  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
$q=2^m$, $m\in\mathbb{N}$, 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.
