A class of quasi-cyclic LDPC codes over GF(2m)

Low Density Parity Check (LDPC) codes over GF(2^m,)are an extension of binary LDPC codes. Performances of GF(2^m,) LDPC codes have been shown to be higher than binary LDPC codes, but the complexity of the encoders/decoders increases. Hence there is a substantial lack of implementations for LDPC codes over GF(2^m,)codes. This paper presents a class of quasi-cyclic LDPC codes over GF(2^m,). These codes can alleviate the encoding/decoding complexity without excessive loss of performances. It is shown how, from a performance point of view, such codes are better than m times bigger binary codes and as good as (2^m,)longer binary codes.