Decoding LDPC Codes Over Integer Residue Rings

This correspondence presents a multistage decoding approach for a free Zopf_q-submodule of Zopf_q ^N of rank K defined by a sparse (N-K)timesN parity-check matrix overZopf _q where q=p^m, p=2 and m>1. The proposed method involves the repeated application of belief propagation decoding to exploit the natural ring epimorphism Zopf_qrarrZopf_p ^l:r|rarr Sigma _i=0 ^l-1r⁽ⁱ⁾pⁱ with kernel p ^lZopf_q for each l, 1lesllesm, where Sigma _i=0 ^m-1r⁽ⁱ⁾pⁱ is the p-adic expansion of r. Computer simulations for codes of rate half and moderate length on an additive white Gaussian noise (AWGN) channel with various modulation schemes show that such a decoding strategy offers an additional coding gain of between 0.07-0.1 dB over a single-stage decoding approach