Generalised array low‐density parity‐check codes

In this study, using Group Permutation Low‐Density Parity‐Check (GP‐LDPC) codes, the authors generalise the concept of array Low‐Density Parity‐Check (LDPC) codes from fields of prime order to those of prime power order. In fact, they consider the additive group of the finite field GF(q), q a prime power, as the underlying group for the GP‐LDPC code construction and since when q is a prime, the author's code construction method coincides with that of quasi‐cyclic array LDPC codes, they call their codes, generalised array LDPC (GA‐LDPC) codes. First, they prove that, like array LDPC codes, GA‐LDPC codes are quasi‐cyclic codes. Then, they analyse the girth of GA‐LDPC codes in a way similar to that for array LDPC codes and introduce some shortened GA‐LDPC codes with girths 8, 10 and 12. For many values of g, J and L, the lengths of (J, L)‐regular shortened GA‐LDPC codes of girth g and rate at least 1 − J/L, constructed in this study, are smaller than the lengths of (J, L)‐regular LDPC codes of girth g and rate at least 1 − J/L, constructed in the literature. Also, simulation results show that GA‐LDPC codes perform well with the iterative message‐passing decoding.