Relaxed Wynerxe2x80x99s Common Information In the problem of coded caching for media delivery, two separate coding opportunities have been identified. The first opportunity is a multiuser advantage and crucially hinges on a public broadcast link in the delivery phase. This has been explored in a plethora of works. The second opportunity has received far less attention and concerns similarities between files in the database. Here, the paradigm is to cache xe2x80x9cthe similarityxe2x80x9d between the files. Upon the request, the encoder refines this by providing the specific details for the requested files. Extending Gray and Wynerxe2x80x99s work (1974), it follows that the right measure of file similarity is Wynerxe2x80x99s Common Information and its generalizations. The present paper surveys and extends the role of Wynerxe2x80x99s Common Information in caching. As a novel result, explicit solutions are found for the Gaussian case under meansquared error, both for the caching problem as well as for the network considered by Gray and Wyner. Our solution leverages and extends the recent technique of factorization of convex envelopes.

On the Fundamental Limit of Coded Caching Systems with a Single Demand Type Caching is a technique to reduce the communication load in peak hours by prefetching contents during offpeak hours. Recently MaddahAli and Niesen introduced an information theoretic framework for coded caching, and showed that significant improvement can be obtained compared to uncoded caching. Considerable efforts have been devoted to identify the precise information theoretic fundamental limit of such systems, however the difficulty of this task has also become clear. One of the reasons for this difficulty is that the original coded caching setting allows multiple demand types during delivery, which in fact introduces tension in the coding strategy to accommodate all of them. In this paper, we seek to develop a better understanding of the fundamental limit of coded caching by investigating single demand type systems. We first show that in the canonical threeuser threefile systems, such single demand type systems already provide important insights. Motivated by these findings, we focus on systems where the number of users and the number of files are the same, and the demand type is when all files are being requested. A novel coding scheme is proposed, which provides several optimal memorytransmission operating points. Outer bounds for this class of systems are also considered, and their relation with existing bounds is discussed.