An Efficient Joint Channel-Network Decoder for Multiuser Diversity Network Codes With LDPC Coding

Abstract

Diversity network codes (DNCs) were recently proposed for multiuser cooperative networks, where nonbinary network codes are superimposed over channel codes to yield high diversity gains. In this letter, we present a joint iterative channel-network decoder for use at the base station in a system employing a DNC. The scheme is based on hybrid soft/hard message passing between constituent low-complexity low-density parity-check (LDPC) decoders. It is shown that the formation of the extrinsic log-likelihood ratios to be passed between the LDPC decoders has a low-complexity implementation involving a set of permutation operations together with the well-known Jacobian logarithm. The proposed joint channel-network decoder has a significantly reduced complexity compared with the decoding structure originally presented for maximum-diversity-achieving DNCs, and achieves significant coding gain as well as full diversity gain.