Combinatorial Multi-Access Coded Caching: Improved Rate-Memory Trade-off with Coded Placement

TL;DR

This paper introduces new coded caching schemes with coded placement for combinatorial multi-access caching, improving the rate-memory trade-off over existing schemes and establishing their optimality in certain regimes.

Contribution

It proposes two novel coded placement schemes using MDS codes for combinatorial multi-access caching, outperforming uncoded placement schemes and deriving tight lower bounds.

Findings

First scheme outperforms optimal uncoded placement when M > N/C.

Second scheme is better for N ≤ number of users.

First scheme is within a constant factor of optimal when r=2.

Abstract

This work considers the combinatorial multi-access coded caching problem introduced in the recent work by Muralidhar \textit{et al.} [P. N. Muralidhar, D. Katyal, and B. S. Rajan, ``Maddah-Ali-Niesen scheme for multi-access coded caching,'' in \textit{IEEE Inf. Theory Workshop (ITW)}, 2021] The problem setting consists of a central server having a library of $N$ files and $C$ caches each with capacity $M$. Each user in the system can access a unique set of $r<C$ caches, and there exist users corresponding to every distinct set of $r$ caches. Therefore, the number of users in the system is $\binom{C}{r}$. For the aforementioned combinatorial multi-access setting, we propose a coded caching scheme with an MDS code-based coded placement. This novel placement technique helps to achieve a better rate in the delivery phase compared to the optimal scheme under uncoded placement when $M> N/C$. For a lower memory regime, we present another scheme with coded placement, which outperforms the optimal scheme under uncoded placement if the number of files is no more than the number of users. Further, we derive an information-theoretic lower bound on the optimal rate-memory trade-off of the combinatorial multi-access coded caching scheme. In addition, using the derived lower bound, we show that the first scheme is optimal in the higher memory regime, and the second scheme is optimal if $N\leq \binom{C}{r}$. Finally, we show that the performance of the first scheme is within a constant factor of the optimal performance, when $r=2$.