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The Rate-Distortion Function of a Poisson Process with a Queueing Distortion Measure

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The Rate-Distortion Function of a Poisson Process with a Queueing Distortion Measure
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" [1] coding problem. Our proof of the converse utilizes McFadden's point process entropy formulation [2] 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 [3], [4] to prove achievability.
Todd P. Coleman, Negar Kiyavash, Vijay G. Subraman
Added 25 Dec 2009
Updated 25 Dec 2009
Type Conference
Year 2008
Where DCC
Authors Todd P. Coleman, Negar Kiyavash, Vijay G. Subramanian
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