A generic framework for coded caching and distributed computation schemes

TL;DR

This paper introduces a unified framework connecting coded caching and distributed computation schemes through combinatorial objects, enabling new scheme constructions with improved performance metrics.

Contribution

It presents a general framework linking coded caching and distributed computation, including a new scheme with linear subpacketization and near constant rate.

Findings

Any PDA-based scheme can be represented within this framework

A new coded caching scheme with linear subpacketization is proposed

The modified framework achieves lower communication load in certain distributed computing scenarios

Abstract

Several network communication problems are highly related such as coded caching and distributed computation. The centralized coded caching focuses on reducing the network burden in peak times in a wireless network system and the coded distributed computation studies the tradeoff between computation and communication in distributed system. In this paper, motivated by the study of the only rainbow $3$-term arithmetic progressions set, we propose a unified framework for constructing coded caching schemes. This framework builds bridges between coded caching schemes and lots of combinatorial objects due to the freedom of the choices of families and operations. We prove that any scheme based on a placement delivery array (PDA) can be represented by a rainbow scheme under this framework and lots of other known schemes can also be included in this framework. Moreover, we also present a new coded caching scheme with linear subpacketization and near constant rate using the only rainbow $3$-term arithmetic progressions set. Next, we modify the framework to be applicable to the distributed computing problem. We present a new transmission scheme in the shuffle phase and show that in certain cases it could have a lower communication load than the schemes based on PDAs or resolvable designs with the same number of files.