Rate-Memory Trade-off for Multi-access Coded Caching with Uncoded Placement

TL;DR

This paper investigates the rate-memory trade-off in multi-access coded caching with uncoded placement, providing new bounds that are order-optimal for large access degrees and improving upon previous results.

Contribution

It introduces new achievable and lower bounds for the rate-memory trade-off in multi-access caching, establishing order-optimality for large access degrees under uncoded placement.

Findings

New achievable rate for all access degrees L ≥ 1.

Lower bound valid for all uncoded placements and L ≥ K/2.

Gap between bounds is at most 2, independent of parameters.

Abstract

We study a multi-access variant of the popular coded caching framework, which consists of a central server with a catalog of $N$ files, $K$ caches with limited memory $M$, and $K$ users such that each user has access to $L$ consecutive caches with a cyclic wrap-around and requests one file from the central server's catalog. The server assists in file delivery by transmitting a message of size $R$ over a shared error-free link and the goal is to characterize the optimal rate-memory trade-off. This setup was studied previously by Hachem et al., where an achievable rate and an information-theoretic lower bound were derived. However, the multiplicative gap between them was shown to scale linearly with the access degree $L$ and thus order-optimality could not be established. A series of recent works have used a natural mapping of the coded caching problem to the well-known index coding problem to derive tighter characterizations of the optimal rate-memory trade-off under the additional assumption that the caches store uncoded content. We follow a similar strategy for the multi-access framework and provide new bounds for the optimal rate-memory trade-off $R^*(M)$ over all uncoded placement policies. In particular, we derive a new achievable rate for any $L \ge 1$ and a new lower bound, which works for any uncoded placement policy and $L \ge K/2$. We then establish that the (multiplicative) gap between the new achievable rate and the lower bound is at most $2$ independent of all parameters, thus establishing an order-optimal characterization of $R^*(M)$ for any $L\ge K/2$. This is a significant improvement over the previously known gap result, albeit under the restriction of uncoded placement policies. Finally, we also characterize $R^*(M)$ exactly for a few special cases.