Construction of Markov Partitions in PL1D Maps

A method is described for the construction of parameters´ subspaces where Markov partitions can be found. The method is illustrated on the three-region piecewise linear 1-D (3PL1D) map, which is a popular approach for the chaos-based random number generator (RNG). For Markov partitions, the 3PL1D chaotic maps behave as Markov sources, and analytical calculation of its information entropy is possible, as demonstrated in this brief. From the knowledge of the stochastic transition matrix of the Markov source, one can exactly measure the appropriateness of the RNG in a given area. For classical RNGs, one typically relies on statistical tests as a quality indicator. Mathematical calculation of the quality of an RNG based on the 3PL1D chaotic maps makes the statistical tests useful only in the postimplementation phase as a verification of the hardware implementation.