Uncoded placement optimization for coded delivery

Abstract

Existing coded caching schemes fail to simultaneously achieve efficient content placement for non-uniform file popularity and efficient content delivery in the presence of common requests, and hence may not achieve desirable average load under a non-uniform, possibly very skewed, popularity distribution. In addition, existing coded caching schemes usually require the splitting of a file into a large number of subfiles, i.e., high subpacketization, and hence may cause huge implementation complexity. To address the above two challenges, we first present a class of centralized coded caching schemes consisting of a general content placement strategy specified by a file partition parameter, enabling efficient and flexible content placement, and a specific content delivery strategy, enabling load reduction by exploiting common requests of different users. Then we consider two cases, namely, the case without considering the subpacketization issue and the case considering the subpacke-tization issue. In the first case, we formulate the coded caching optimization problem over the considered class of schemes with N2K variables to minimize the average load under an arbitrary file popularity. Imposing some conditions on the file partition parameter, we transform the original optimization problem into a linear optimization problem with N(K + 1) variables under an arbitrary file popularity and a linear optimization problem with K +1 variables under the uniform file popularity. We also show that Yu et al.'s centralized coded caching scheme corresponds to an optimal solution of our problem. In the second case, taking into account the subpacketization issue, we first formulate the coded caching optimization problem over the considered class of schemes to minimize the average load under an arbitrary file popularity subject to a subpacketization constraint involving the ℓ0-norm. By imposing the same conditions and using an exact DC (difference of two convex functions) reformulation method, we convert the original problem with N2K variables into a simplified DC problem with N(K + 1) variables. Then, we use a DC algorithm to solve the simplified DC problem.