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.

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Todd P. Coleman, Negar Kiyavash, Vijay G. Subramanian
• Keywords: Computer Graphics, DCC 2008, Distortion Measure, Rate Distortion Function, Squared-error Distortion Measure