Construction of LDPC Codes Using Cole's Modified Importance Sampling Method

Abstract

Purpose of research is a modification of Cole's importance sampling method for finding trapping sets in an LDPC code to speed up their search.Methods. Cole proposed a method for searching for trapping sets in an LDPC code by using a Monte Carlo method that causes the decoding algorithm to fail at nodes potentially contained in trapping sets. His method makes it possible to accelerate the study of the efficiency of medium-length LDPC codes in the region of large SNRs. The modified method uses the properties of automorphisms of Tanner graphs, which make it possible to exclude a significant number of symbolic nodes from the enumeration. The modified method also provides for an ordered enumeration over subgraphs containing cycles.Results. The proposed method made it possible to speed up the search for trapping sets in Mackay's PEG(1008, 504) LDPC code by 5027 times compared to the Velasquez-Subramani method, and 43 times faster compared to the original Cole method. In the case of (2640, 1320) LDPC Margulis code, the proposed method is 28 times faster than the Velasquez-Subramani quasi-cyclic method and 134 times faster than the original Cole method.Conclusion. The result of experimental studies showed the possibility of using the developed method to improve the connectivity spectrum, increase the code distance of QC-LDPC codes. This made it possible to reduce the probability of a bit error at the decoder output by orders of magnitude at high signal-to-noise ratios in the AWGN channel.