Uncoded Placement Optimization for Coded Delivery

Abstract

We consider the classical coded caching problem as defined by Maddah-Ali and Niesen, where a server with a library of N files of equal size is connected to K users via a shared error-free link.Each user is equipped with a cache with capacity of M files. The goal is to design a static content placement and delivery scheme such that the average load over the shared link is minimized. 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 level. 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. For the proposed class of schemes, we consider two cases for the optimization of the file partition parameter, depending on whether a large subpacketization level is allowed or not. In the case of an unrestricted subpacketization level, we formulate the coded caching optimization in order to minimize the average load under an arbitrary file popularity. A direct formulation of the problem involves N 2 K variables. By imposing some additional conditions, the problem is reduced to a linear program with N (K + 1) variables under an arbitrary file popularity and with K + 1 variables under the uniform file popularity. We can recover Yu et al.'s optimal scheme for the uniform file popularity as an optimal solution of our problem. When a low subpacketization level is desired, we introduce a subpacketization level constraint involving the ℓ 0 norm for each file. Again, by imposing the same additional conditions, we can simplify the problem to a difference of two convex functions (DC) problem with N (K + 1) variables that can be efficiently solved.

Memory-Rate Tradeoff for Caching with Uncoded Placement under Nonuniform Random Demands

“…Our approach is to first formulate the cache placement optimization problem for the MCCS to minimize the average rate. We restrict the cache placement to the class of popularity-first placements, which simplifies the optimization problem and has also been numerically shown to be optimal for the MCCS [32]. We then develop two information-theoretic lower bounds on the average rate for caching with uncoded placement, one for general cache placements and the other restricted to the popularity-first cache placements.…”

“…When heterogeneity exists in the system, the characterization of the memory-rate tradeoff is generally an open problem. For nonuniform file popularity, the cache placement problem was studied for the CCS [20]- [26], [30] and the MCCS [32] to minimize the achievable delivery rate. For the CCS, to simplify the placement problem amid nonuniformity, suboptimal file-grouping-based cache placement strategies were proposed in [20]- [23].…”

“…Only recently, for two files of nonuniform popularity, a coded caching scheme was proposed [31], which achieves the lower bound for caching with uncoded placement. For the MCCS, existing studies are scarce, and only [32] studied the cache placement optimization under nonuniform file popularity. In general, for files with nonuniform popularity and sizes, characterizing the memory-rate tradeoff for caching with uncoded placement is challenging.…”

“…In particular, the optimal cache placement structure has been entirely characterized in [26]. As the delivery strategy in the MCCS is more complicated than that in the CCS, the cache placement optimization for the MCCS was only studied in [32] through numerical methods. The optimal cache placement structure for the MCCS is still unknown.…”

“…The optimal cache placement structure for the MCCS is still unknown. Furthermore, in the existing coded caching schemes, since subfiles may be of different sizes, zero-padding is commonly used in the coded messages to simplify the delivery [24]- [26], [30], [32]. However, the impact of zeropadding on the coded delivery (for both the CCS and the MCCS) has, to our best knowledge, never been studied or known.…”