Methods of Searching for Trapping Sets of Quasi-Cyclic LDPC Codes and their Applications in Code Construction

Abstract

We present a methodology to search for harmful subgraphs in the Tanner graph of a regular column-weightthree low-density parity-check (LDPC) code. These harmful subgraphs, which are more commonly known under the name "trapping sets," cause a degradation in the error correcting performance of LDPC codes in the high signal-to-noise ratio (SNR) region. Our method of searching for trapping sets utilizes the Trapping Set Ontology, a database in which trapping sets are arranged according to their topological relationships. Based on the topological relationships, larger trapping sets are searched for by expanding smaller ones. This reduces the complexity and the run-times of the search algorithms and allows large trapping sets to be searched for efficiently. Besides, if the LDPC code is quasi-cyclic then our search algorithms can be futher simplified. Our method of searching for trapping sets is useful in the performance analysis of LDPC codes and in the construction of good LDPC codes. In this paper, we demonstrate the use of the method in the construction of good LDPC codes.