Mixing properties of triangular feedback shift registers

t ) t 0 be a (memoryless) source, i.e. a sequence of identically distributed, independent random variables. Informally, a source is an object that emits symbols (in general from a finite alphabet) according to some random mechanism. This could be, for example, a physical random generator or in first-order approximation a natural alphabet-based (plain) text. The objective of this paper is to investigate the Markov behaviour of a class of feedback shift registers when the input symbols are modified by the random source. To model the influence of the random source we will assume that the underlying alphabet carries a group structure. We will show that for non-degenerate sources and non-singular triangular feedback shift registers, the associated Markov chains are rapidly mixing. We will also give estimates for mixing (convergence) rate using the Dobrushin coe cients of the associated stochastic matrices.