Decoding LDPC Codes Over Integer Residue Rings
M.A. Armand, Kian Siang Ng · IEEE Transactions on Information Theory · 2006
This correspondence presents a multistage decoding approach for a free Zopfq-submodule of ZopfqNof rank K defined by a sparse (N-K)timesN parity-check matrix overZopfqwhere q=pm, p=2 and m>1. The proposed method involves the repeated application of belief propagation decoding to exploit the natural ring epimorphism ZopfqrarrZopfpl:r|rarr Sigmai=0l-1r(i)piwith kernel plZopfqfor each l, 1lesllesm, where Sigmai=0m-1r(i)piis 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