Cache-Aided General Linear Function Retrieval.

Kai Wan,Hua Sun,Giuseppe Caire,Daniela Tuninetti,Mingyue Ji

doi:10.3390/e23010025

Abstract

Coded Caching, proposed by Maddah-Ali and Niesen (MAN), has the potential to reduce network traffic by pre-storing content in the users’ local memories when the network is underutilized and transmitting coded multicast messages that simultaneously benefit many users at once during peak-hour times. This paper considers the linear function retrieval version of the original coded caching setting, where users are interested in retrieving a number of linear combinations of the data points stored at the server, as opposed to a single file. This extends the scope of the authors’ past work that only considered the class of linear functions that operate element-wise over the files. On observing that the existing cache-aided scalar linear function retrieval scheme does not work in the proposed setting, this paper designs a novel coded caching scheme that outperforms uncoded caching schemes that either use unicast transmissions or let each user recover all files in the library.

Highlights

Content caching is an efficient technique to handle the increase of requests for massive amounts of data and content over communication networks
Traditional caching techniques aim at prefetching popular content by predicting the user demands, realizing a “local caching gain” [1]
For the class of functions considered in [7], which are restricted to operate element-wise on the file entries, it was surprisingly shown that the YMA load can be achieved, that is, there is no penalty in terms of load in retrieving scalar linear functions under the constraint of uncoded cache placement

Summary

Introduction

Content caching is an efficient technique to handle the increase of requests for massive amounts of data and content over communication networks. For the class of functions considered in [7], which are restricted to operate element-wise on the file entries, it was surprisingly shown that the YMA load can be achieved, that is, there is no penalty in terms of load in retrieving scalar linear functions under the constraint of uncoded cache placement. It was noted in [7] that the proposed scalar linear function scheme can be extended to all scenarios to which the original MAN scheme has been extended, such as for example demand-private retrieval [8] and Device-to-Device networks [9,10]. The proposed scheme outperforms the baseline scheme in all parameter regimes

Paper Organization

Notation Convention

System Model

Main Result

Numerical Evaluations

Conclusions