Improved Trellis-Based Algorithm for Locating and Breaking Cycles in Bipartite Graphs with Applications to LDPC Codes

LDPC codes are typically decoded using belief propagation decoding algorithms applied to their Tanner graphs. Cycles of short lengths in these graphs, which are bipartite graphs representing parity-check equations of the codes, can negatively impact the performance of the decoder. In this paper, a trellis-based algorithm is presented to locate cycles in bipartite graphs. This algorithm is an improvement in complexity and run-time over the one developed by Lan et al. in 2004. When applied to Tanner graphs of quasi-cyclic LDPC codes, the newly proposed algorithm can exploit the structure of their parity-check matrices to cut the complexity further. Locating cycles in the Tanner graphs of codes allows for eliminating them to increase the girth and thus improve performance.