Optimized puncturing and shortening distributions for nonbinary LDPC codes over the binary erasure channel

This paper investigates optimal puncturing and shortening distributions for nonbinary LDPC codes over the binary erasure channel (BEC). The analysis is done by means of density evolution and optimal distributions are found with differential evolution. We show that puncturing or shortening entire variable nodes results in bad performance; instead, for best performance, puncturing and shortening distributions have to be designed carefully, where generally, most variable nodes are punctured/shortened only partially. Our results indicate that properly designed punctured and shortened nonbinary LDPC codes can maintain a very small gap to capacity through a wide range of rates.