Symmetric channels capacity computation by using groups and the Kullback-Leibler distance

In this work it is proposed a method to compute the capacity of channels with finite input alphabet. This method is based on the constancy of the Kullback-Leibler distances between the different conditional probability densities of the the output alphabet and the full densities of the output alphabet. After that, it is studied a general symmetric channels in terms of abstract groups and it is shown that the capacity of this kind of channels is achieved when its input random variable is uniform. Finally, it is made the analysis of the capacity of classical symmetric channels en terms of permutation and rotation groups.