Structured low-density parity-check codes

This article describes the different methods to design regular low density parity-check (LDPC) codes with large girth. In graph terms, this corresponds to designing bipartite undirected regular graphs with large girth. Large girth speeds the convergence of iterative decoding and improves the performance at least in the high SNR range, by slowing down the onsetting of the error floor. We reviewed several existing constructions from exhaustive search to highly structured designs based on Euclidean and projective finite geometries and combinatorial designs. We describe GB and TS LDPC codes and compared the BER performance with large girth to the BER performance of random codes. These studies confirm that in the high SNR regime these codes with high girth exhibit better BER performance. The regularity of the codes provides additional advantages that we did not explore in this article like the simplicity of their hardware implementation and fast encoding.