Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels
Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity- achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is sho