Cache-aided General Linear Function Retrieval

TL;DR

This paper extends coded caching to the retrieval of linear functions of data, proposing a new scheme that outperforms existing unicast and uncoded caching methods in this setting.

Contribution

It introduces a novel coded caching scheme for linear function retrieval, expanding the scope beyond element-wise linear functions and improving performance.

Findings

The new scheme outperforms uncoded caching methods.

Existing scalar linear function schemes are not suitable for this setting.

The scheme reduces network traffic during peak hours.

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.