On the Gilbert-Varshamov distance of abelian group codes
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.
