On typical encodings of multivariate ergodic sources

06/06/2019

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by   Michal Kupsa, et al.

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We show that the typical coordinate-wise encoding of multivariate ergodic source changes the entropy profile of the source into the entropy profile that is arbitrarily close to the convolution of the original profile and a modular polymatroid that is determined by the cardinalities of the output alphabets. We show that the proportion of the exceptional encodings that are not close to the convolution goes to zero doubly exponentially. The result holds even for a larger class of multivariate sources that satisfy asymptotic equipartition property described via the mean fluctuation of the information functions. We also proved that the asymptotic equipartition property holds then for the output variables.