An alternative proof of the rate-distortion function of poisson processes with a queueing distortion measure.
Coleman, Todd P. and Kiyavash, Negar and Subramanian, Vijay G. (2008) An alternative proof of the rate-distortion function of poisson processes with a queueing distortion measure. An Alternative Proof of the Rate-Distortion .
This paper presents a proof of the rate distortion function of a Poisson process with a queuing distortion measure that is in complete analogy with the proofs associated with the rate distortion functions of a Bernoulli source with Hamming distortion measure and a Gaussian source with squared-error distortion measure. Analogous to those problems, the distortion measure that we consider is related to the logarithm of the conditional distribution relating the input to the output of a well-known channel coding problem, specifically the Anantharam and Verdu “Bits through Queues”  coding problem. Our proof of the converse utilizes McFadden’s point process entropy formulation  and involves a number of mutual information inequalities, one of which exploits the maximum-entropy achieving property of the Poisson process. Our test channel uses Burke’s theorem ,  to prove achievability.
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