Low density parity check lattices based on construction D' and cycle-free Tanner graphs.

Mohammad Ali Sadeghi, Daniel Panario

Fengfan Yang

The linear block code is called a binary Low-Density Parity-Check code if whose parity-check matrix is a sparse matrix. For the features of parity-check matrix, a LDPC code can be illustrated by a Tanner graph. Cycles, especially short cycles in the Tanner graph, lead to inefficient decoding and prevent the decoding algorithm from converging to the optimal decoding result. In this paper, a simple algorithm of constructing four-cycle-free regular A(n,d_v,d_c)LDPC codes, d_v3, is introduced. And we analyse the relationship between the performance and the cycle.

Mohammad-Reza Rafsanjani-Sadeghi

Wittawat Kositwattanarerk

Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check (LDPC) codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.

李铁楠, 单秀玲

Bahram Honary, Shu Lin, E.M. Gabidulin +4 more