# On Multiple Hypotheses LAO Testing by Informed Statistician for Arbitrarily Varying Markov Source and on Such Source Coding Reliability Function

## Abstract

In this paper the problem of multiple hypotheses testing for arbitrarily varying Markov source (AVMS) with state sequence known to the statistician is solved from the point of view of logarithmically asymptotically optimal (LAO) testing. The matrix

of asymptotic interdependencies of all possible pairs of the error probability exponents

(reliabilities) in optimal testing for this model is studied. The LAO test, assuming that exponents of some number of the error probabilities are given, ensure the best asymptotic exponents for the rest of them. We ¯nd LAO test and the corresponding

matrix of all error probability exponents. As an application to information theory, the E-optimal rate R(E) (the minimum rate R of the source sequences compression when the decoding error probability is less than exp{–NE}, E > 0) and the reliability function E(R) of AVMS coding are determined.

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*Mathematical Problems of Computer Science*,

*31*, 60–72. Retrieved from https://mpcs.sci.am/index.php/mpcs/article/view/392