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"""Decoding module."""
import numpy as np
import warnings
import test_pyldpc_utils as utils
from numba import njit, int64, types, float64
np.set_printoptions(linewidth=180, threshold=1000, edgeitems=20)
def decode(H, y, snr, maxiter=100):
"""Decode a Gaussian noise corrupted n bits message using BP algorithm.
Decoding is performed in parallel if multiple codewords are passed in y.
Parameters
----------
H: array (n_equations, n_code). Decoding matrix H.
y: array (n_code, n_messages) or (n_code,). Received message(s) in the
codeword space.
maxiter: int. Maximum number of iterations of the BP algorithm.
Returns
-------
x: array (n_code,) or (n_code, n_messages) the solutions in the
codeword space.
"""
m, n = H.shape
bits_hist, bits_values, nodes_hist, nodes_values = utils.bitsandnodes(H)
var = 10 ** (-snr / 10)
if y.ndim == 1:
y = y[:, None]
# step 0: initialization
Lc = 2 * y / var
_, n_messages = y.shape
Lq = np.zeros(shape=(m, n, n_messages))
Lr = np.zeros(shape=(m, n, n_messages))
for n_iter in range(maxiter):
#print(f'============================ iteration {n_iter} ============================')
Lq, Lr, L_posteriori = _logbp_numba(bits_hist, bits_values, nodes_hist,
nodes_values, Lc, Lq, Lr, n_iter)
#print("Lq=", Lq.flatten())
#print("Lr=", Lr.flatten())
#print("L_posteriori=", L_posteriori.flatten())
#print('L_posteriori=[')
#for row in L_posteriori.reshape([-1, 16]):
# for val in row:
# cc = '\033[91m' if val < 0 else ('\033[92m' if val > 0 else '\033[94m')
# print(f"{cc}{val: 012.6g}\033[38;5;240m", end=', ')
# print()
x = np.array(L_posteriori <= 0).astype(int)
product = utils.incode(H, x)
if product:
print(f'found, n_iter={n_iter}')
break
if n_iter == maxiter - 1:
warnings.warn("""Decoding stopped before convergence. You may want
to increase maxiter""")
return x.squeeze()
output_type_log2 = types.Tuple((float64[:, :, :], float64[:, :, :],
float64[:, :]))
#@njit(output_type_log2(int64[:], int64[:], int64[:], int64[:], float64[:, :],
# float64[:, :, :], float64[:, :, :], int64), cache=True)
def _logbp_numba(bits_hist, bits_values, nodes_hist, nodes_values, Lc, Lq, Lr,
n_iter):
"""Perform inner ext LogBP solver."""
m, n, n_messages = Lr.shape
# step 1 : Horizontal
bits_counter = 0
nodes_counter = 0
for i in range(m):
#print(f'=== i={i}')
ff = bits_hist[i]
ni = bits_values[bits_counter: bits_counter + ff]
bits_counter += ff
for j_iter, j in enumerate(ni):
nij = ni[:]
#print(f'\033[38;5;240mj={j:04d}', end=' ')
X = np.ones(n_messages)
if n_iter == 0:
for kk in range(len(nij)):
if nij[kk] != j:
lcv = Lc[nij[kk],0]
lcc = '\033[91m' if lcv < 0 else ('\033[92m' if lcv > 0 else '\033[94m')
#print(f'nij={nij[kk]:04d} Lc={lcc}{lcv:> 8f}\033[38;5;240m', end=' ')
X *= np.tanh(0.5 * Lc[nij[kk]])
else:
for kk in range(len(nij)):
if nij[kk] != j:
X *= np.tanh(0.5 * Lq[i, nij[kk]])
#print(f'\n==== {i:03d} {j_iter:01d} {X[0]:> 8f}')
num = 1 + X
denom = 1 - X
for ll in range(n_messages):
if num[ll] == 0:
Lr[i, j, ll] = -1
elif denom[ll] == 0:
Lr[i, j, ll] = 1
else:
Lr[i, j, ll] = np.log(num[ll] / denom[ll])
# step 2 : Vertical
for j in range(n):
ff = nodes_hist[j]
mj = nodes_values[bits_counter: nodes_counter + ff]
nodes_counter += ff
for i in mj:
mji = mj[:]
Lq[i, j] = Lc[j]
for kk in range(len(mji)):
if mji[kk] != i:
Lq[i, j] += Lr[mji[kk], j]
# LLR a posteriori:
L_posteriori = np.zeros((n, n_messages))
nodes_counter = 0
for j in range(n):
ff = nodes_hist[j]
mj = nodes_values[bits_counter: nodes_counter + ff]
nodes_counter += ff
L_posteriori[j] = Lc[j] + Lr[mj, j].sum(axis=0)
return Lq, Lr, L_posteriori
def get_message(tG, x):
"""Compute the original `n_bits` message from a `n_code` codeword `x`.
Parameters
----------
tG: array (n_code, n_bits) coding matrix tG.
x: array (n_code,) decoded codeword of length `n_code`.
Returns
-------
message: array (n_bits,). Original binary message.
"""
n, k = tG.shape
rtG, rx = utils.gausselimination(tG, x)
message = np.zeros(k).astype(int)
message[k - 1] = rx[k - 1]
for i in reversed(range(k - 1)):
message[i] = rx[i]
message[i] -= utils.binaryproduct(rtG[i, list(range(i+1, k))],
message[list(range(i+1, k))])
return abs(message)
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