Chaos 2006 Mar;16(1):013103
Nonlinear Dynamics and Chaos Group, Departamento de Matemáticas y Física Aplicadas y Ciencias de la Naturaleza, Universidad Rey Juan Carlos, C/ Tulipán, s/n, 28933 Móstoles, Madrid, Spain.
In this paper we address the design of channel encoding algorithms using one-dimensional nonlinear chaotic maps starting from the desired invariant probability density function (pdf) of the data sent to the channel. We show that, with some simple changes, it is straightforward to make use of a known encoding framework based upon the Bernoulli shift map and adapt it readily to carry the information bit sequence produced by a binary source in a practical way. On the decoder side, we introduce four already known decoding algorithms and compare the resulting performance of the corresponding transmitters. The performance in terms of the bit error rate shows that the most important design clue is related not only to the pdf of the data produced by the chosen discrete map: the own dynamics of the maps is also of the highest importance and has to be taken into account when designing the whole transmitting and receiving system. We also show that a good performance in such systems needs the extensive use of all the evidence stored in the whole chaotic sequence.