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

‍ ‍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 $x^n-\mathrm{1}$ 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.