Multi-Access Coded Caching Schemes from Maximal Cross Resolvable Designs

TL;DR

This paper introduces a new multi-access coded caching scheme based on maximal cross resolvable designs, optimizing rate and subpacketization for general user-to-cache associations beyond cyclic patterns.

Contribution

It proposes a novel MACC scheme using maximal cross resolvable designs that improves upon existing cyclic association methods in rate and subpacketization.

Findings

Achieves lower rate than cyclic association schemes for certain user-to-cache graphs.

Reduces subpacketization complexity compared to previous schemes.

Provides a new combinatorial framework for flexible user-to-cache associations.

Abstract

We study the problem of multi-access coded caching (MACC): a central server has $N$ files, $K$ ($K \leq N$) caches each of which stores $M$ out of the $N$ files, $K$ users each of which demands one out of the $N$ files, and each user accesses $z$ caches. The objective is to jointly design the placement, delivery, and user-to-cache association, to optimize the achievable rate. This problem has been extensively studied in the literature under the assumption that a user accesses only one cache. However, when a user accesses more caches, this problem has been studied only under the assumption that a user accesses $z$ consecutive caches with a cyclic wrap-around over the boundaries. A natural question is how other user-to-cache associations fare against the cyclic wrap-around user-to-cache association. A bipartite graph can describe a general user-to-cache association. We identify a class of bipartite graphs that, when used as a user-to-cache association, achieves either a lesser rate or a lesser subpacketization than all other existing MACC schemes using a cyclic wrap-around user-to-cache association. The placement and delivery strategy of our MACC scheme is constructed using a combinatorial structure called maximal cross resolvable design.