Fundamental limits of caching: Improved rate-memory trade-off with coded prefetching

Abstract

We consider a cache network in which a single server is connected to multiple users via a shared error free link. The server has access to a database with N files of equal length F , and serves K users each with a cache memory of M F bits. A novel centralized coded caching scheme is proposed for scenarios with more users than files N ≤ K and cache capacities satisfying 1 K ≤ M ≤ N K. The proposed scheme outperforms the best ratememory region known in the literature if N ≤ K ≤ N 2 +1 2. Index Terms-Coded caching, network coding, index coding.

Symmetry, Outer Bounds, and Code Constructions: A Computer-Aided Investigation on the Fundamental Limits of Caching

“…Chen et al [15] extended a special scheme for the case N = K = 2 discussed in [6] to the general case N ≤ K, and showed that the tradeoff pair 1 K , N (K−1) K is achievable. There were also several other notable efforts in attempting to find better binary codes [16][17][18]21]. Tian and Chen [20] proposed a class of codes for N ≤ K, the origin of which will be discussed in more details in Section 5.…”

“…Tian and Chen [20] proposed a class of codes for N ≤ K, the origin of which will be discussed in more details in Section 5. Gómez-Vilardebó [21] also proposed a new code, which can provide further improvement in the small cache memory regime. Tradeoff points achieved by the codes in [20] can indeed be optimal in some cases.…”

“…Tradeoff points achieved by the codes in [20] can indeed be optimal in some cases. It is worth noting that while all the schemes [6,[15][16][17][18][19]21] are binary codes, the codes in [20] use a more general finite field.…”

“…Subsequent works extended it to decentralized caching placements [7], caching with nonuniform demands [8], online caching placements [9], hierarchical caching [10], caching with random demands [11], among other things. There have been significant research activities recently [12][13][14][15][16][17][18][19][20][21] in both refining the outer bounds and finding stronger codes for caching. Despite these efforts, the fundamental tradeoff had not been fully characterized except for the case with only two users and two files [6] before our work.…”

On Coded Caching Systems with Offline Users

“…For the the original coded caching model [3], coded placement is known not only to strictly improve performance compared to uncoded placement, but to be exactly optimal in some regimes: [9] shows how to achieve the cut-set bound in the small memory regime when there are more users than files; [10] proposes a scheme based on interference elimination for the case of more users than files; [11] shows an improved performance compared to [10] in small memory regime when more users than files; [12] derives the optimal performance for the case of two users (and any number of files), and a partial characterization for the case of two files (and any number 1 Uncoded cache placement means that bits of the files are directly copied into the caches without any coding. of users); [13] extends beyond [9] the memory regime over which the optimal coded placement strategy is known, but it is restricted to the case when the number users and the number files are the same.…”