Capacidade de canais simétricos possuindo grupos cíclicos como alfabeto de entrada

The channel capacity independent from any internal structure of the channel input alphabet X. Also, the noisy channel coding theorem do not depend from any internal structure of X. However, all the major linear encoding schemes require that X must have some kind of algebraic structure that can be a field or else a ring. This algebraic structure of X is induced from the alphabet of information source U by the encoding mapping. In this work we study the case U = Zpr , where Zpr = {0,1,2,...,pr − 1} is a cyclic group with p prime, and consider CU := “channel capacity with U as input alphabet”. By the data processing theorem, we know that CU ≤C, but for the case U =Zpr we show that the coding reach the channel capacity, that is, CU = C.