Coded Caching with Heterogeneous Cache Sizes and Link Qualities: The Two-User Case

Abstract

Centralized coded caching problem is studied for the two-user scenario, considering heterogeneous cache capacities at the users and private channels from the server to the users, in addition to a shared channel. Optimal caching and delivery strategies that minimize the worst-case delivery latency are presented for an arbitrary number of files. The converse proof follows from the sufficiency of fileindex-symmetric caching and delivery codes, while the achievability is obtained through memory-sharing among a number of special memory capacity pairs. The optimal scheme is shown to exploit the private link capacities by transmitting part of the corresponding user's request in an uncoded fashion. When there are no private links, the results presented here improve upon the two known results in the literature, namely, i) equal cache capacities and arbitrary number of files; and ii) unequal cache capacities and N = 2 files. The results are then extended to the caching problem with heterogeneous distortion requirements.

Device-to-Device Coded-Caching With Distinct Cache Sizes

“…That is, the placement and delivery design must be such that the server does not participate in delivery at all, thus saving its resources to serve those outside the D2D network. This distinction calls for new placement and delivery schemes as compared to serve-based delivery architectures [10]- [15], [25]- [27]. In the same spirit as [13], we show that a linear program minimizes the D2D delivery load by optimizing over the partitioning of the files in the placement phase and the size and structure of the D2D transmissions, and find the optimal design.…”

“…More realistic caching models that reflect the heterogeneity in content delivery networks consider systems with distinct cache sizes [10]- [15], [25]- [27], unequal file sizes [26], [28], [29], distinct distortion requirements [25], [30], [31], and non-uniform popularity distributions [32]- [37]. In this work, we focus on the distinct cache sizes, i.e., the varying storage capabilities of the users.…”

“…In this work, we focus on the distinct cache sizes, i.e., the varying storage capabilities of the users. This setup has been considered in [10]- [15], [25]- [27] for the server-based delivery problem of [4]. In particular, in [13], [15], we have shown that the delivery load is minimized by solving a linear program over the parameters of the uncoded placement and linear delivery schemes.…”

“…end for in(28),(32) follows from the structure of the multicast signals in (30), (33) generalizes the redundancy constraints in (22)-(24), and (34) generalizes the delivery completion constraints in (25)-(27). The delivery procedure is summarized in Algorithm 1.…”

Benefits of Coded Placement for Networks with Heterogeneous Cache Sizes

“…For systems with equal cache sizes, references [9], [10] have shown that coded placement is beneficial in the small memory regime when the number of files is less than or equal the number of users. Recent reference [11] has shown that coded placement is essential in achieving the optimal delivery load in a two-user system when the cache sizes of the two users differ.…”