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, 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 from first principles and 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=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 of q-ary channels.