ],
[ 10, 19, 66 ],
[ 11, 36, 60 ],
[ 12, 37, 58 ],
[ 14, 32, 43 ],
[ 15, 63, 80 ],
[ 17, 28, 77 ],
[ 18, 74, 83 ],
[ 22, 53, 81 ],
[ 23, 30, 34 ],
[ 24, 31, 40 ],
[ 26, 41, 76 ],
[ 27, 57, 70 ],
[ 29, 49, 65 ],
[ 3, 38, 78 ],
[ 5, 39, 82 ],
[ 46, 50, 73 ],
[ 51, 52, 74 ],
[ 55, 71, 72 ],
[ 44, 67, 72 ],
[ 43, 68, 78 ],
[ 1, 32, 59 ],
[ 2, 6, 71 ],
[ 4, 16, 54 ],
[ 7, 65, 67 ],
[ 8, 30, 42 ],
[ 9, 22, 31 ],
[ 10, 18, 76 ],
[ 11, 23, 82 ],
[ 12, 28, 61 ],
[ 13, 52, 79 ],
[ 14, 50, 51 ],
[ 15, 81, 83 ],
[ 17, 29, 60 ],
[ 19, 33, 64 ],
[ 20, 26, 73 ],
[ 21, 34, 40 ],
[ 24, 27, 77 ],
[ 25, 55, 58 ],
[ 35, 53, 66 ],
[ 36, 48, 68 ],
[ 37, 46, 75 ],
[ 38, 45, 47 ],
[ 39, 57, 69 ],
[ 41, 56, 62 ],
[ 20, 49, 53 ],
[ 46, 52, 63 ],
[ 45, 70, 75 ],
[ 27, 35, 80 ],
[ 1, 15, 30 ],
[ 2, 68, 80 ],
[ 3, 36, 51 ],
[ 4, 28, 51 ],
[ 5, 31, 56 ],
[ 6, 20, 37 ],
[ 7, 40, 82 ],
[ 8, 60, 69 ],
[ 9, 10, 49 ],
[ 11, 44, 57 ],
[ 12, 39, 59 ],
[ 13, 24, 55 ],
[ 14, 21, 65 ],
[ 16, 71, 78 ],
[ 17, 30, 76 ],
[ 18, 25, 80 ],
[ 19, 61, 83 ],
[ 22, 38, 77 ],
[ 23, 41, 50 ],
[ 7, 26, 58 ],
[ 29, 32, 81 ],
[ 33, 40, 73 ],
[ 18, 34, 48 ],
[ 13, 42, 64 ],
[ 5, 26, 43 ],
[ 47, 69, 72 ],
[ 54, 55, 70 ],
[ 45, 62, 68 ],
[ 10, 63, 67 ],
[ 14, 66, 72 ],
[ 22, 60, 74 ],
[ 35, 39, 79 ],
[ 1, 46, 64 ],
[ 1, 24, 66 ],
[ 2, 5, 70 ],
[ 3, 31, 65 ],
[ 4, 49, 58 ],
[ 1, 4, 5 ],
[ 6, 60, 67 ],
[ 7, 32, 75 ],
[ 8, 48, 82 ],
[ 9, 35, 41 ],
[ 10, 39, 62 ],
[ 11, 14, 61 ],
[ 12, 71, 74 ],
[ 13, 23, 78 ],
[ 11, 35, 55 ],
[ 15, 16, 79 ],
[ 7, 9, 16 ],
[ 17, 54, 63 ],
[ 18, 50, 57 ],
[ 19, 30, 47 ],
[ 20, 64, 80 ],
[ 21, 28, 69 ],
[ 22, 25, 43 ],
[ 13, 22, 37 ],
[ 2, 47, 51 ],
[ 23, 54, 74 ],
[ 26, 34, 72 ],
[ 27, 36, 37 ],
[ 21, 36, 63 ],
[ 29, 40, 44 ],
[ 19, 26, 57 ],
[ 3, 46, 82 ],
[ 14, 15, 58 ],
[ 33, 52, 53 ],
[ 30, 43, 52 ],
[ 6, 9, 52 ],
[ 27, 33, 65 ],
[ 25, 69, 73 ],
[ 38, 55, 83 ],
[ 20, 39, 77 ],
[ 18, 29, 56 ],
[ 32, 48, 71 ],
[ 42, 51, 59 ],
[ 28, 44, 79 ],
[ 34, 60, 62 ],
[ 31, 45, 61 ],
[ 46, 68, 77 ],
[ 6, 24, 76 ],
[ 8, 10, 78 ],
[ 40, 41, 70 ],
[ 17, 50, 53 ],
[ 42, 66, 68 ],
[ 4, 22, 72 ],
[ 36, 64, 81 ],
[ 13, 29, 47 ],
[ 2, 8, 81 ],
[ 56, 67, 73 ],
[ 5, 38, 50 ],
[ 12, 38, 64 ],
[ 59, 72, 80 ],
[ 3, 26, 79 ],
[ 45, 76, 81 ],
[ 1, 65, 74 ],
[ 7, 18, 77 ],
[ 11, 56, 59 ],
[ 14, 39, 54 ],
[ 16, 37, 66 ],
[ 10, 28, 55 ],
[ 15, 60, 70 ],
[ 17, 25, 82 ],
[ 20, 30, 31 ],
[ 12, 67, 68 ],
[ 23, 75, 80 ],
[ 27, 32, 62 ],
[ 24, 69, 75 ],
[ 19, 21, 71 ],
[ 34, 53, 61 ],
[ 35, 46, 47 ],
[ 33, 59, 76 ],
[ 40, 43, 83 ],
[ 41, 42, 63 ],
[ 49, 75, 83 ],
[ 20, 44, 48 ],
[ 42, 49, 57 ]
]
kFTX_LDPC_Num_rows = [
7, 6, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 7, 6, 6,
6, 7, 6, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6,
6, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 7, 6, 6,
6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 7,
6, 6, 6, 7, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7,
6, 6, 6
]
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