A Complete Sufficient Statistic for Finite-State Markov Processes with Application to Source Coding

Abstract-A complete sufficient statistic is presented in this paper for the class of all finite-state, finite-order stationary discrete Markov pro-cesses. This sufficient statistic is complete in the sense that it summarizes in entirety the whole of the relevant information supplied by any process sample. The sufficient statistic has application to source coding problems such as source matching and calculation of the rate distortion function. Index Terms-Complete sufficient statistic, markov chain, source cod-ing. I