From Centralized to Decentralized Coded Caching

TL;DR

This paper introduces a simple method to convert centralized coded caching schemes into decentralized ones, maintaining efficiency and low overhead even as users join or leave the system.

Contribution

It proposes a translation scheme that transforms any constant rate centralized scheme into a decentralized scheme with guaranteed coding gain and manageable file size growth.

Findings

The scheme guarantees a target coding gain g in decentralized caching.

File size remains subexponential in g if original centralized scheme is subexponential in K.

System maintains performance with minimal rate degradation during user dynamics.

Abstract

We consider the problem of designing decentralized schemes for coded caching. In this problem there are $K$ users each caching $M$ files out of a library of $N$ total files. The question is to minimize $R$, the number of broadcast transmissions to satisfy all the user demands. Decentralized schemes allow the creation of each cache independently, allowing users to join or leave without dependencies. Previous work showed that to achieve a coding gain $g$, i.e. $R \leq K (1-M/N)/g$ transmissions, each file has to be divided into number of subpackets that is exponential in $g$. In this work we propose a simple translation scheme that converts any constant rate centralized scheme into a random decentralized placement scheme that guarantees a target coding gain of $g$. If the file size in the original constant rate centralized scheme is subexponential in $K$, then the file size for the resulting scheme is subexponential in $g$. When new users join, the rest of the system remains the same. However, we require an additional communication overhead of $O(\log K)$ bits to determine the new user's cache state. We also show that the worst-case rate guarantee degrades only by a constant factor due to the dynamics of user arrival and departure.