Optimization of binary LDPC codes for the q-ary symmetric channel with moderate q

We study the optimization of binary LDPC codes for the q-ary symmetric channel with moderate alphabet sizes q. For q = 2^m, a coding scheme can be viewed as a front-end mapping q-ary symbols to groups of m bits connected to a binary code. We derive a factor graph representation of the front-end and show that it can be processed with a complexity linear in m, the number of bits per symbol. We perform an extrinsic information transfer chart analysis and use it for code optimization.