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
=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.