The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching

Abstract

Abstract-We consider a basic cache network, in which a single server is connected to multiple users via a shared bottleneck link. The server has a database of files (content). Each user has an isolated memory that can be used to cache content in a prefetching phase. In a following delivery phase, each user requests a file from the database, and the server needs to deliver users' demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of the rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. In particular, we propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination.

An Index Coding Approach to Caching With Uncoded Cache Placement

“…Our novel IC bound achieves our novel converse A generalized version of the scheme in [13] from the viewpoint of index coding knowledge, the best random coding achievable bound for the general IC problem to date. We then show that our novel IC scheme matches our converse bound for centralized cache-aided systems with uncoded cache placement when there are less files than users, and attains the same load as the scheme in [26].…”

“…In [1], Maddah-Ali and Niesen analytically showed that the load of their proposed scheme is to within a factor of 12 of a cut-set-type converse bound, but it was noted in [11] that it numerically appeared to be optimal to within a factor 4.7. The scheme in [1] has been improved in many ways; examples of schemes with uncoded cache placement are [4], [5], [12], [13], while with coded cache placement are [14]- [18].…”

“…The exact memory-load tradeoff for cache-aided systems under the constraint of uncoded cache placement was characterized in [13]. The converse bound in [13] is derived by a genie-based idea (instead of directly leveraging the acyclic IC converse bound as we did in [4], [5]), which is equivalent to our approach here -see the first remark Section III-D. The genie-based idea was also extended to the case of average load (as opposed to worst case load) with uniform independent and identically distributed demands.…”

“…Optimality for uncoded cache placement: By enhancing the cut-set-type converse bound by an additional non-negative term, the achievable load in [1] and its enhanced version in [13] were proved to be optimal to within a factor 2 [26]. This is, to the best of our knowledge, the sharpest known multiplicative gap, and implies that coded cache placement can at most half the network load compared to the results presented in [4] (and in this paper) and in [13].…”

“…In Section IV, we propose an IC achievable bound based on Han's coding scheme [29], Slepian-Wolf coding [30] and non-unique decoding [31]. This achievable scheme is shown to strictly outperform the composite (index) coding scheme, and is, to the best our [4], [5], and later in [13]…”