One shot approach to lossy source coding under average distortion constraints

01/12/2020

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by   Nir Elkayam, et al.

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This paper present a one shot analysis of the lossy compression problem under average distortion constraints. We calculate the exact expected distortion of a random code. The result is given as an integral formula using a newly defined functional D̃(z,Q_Y) where Q_Y is the random coding distribution and z∈ [0,1]. When we plug in the code distribution as Q_Y, this functional produce the average distortion of the code, thus provide a converse result utilizing the same functional. Two alternative formulas are provided for D̃(z,Q_Y), the first involves a supremum over some auxiliary distribution Q_X which has resemblance to the channel coding meta-converse and the other involves an infimum over channels which resemble the well known Shannon distortion-rate function.