Characterization of linear block codes as cyclic sources with memory

Considering the input data generated by a binary Markov source X, linear, binary, block codes are characterized as cyclic sources with memory. The encoding graph for systematic linear block codes is determined. It is shown the encoded data are the output of a binary, cyclic source with memory. The states of this source Y are organized in n classes of states, where n is the length of the code words. The matrix P_Y of transition probabilities between states is derived, as well as the matrix π_y containing the states probabilities. Finally, the entropy H(Y) is computed and a relationship between H(Y) and H(X) is derived.