Improved Constructions of Coded Caching Schemes for Combination Networks

TL;DR

This paper introduces improved coded caching schemes for combination networks using a new algorithm and direct CPDA constructions, resulting in lower subpacketization levels and more flexible implementations compared to previous methods.

Contribution

It proposes a novel algorithm for coded caching in combination networks and directly constructs CPDAs for any H and r, surpassing prior grouping-based approaches.

Findings

Reduced subpacketization levels in caching schemes

More flexible implementation of coded caching schemes

Significant improvements in transmission rates

Abstract

In an $(H,r)$ combination network, a single content library is delivered to ${H\choose r}$ users through deployed $H$ relays without cache memories, such that each user with local cache memories is simultaneously served by a different subset of $r$ relays on orthogonal non-interfering and error-free channels. The combinatorial placement delivery array (CPDA in short) can be used to realize a coded caching scheme for combination networks. In this paper, a new algorithm realizing a coded caching scheme for combination network based on a CPDA is proposed such that the schemes obtained have smaller subpacketization levels or are implemented more flexible than the previously known schemes. Then we focus on directly constructing CPDAs for any positive integers $H$ and $r$ with $r<H$. This is different from the grouping method in reference (IEEE ISIT, 17-22, 2018) under the constraint that $r$ divides $H$. Consequently two classes of CPDAs are obtained. Finally comparing to the schemes and the method proposed by Yan et al., (IEEE ISIT, 17-22, 2018) the schemes realized by our CPDAs have significantly advantages on the subpacketization levels and the transmission rates.