低信噪比下循环码识别

Blind Recognition of Cyclic Codes at Low SNR

针对硬判决分析方法存在计算复杂度高且容错性差的缺点,本文提出了一种直接利用软判决序列完成循环码识别的新算法.首先从编码代数结构出发,推导出循环码生成多项式因子对应的对偶空间与码字能构成校验关系这一结论;其次基于该结论,遍历码长可能值,在GF(2)上,将多项式x n+1分解为不可约因子及其对应幂次的乘积,当所遍历因子的对偶空间正好与码字序列构成校验关系时,即可识别出循环码码长;最后遍历构成校验关系因子的幂次,最终完成生成多项式的识别.为利用软判决序列完成校验关系检测,引入了平均校验符合度概念,基于其统计特性和最小错误判决准则,实现了生成多项式不可约因子以及幂次的快速识别.仿真结果表明,推导的符合度统计特性与实际情况相吻合,同时算法具有较好的低信噪比容错性能,在3dB的噪声环境下,码长以及生成多项式识别率能够达到95%以上,与硬判决方法相比,在增加较小的计算复杂度下,识别性能提升将近1dB.在智能通信或是认知无线电领域具有较好的应用前景.

In order to overcome the shortcomings as high computational complexity and low fault tolerance in recognition of cyclic code by the hard-dicision algorithms,a algorithm based on soft-decision is proposed.Firstly,based on the structure of coding algebra,it is deduced that the dual space corresponding to the polynomial factor are orthogonal to the codeword space.Secondly,based on the deduced conclusion,the possible length of code is traversed,then the polynomial x n+1 is decomposed into the product of irreducible factors and their powers,when the dual space of the traversing factor coincides with the parity-check of the code word sequence,the length can be recognized.Finally,by traversing the polynomial factors and the corresponding power,the generated polynomial can be identified.In addition,the concept of average checking conformity is introduced in parity-check matching.Based on its statistical property and minimum error decision criterion,the fast identification of generating polynomial factor and power is completed.The simulation results show that the derived statistical property are consistent with the actual situation,and at the same time,the proposed algorithm has better performance in low SNR,which can achieve over 95%of correct recognition rate in 3dB noise environment.Compared with the existing methods,although it increases the computational complexity slightly,its performance improved by nearly 1dB.It has a good application prospect in intelligent communication or cognitive radio.