Information-Theoretic Caching: Sequential Coding for Computing

TL;DR

This paper models caching as a distributed source coding problem with side information, providing optimal rate regions and strategies, and compares this information-theoretic approach to existing caching models, revealing key differences.

Contribution

It introduces a novel information-theoretic framework for caching, deriving single-letter characterizations and closed-form solutions for key cases, and compares it with existing models.

Findings

Optimal rate region for single-user caching established

Closed-form solutions for special cases including uniform requests

Differences between the new model and Maddah-Ali and Niesen's model demonstrated

Abstract

Under the paradigm of caching, partial data is delivered before the actual requests of users are known. In this paper, this problem is modeled as a canonical distributed source coding problem with side information, where the side information represents the users' requests. For the single-user case, a single-letter characterization of the optimal rate region is established, and for several important special cases, closed-form solutions are given, including the scenario of uniformly distributed user requests. In this case, it is shown that the optimal caching strategy is closely related to total correlation and Wyner's common information. Using the insight gained from the single-user case, three two-user scenarios admitting single-letter characterization are considered, which draw connections to existing source coding problems in the literature: the Gray--Wyner system and distributed successive refinement. Finally, the model studied by Maddah-Ali and Niesen is rephrased to make a comparison with the considered information-theoretic model. Although the two caching models have a similar behavior for the single-user case, it is shown through a two-user example that the two caching models behave differently in general.