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.

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Abstract

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.

Item Type:	Article
Keywords:	Rate-distortion function; Poisson process; Queueing distortion measure; Bernoulli source; Gaussian source; Hamilton Institute;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	1669
Depositing User:	Hamilton Editor
Date Deposited:	17 Nov 2009 09:59
Journal or Publication Title:	An Alternative Proof of the Rate-Distortion
Publisher:	IEEE
Refereed:	Yes
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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