A Fresh Look at Coding for q-ary Symmetric Channels
Abstract
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=2m, 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=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.