Methodologies for designing LDPC codes using protographs and circulants

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.