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In order to reconstruct the sparse check matrix of LDPC, a new algorithm which could directly reconstruct the LDPC was proposed.Firstly, according to the principle of the traditional reconstruction algorithm, the defects of the traditional algorithm and the reasons for the defects were analyzed in detail.Secondly, based on the characteristics of sparse matrix, some bit sequences in code words were randomly extracted for Gaussian elimination.At the same time, in order to reliably realize that the extracted bits sequence could contain parity check nodes, the multiple random variables were determined based on the probability of containing check nodes in one extraction.Finally, the statistical characteristics of LDPC under the suspected check vector was analyzed.Based on the minimum error decision rule, the sparse check vector was determined.The simulation results show that the rate of reconstruction of most LDPC in IEEE 802.11 protocol can reach more than 95% at BER of 0.001, and the noise robustness of the proposed method is better than that of the traditional algorithm.At the same time, the new algorithm not only does not need sparseness of parity check matrix, but also has the good performance for both diagonal and non-diagonal check matrix.

In order to solve the problem of the blind recognition of polar codes, the theorem 1 and theorem 2 were proved firstly, which reflects the relationship between length and rate of actual polar codes, and then theorem 3 which could distinguish frozen bit and information bit positions was also proved.Based on these three theorems, the codewords matrixes and Kronecker matrixes were constructed by traversing the possible code length values.Then the information bits were traversed to detect the check relationship between the codewords and the suspected dual space.In order to detect the check relationship, log likelihood ratio was introduced, based on its characteristics and optimal criteria, the code rate and information bit positions were estimated.The simulation results show that the conclusions of the three theorems are consistent with the results.At the same time, the proposed algorithm has a strong error tolerance.Under 6.5 dB and code length of 1024, the rate of recognition can reach more than 98%.

In order to overcome the poor performance of existing algorithms for recognition of BCH code in low signal-to-noise ratio (SNR),a recognition algorithm based on average cosine conformity was proposed.Firstly,by traversing the possible values of code length and m-level primitive polynomial fields,the code length was identified by matching the initial code roots.Secondly,on the premise of recognizing the code length,the GF(2m) domain was traversed under the m-level primitive polynomial and the primitive polynomial with the strongest error-correcting ability was the generator polynomial for the domain.Finally,the minimum common multiple corresponding to the minimum polynomial of code roots was obtained,and the BCH code generator polynomial was recognized.In checking matching,the statistic of average cosine conformity was introduced.The optimal threshold was solved based on the minimum error decision criterion and distribution of the statistic to realize the fast identification of the BCH.The simulation results show that the deduced statistical characteristics are consistent with the actual situation,and the proposed algorithm can achieve reliable recognition under SNR of 5 dB and code length of 511.Comparing with existing algorithms,the performance of the proposed algorithm is better than that of the existing soft-decision algorithm and 1~3.5 dB better than that of the hard-decision algorithms.

A new algorithm based on logarithmic conformity was proposed.Firstly,based on the probability of total RSC coding equation,the concept of logarithmic coincidence degree,which could measure the establishment of coding equation,was introduced.Then because of constraint length of RSC,the polynomial database could be generated,and then logarithmic conformity of every polynomial could be calculated when traversing the database.As the results,the RSC could be recognized,because the correct polynomial could make the conformity maximum.The algorithm has small amount of calculation because of finite traversal,which was only related to amount of intercepted data,besides,this algorithm has good error tolerance by soft decisions.The simulation results show that the correct ratio of recognition can reach 90% at SNR of 0 dB and its performances are obviously superior to those of existing algorithms.