Caching (Bivariate) Gaussians

Caching is a technique that alleviates networks during peak hours by transmitting partial information before a request for any is made. In a lossy setting of Gaussian databases, we study a single-user model in which good caching strategies minimize the data still needed on average once the user requests a file. The encoder decides on a caching strategy by weighing the benefit from two key parameters: the prior preference for a file and the correlation among the files. Considering uniform prior preference but correlated files, caching becomes an application of Wyner's common information and Watanabe's total correlation. We show this case triggers a split: caching Gaussian sources is a non-convex optimization problem unless one spends enough rate to cache all the common information between files. Combining both correlation and user preference we explicitly characterize the full trade-off when the encoder uses Gaussian codebooks in a database of two files: we show that as the size of the cache increases, the encoder should change strategy and increasingly prioritize user preference over correlation. In this specific case we also address the loss in performance incurred if the encoder has no knowledge of the user's preference and show that this loss is bounded.