基于m序列三阶相关性的同步扰码反馈多项式重构

在已有的卷积码同步加扰的扰码反馈多项式重构方法中，卷积码对偶码字需要先验已知.为了解决该问题，本文基于m序列的三阶相关性，提出一种卷积码加扰的扰码反馈多项式重构新方法.首先对卷积码加扰序列进行分块处理，数据块的长度为卷积码编码约束长度，相邻数据块的起始位间隔一个码长；然后证明了加扰数据块与对偶码字相乘后，输出序列为与扰码周期相同的m序列，由此基于m序列的三阶相关峰值特性估计出对偶码字；最后利用三阶相关峰的位置信息重构出同步扰码反馈多项式.在有误码情况下，推导了峰值与非峰值位置处三阶相关函数值的概率分布，得到三阶相关峰的检测门限与重构结果正确的置信度.仿真实验验证了本文方法的有效性，与已有的重构方法相比，该方法无需先验已知对偶码字，消除了重构结果的不确定性，具有更好的容错性.

Reconstruction of Feedback Polynomial of Synchronous Scrambler Placed after Convolutional Encoder Based on Triple Correlation Property of m-Sequences

The existing methods need to know a priori dual word of a convolutional code to reconstruct the feedback polynomial of a synchronous scrambler placed after a convolutional encoder.To overcome this limitation,a novel reconstruction method is proposed based on the triple correlation property of m-sequences.First,the scrambled bit sequence is divided into multiple blocks.The length of each block equals the constraint length of the convolutional encoder,and the interval between two start points of adjacent blocks is the codeword length.Then,it is proved that the generated sequence by the dot product of scrambled bit blocks with a dual word is also an m-sequence,having the same period as the synchronous scrambler.With this result,a dual word of the convolutional encoder can be estimated based on the triple correlation property of m-sequences.Finally,the feedback polynomial is reconstructed by using two locations of triple correlation peaks.For the case that there are bit errors in the received sequence,the probability distributions of the peak and non-peak values of triple correlation are derived.Therefore,the threshold for detecting triple correlation peaks is obtained,and the confidence level of the correct reconstruction is analyzed.Simulation results show the effectiveness of the proposed method.Compared with the existing methods,the proposed method does not require the prior knowledge of a dual word and eliminates the uncertainty in the reconstruction results.Moreover,the proposed method is more robust to bit errors.