On Coded Caching with Correlated Files

Abstract

This paper studies the fundamental limits of the shared-link caching problem with correlated files, where a server with a library of N files communicates with K users who can store M files. Given an integer r ∈ [N], correlation is modelled as follows: each r−subset of files contains a common block. The tradeoff between the cache size and the average transmitted load is considered. We first propose a converse bound under the constraint of uncoded cache placement (i.e., each user directly caches a subset of the library bits). We then propose an interference alignment scheme for the cases where users have different requests. The proposed scheme achieves the optimal average load under uncoded cache placement when users demand distinct files. In addition, an extension of the proposed scheme achieves an optimal average load among all possible demands (i.e., not necessarily distinct demands) for KrM ≤ 2N or KrM ≥ (K − 1)N or r ∈ {1, 2, N − 1, N}. As a by-product, we show that the proposed scheme reduces the load of existing schemes for the caching problem with multi-requests.T ⊆{du 1 ,...,du j }:|T |=2

Demand-Private Coded Caching and the Exact Trade-off for N=K=2

“…1) We first show in Theorem 2 that the memory-rate pair (M, min{N, K}(1 − M/N )) is achievable for coded caching under information theoretic demand privacy. Our achievable scheme uses broadcast transmissions in the delivery phase, and this complements a similar result in [2] for their model using private unicast transmissions in the delivery stage. 2) We show in Theorem 3 that a demand-private scheme for N files and K users with the same memory-rate pair (M, R) can be obtained from a non-private scheme that serves only a subset of demands for N files and N K users.…”

“…2) We show in Theorem 3 that a demand-private scheme for N files and K users with the same memory-rate pair (M, R) can be obtained from a non-private scheme that serves only a subset of demands for N files and N K users. This is a refinement of results of [2], [3], and the scheme uses the idea in [3]. However, the observation that the particular non-private scheme is required to serve only a subset of demands is new, and this is used later for the case of N = K = 2, discussed in the next item.…”

“…In this paper, we consider the coded caching problem under privacy requirement on the demands of the users, i.e., no user should learn anything about the demands of the other users. Recently, demand privacy for the coded caching setup has been studied from an information theoretic perspective [2], [3], [4]. In [2], it was studied under a setup where the delivery phase uses private multicasts to subsets of users.…”

“…Recently, demand privacy for the coded caching setup has been studied from an information theoretic perspective [2], [3], [4]. In [2], it was studied under a setup where the delivery phase uses private multicasts to subsets of users. This was adapted to the broadcast delivery model under computational privacy guarantee.…”

“…privacy under broadcast delivery. In both [2], [3], construction techniques were proposed for deriving a demand-private scheme for N files and K users from a non-private coded caching scheme for N files and N K users. The achievable memory-rate pairs of the derived schemes are the same as that of the original non-private schemes.…”