__all__ = [
"BCH_31_26_GEN",
"BCH_63_24_GEN",
"bch_31_26_encode",
"bch_63_24_encode",
]
import numpy as np
# TXS-10002-2025 6.2.3.1 / 6.2.3.2 BCH编码器
def _gf2_poly_mod(dividend: np.ndarray, divisor: np.ndarray) -> np.ndarray:
"""GF(2)多项式模运算。
多项式用比特数组表示，索引i对应d^i的系数。
"""
r = dividend.copy()
deg = len(divisor) - 1
for i in range(len(r) - 1, deg - 1, -1):
if r[i]:
r[i - deg:i + 1] ^= divisor
return r[:deg]
# BCH(31,26) 生成多项式: G(d) = 0045 (八进制) = x^5 + x^2 + 1
BCH_31_26_GEN = np.array([1, 0, 1, 0, 0, 1], dtype=int)
# BCH(63,24) 生成多项式: 通过GF(2^6)最小多项式乘积计算得出
# 本原多项式 x^6+x+1, 连续根 α^1..α^14, 生成多项式阶数39
BCH_63_24_GEN = np.array([
1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1,
], dtype=int)
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def bch_31_26_encode(info_26: np.ndarray) -> np.ndarray:
"""BCH(31,26)系统编码。
按标准6.2.3.1:
C(d) = d^5 * Ã(d) mod G(d)
S(d) = Ã(d) + d^26 * C(d)
:param info_26: 26比特信息序列（Ã(d)的系数，索引0=d^0）
:returns: 31比特码字
"""
g = BCH_31_26_GEN # 阶数5
n_parity = 5
# d^5 * Ã(d)
shifted = np.zeros(26 + n_parity, dtype=int)
shifted[n_parity:] = info_26
parity = _gf2_poly_mod(shifted, g)
codeword = np.zeros(31, dtype=int)
codeword[:26] = info_26
codeword[26:31] = parity
return codeword
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def bch_63_24_encode(info_24: np.ndarray) -> np.ndarray:
"""BCH(63,24)系统编码。
按标准6.2.3.2:
C(d) = d^39 * A(d) mod G(d)
S(d) = A(d) + d^24 * C(d)
:param info_24: 24比特信息序列（A(d)的系数，索引0=d^0）
:returns: 63比特码字
"""
g = BCH_63_24_GEN # 阶数39
n_parity = 39
# d^39 * A(d)
shifted = np.zeros(24 + n_parity, dtype=int)
shifted[n_parity:] = info_24
parity = _gf2_poly_mod(shifted, g)
codeword = np.zeros(63, dtype=int)
codeword[:24] = info_24
codeword[24:63] = parity
return codeword