基于软判决下的校验关系的循环码参数盲识别

Soft-decision Based Blind Identification of Cyclic Code Parameters with Parity-check Relation

  • 摘要: 针对目前循环码参数盲识别算法存在的容错性差以及识别循环码码型不全的问题,提出一种基于软判决下循环码校验关系进行参数识别的算法。首先根据循环码码字向量与其校验矩阵的乘积为零向量的校验关系,得到码字与校验多项式反多项式的倍式相乘的校验关系表达式;将所有可能包含校验多项式的多项式分别代入,以截获的软判决信息来近似代替对数似然比,以简化计算,并以计算出的总的对数似然符合度值来表征代入表达式中的多项式是否包含校验多项式;然后将校验多项式与码长n对应的多项式xn-1的关系分三种情况,得到这三种情况下校验关系的对数似然符合度在各码长或码长因数倍数下的变化规律;最后根据正确参数和错误参数下对数似然符合度的区别识别出循环码各参数。理论推导及实验仿真均证明了算法的有效性,对于各码长下不同生成多项式的循环码,算法均能在一定的信噪比及一定的码字截获量下对其码长、同步起点以及生成多项式进行正确识别,跟现有算法相比,识别性能有一定提升,且克服了部分算法仅能识别部分类型循环码的问题。对于长码(63,51)循环码,算法在信噪比为1.75 dB时对循环码码长和同步起点的正确识别率在99%以上,在信噪比为2.75 dB时对生成多项式的正确识别率在99%以上。

     

    Abstract: ‍ ‍In order to overcome the problem of poor fault-tolerance and incomplete code type in blind identification of cyclic codes, a new parameter identification algorithm based on the check relation of cyclic code under soft-decision is proposed. Firstly, according to the check relation that the product of the cyclic code word vector and its check matrix is zero vector, the expression of check relation between cyclic code and multiple of check polynomial’s inverse polynomial is obtained. Substituting all polynomials that may contain check polynomials into the expression respectively, and the intercepted soft decision information approximately replaces the log likelihood ratio to simplify the calculation, and the calculated total log likelihood compliance value is used to indicate whether the polynomial substituted into the expression contains check polynomials. Then, according to the three possible relations between the check polynomial and the polynomial xn-1 corresponding to the code length, the law of the log likelihood coincidence of the check relation under each multiple of code length or code length factor is obtained. Finally, the cyclic code parameters are identified according to the difference of logarithmic likelihood coincidence degree between the correct parameters and the wrong parameters. Theoretical derivation and experimental simulation have proved the effectiveness of the algorithm. For cyclic codes with different generated polynomials under different code lengths, the algorithm can correctly identify their code lengths, synchronization starting points and generated polynomials under a certain SNR and a certain amount of code word interception. Compared with existing algorithms, the recognition performance is improved to some extent, and the problem that some algorithms can only identify some types of cyclic codes is overcome. For (63,51) cyclic codes, the correct recognition rate of cyclic code length and synchronization is 100% when the SNR is 1.75 dB, and the correct recognition rate of generating polynomial is 100% when the SNR is 2.75 dB.

     

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