Characterization of linear block codes as cyclic sources with memory

Gheorghe Zaharia (1) , Valeriu Munteanu (2) , Daniela Tarniceriu (2)

1 IETR - Institut d'Électronique et des Technologies du numéRique
2 Faculté d'Electronique, Télécommunications et de la Technologie de l'Information

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 proposed. 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 PY of transition probabilities between states is derived, as well as the matrix πy containing the states probabilities. Finally, the entropy H(Y) is computed and a relationship between H(Y) and H(X) is derived.

Gheorghe Zaharia, Valeriu Munteanu, Daniela Tarniceriu. Characterization of linear block codes as cyclic sources with memory. Signals, Circuits and Systems (ISSCS), 2011 10th International Symposium on, Jun 2011, Iasi, Romania. 4 p., ⟨10.1109/ISSCS.2011.5978762⟩. ⟨hal-00641363⟩