Methodologies for designing LDPC codes using protographs and circulants

Abstract

A method is presented for constructing LDPC codes with excellent performance, simple hardware implementation, low encoder complexity, and which can be concisely documented. The simple code structure is achieved by using a base graph, expanded with circulants. The base graph is chosen by computer search using simulated annealing, driven by density evolution's decoding threshold as determined by the reciprocal channel approximation. To build a full parity check matrix, each edge of the base graph is replaced by a circulant permutation, chosen to maximize loop length by using a Viterbi-like algorithm.