The Infinite-message Limit of Two-terminal Interactive Source Coding

Nan Ma; Prakash Ishwar

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arXiv · 0908.3512

The Infinite-message Limit of Two-terminal Interactive Source Coding

Nan Ma·Prakash Ishwar

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Abstract

A two-terminal interactive function computation problem with alternating messages is studied within the framework of distributed block source coding theory. For any finite number of messages, a single-letter characterization of the sum-rate-distortion function was established in previous works using standard information-theoretic techniques. This, however, does not provide a satisfactory characterization of the infinite-message limit, which is a new, unexplored dimension for asymptotic-analysis in distributed block source coding involving potentially an infinite number of infinitesimal-rate messages. In this paper, the infinite-message sum-rate-distortion function, viewed as a functional of the joint source pmf and the distortion levels, is characterized as the least element of a partially ordered family of functionals having certain convex-geometric properties. The new characterization does not involve evaluating the infinite-message limit of a finite-message sum-rate-distortion expression. This characterization leads to a family of lower bounds for the infinite-message sum-rate-distortion expression and a simple criterion to test the optimality of any achievable infinite-message sum-rate-distortion expression. For computing the amplewise Boolean AND function, the infinite-message minimum sum-rates are characterized in closed analytic form. These sum-rates are shown to be achievable using infinitely many infinitesimal-rate messages. The new convex-geometric characterization is used to develop an iterative algorithm for evaluating any finite-message sumrate-distortion function. It is also used to construct the first examples which demonstrate that for lossy source reproduction, two messages can strictly improve the one-message Wyner-Ziv rate-distortion function settling an unresolved question from a 1985 paper.

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Nan Ma, Prakash Ishwar. 2009-08-25. The Infinite-message Limit of Two-terminal Interactive Source Coding. https://arxiv.org/abs/0908.3512

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