On the Encoding Capacity of Some Non-Abelian Group Codes

In this work we study group codes over non-Abelian groups which are extensions. Extension of groups is a general- ization of semi-direct product and direct product of groups. For channels having as its input alphabet a signal set, one-to-one matched to a non-Abelian group which is an extension, is given a definition of encoding capacity adapted from an existent one that covers the Abelian group case. By using this adapted definition, formulas to compute the encoding capacity of the channel, are derived. Two important examples of application are given.