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The Infinite-Message Limit of Two-Terminal Interactive Source Coding

机译：两终端交互式源编码的无穷大

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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 distribution 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. The new convex-geometric characterization is used to develop an iterative algorithm for evaluating any finite-message sum-rate-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. It is shown that a single backward message of arbitrarily small rate can lead to an arbitrarily large gain in the sum-rate.
机译：在分布式块源编码理论的框架内研究了带有交替消息的两终端交互函数计算问题。对于任何有限数量的消息，以前的工作中都使用标准的信息理论技术来确定总和率失真函数的单字母特征。但是，这不能提供令人满意的无穷大消息限度，这是用于分布式块源编码中渐进分析的一种新的，尚未探索的维度，涉及可能无限数量的无穷小速率消息。在本文中，无穷大消息和率失真函数被视为联合源分布和失真级别的函数，其特征是具有某些凸几何特性的部分有序函数族的最小元素。新的特征不涉及评估有限消息和率失真表达式的无限消息极限。这种表征导致无限消息和率失真表达式的下界族和测试任何可实现的无限消息和率失真表达式的最优性的简单准则。新的凸几何特征用于开发一种迭代算法，用于评估任何有限消息和率失真函数。它也可以用来构造第一个示例，以证明对于有损源的再现，两条消息可以严格改善1985年论文中未解决问题的单消息Wyner-Ziv率失真函数。结果表明，任意一个低速率的反向消息都可以导致总速率的任意大的增益。

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