On the Gilbert-Varshamov distance of Abelian group codes
Giacomo Como, Fabio Fagnani · 2007
The problem of the minimum Bhattacharyya distance of group codes over symmetric channels is addressed. Ensembles of Zm-linear codes are introduced and their typical minimum distance characterized in terms of the Gilbert- Varshamov distances associated to the subgroups of Zm. For the AWGN channel with 8-PSK as input it is shown that the typical Z8-linear code achieves the Gilbert-Varshamov bound.