def findErrors(self, forney_syndromes: Polynomial,
length_message: int) -> list:
"""
Berlekamp-Massey + Chien search to find the 0s of the error locator polynomial
:param forney_syndromes: the polynomial representation of the Forney syndromes
:param length_message: the length of the message + parity bits
:return: the error locator polynomial
"""
error_loc_polynomial = Polynomial([1])
last_known = Polynomial([1])
# generate the error locator polynomial
# - Berklekamp-Massey algorithm
for i in range(0, len(forney_syndromes)):
# d = S[k] + C[1]*S[k-1] + C[2]*S[k-2] + ... + C[l]*S[k-L]
# This is the discrepancy delta
delta = forney_syndromes[i]
for j in range(1, len(error_loc_polynomial)):
delta ^= self.GF.gfMul(error_loc_polynomial[-(j + 1)],
forney_syndromes[i - j])
# Calculate the next degree of the polynomial
last_known.append(0)
# If delta is not 0, correct for it
if delta != 0:
if len(last_known) > len(error_loc_polynomial):
new_polynomial = last_known.scale(delta)
last_known = error_loc_polynomial.scale(
self.GF.gfInv(delta))
error_loc_polynomial = new_polynomial
error_loc_polynomial += last_known.scale(delta)
error_loc_polynomial = error_loc_polynomial[::-1]
# Stop if too many errors
error_count = len(error_loc_polynomial) - 1
if error_count * 2 > len(forney_syndromes):
raise ReedSolomonError("Too many errors to correct")
# Find the zeros of the polynomial using Chien search
error_list = []
for i in range(self.GF.lowSize):
error_z = error_loc_polynomial.eval(self.GF.gfPow(2, i))
if error_z == 0:
error_list.append(length_message - i - 1)
# Sanity checking
if len(error_list) != error_count:
raise ReedSolomonError("Too many errors to correct")
else:
return error_list
def findErrors(self, forney_syndromes: Polynomial, length_message: int) -> list:
"""
BM算法和Chien钱搜索找到0的错误定位多项式
:param forney_syndromes: 表示forney伴随式的多项式
:param length_message: 信息长度和校验位长度之和
:return: 错误定位多项式
"""
error_loc_polynomial = Polynomial([1])
last_known = Polynomial([1])
# 生成错误定位多项式
# BM算法
for i in range(0, len(forney_syndromes)):
# d = S[k] + C[1]*S[k-1] + C[2]*S[k-2] + ... + C[l]*S[k-L]
# 偏差delta
delta = forney_syndromes[i]
for j in range(1, len(error_loc_polynomial)):
delta ^= self.GF.gfMul(error_loc_polynomial[-(j+1)], forney_syndromes[i - j])
# 计算多项式次幂
last_known.append(0)
# 如果偏差delta不为0 改正
if delta != 0:
if len(last_known) > len(error_loc_polynomial):
new_polynomial = last_known.scale(delta)
last_known = error_loc_polynomial.scale(self.GF.gfInv(delta))
error_loc_polynomial = new_polynomial
error_loc_polynomial += last_known.scale(delta)
error_loc_polynomial = error_loc_polynomial[::-1]
# 如果错误太多 停止
error_count = len(error_loc_polynomial) - 1
if error_count * 2 > len(forney_syndromes):
raise ReedSolomonError("Too many errors to correct")
# 用钱（Chien）搜索找到多项式的零点
error_list = []
for i in range(self.GF.lowSize):
error_z = error_loc_polynomial.eval(self.GF.gfPow(2, i))
if error_z == 0:
error_list.append(length_message - i - 1)
# 完整性检查
if len(error_list) != error_count:
raise ReedSolomonError("Too many errors to correct")
else:
return error_list
def interpolateLagrange(points): runningSum = Polynomial([0.0]) for j in range(len(points)): runningProduct = Polynomial([1]) for k in range(len(points)): if k != j: scale = points[j][0] - points[k][0] runningProduct *= Polynomial([-points[k][0]/scale, 1/scale]) runningSum += runningProduct.scale(points[j][1]) return runningSum
def interpolateLagrange(points):
runningSum = Polynomial([0.0])
for j in range(len(points)):
runningProduct = Polynomial([1])
for k in range(len(points)):
if k != j:
scale = points[j][0] - points[k][0]
runningProduct *= Polynomial(
[-points[k][0] / scale, 1 / scale])
runningSum += runningProduct.scale(points[j][1])
return runningSum
