A Fresh Look at Coding for q-ary Symmetric Channels

Claudio Weidmann (1) , Gottfried Lechner (2)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
2 ITR - Institute for Telecommunications Research [Mawson Lakes]

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.

Mots clés: q-ary symmetric channel; low-density parity-check (LDPC) codes; decoder front-end

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Claudio Weidmann, Gottfried Lechner. A Fresh Look at Coding for q-ary Symmetric Channels. IEEE Transactions on Information Theory, 2012, 58 (11), pp.6959 - 6967. ⟨10.1109/TIT.2012.2208576⟩. ⟨hal-00749509⟩