A Fresh Look at Coding for q-ary Symmetric Channels

This paper studies coding schemes for the q-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet size q = 2, m ∈ N, thus complementing some recently proposed packet-based schemes requiring large q. 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 once from first principles and once using a factor-graph representation of a front-end that maps q-ary symbols to groups of m bits connected to a binary code. The front-end can be processed with a complexity that is linear in m = log 2 q. 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 of q-ary channels. Index Terms q-ary symmetric channel, low-density parity-check (LDPC) codes, decoder front-end.