def correct(self, message, syndrome_polynomial: Polynomial, errors: list) -> Polynomial: """ Using the calculated erasures and errors, recover the original message :param message: the transmitted message + parity bits :param syndrome_polynomial: the syndrome polynomial :param errors: a list of erasures + errors :return: the decoded and corrected message """ # Calculate error locator polynomial for both erasures and errors coefficient_pos = [len(message) - 1 - p for p in errors] error_locator = Polynomial.errorLocatorPolynomial(coefficient_pos) # Calculate the error evaluator polynomial error_eval = Polynomial.errorEvaluatorPolynomial( syndrome_polynomial[::-1], error_locator, len(error_locator)) # Calculate the error positions polynomial error_positions = [] for i in range(len(coefficient_pos)): x = self.GF.lowSize - coefficient_pos[i] error_positions.append(self.GF.gfPow(2, -x)) # This is the Forney algorithm error_magnitudes = Polynomial([0] * len(message)) for i, error in enumerate(error_positions): error_inv = self.GF.gfInv(error) # Formal derivative of the error locator polynomial error_loc_derivative_tmp = Polynomial([]) for j in range(len(error_positions)): if j != i: error_loc_derivative_tmp.append( 1 ^ self.GF.gfMul(error_inv, error_positions[j])) # Error locator derivative error_loc_derivative = 1 for coef in error_loc_derivative_tmp: error_loc_derivative = self.GF.gfMul(error_loc_derivative, coef) # Evaluate the error evaluation polynomial according to the inverse of the error y = error_eval.eval(error_inv) # Compute the magnitude of error magnitude = self.GF.gfDiv(y, error_loc_derivative) error_magnitudes[errors[i]] = magnitude # Correct the message using the error magnitudes message_polynomial = Polynomial(message) message_polynomial += error_magnitudes return message_polynomial
def correct(self, message, syndrome_polynomial: Polynomial, errors: list) -> Polynomial: """ 使用计算过的擦除和错误,恢复原始信息 :param message: 传输的信息+校验位 :param syndrome_polynomial: 伴随多项式 :param errors: 一个擦除+错误的列表 :return:解码并改正的信息 """ # 为擦除和错误计算错误定位多项式 coefficient_pos = [len(message) - 1 - p for p in errors] error_locator = Polynomial.errorLocatorPolynomial(coefficient_pos) # 计算误差评估多项式 error_eval = Polynomial.errorEvaluatorPolynomial(syndrome_polynomial[::-1], error_locator, len(error_locator)) # 计算误差位置多项式 error_positions = [] for i in range(len(coefficient_pos)): x = self.GF.lowSize - coefficient_pos[i] error_positions.append(self.GF.gfPow(2, -x)) # 这是福尼算法 error_magnitudes = Polynomial([0] * len(message)) for i, error in enumerate(error_positions): error_inv = self.GF.gfInv(error) # 错误定位多项式的形式导数(Formal derivative of the error locator polynomial) error_loc_derivative_tmp = Polynomial([]) for j in range(len(error_positions)): if j != i: error_loc_derivative_tmp.append(1 ^ self.GF.gfMul(error_inv, error_positions[j])) # 错误定位导数 Error locator derivative error_loc_derivative = 1 for coef in error_loc_derivative_tmp: error_loc_derivative = self.GF.gfMul(error_loc_derivative, coef) # 根据误差的倒数求出误差评价多项式 y = error_eval.eval(error_inv) # 计算误差的大小 magnitude = self.GF.gfDiv(y, error_loc_derivative) error_magnitudes[errors[i]] = magnitude # 使用错误大小纠正消息 message_polynomial = Polynomial(message) message_polynomial += error_magnitudes return message_polynomial