A Fresh Look at Coding for $q$-ary Symmetric Channels
Claudio Weidmann, Gottfried Lechner · IEEE Transactions on Information Theory · 2012
This paper studies coding schemes for theq-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet sizeq=2m,m∈N, thus complementing some recently proposed packet-based schemes requiring largeq. First, theoretical optimality of a simple layered scheme is shown; then, a practical coding scheme based on a simple modification of standard binary LDPC decoding is proposed. The decoder is derived from first principles and using a factor-graph representation of a front end that mapsq-ary symbols to groups ofmbits connected to a binary code. The front end can be processed with a complexity that is linear inm=log2q. An extrinsic information transfer chart analysis is carried out and used for code optimization. Finally, it is shown how the same decoder structure can also be applied to a larger class ofq-ary channels.