Coded Caching with Polynomial Subpacketization

TL;DR

This paper introduces a family of centralized coded caching schemes with polynomial subpacketization, enabling scalable and efficient data distribution for large networks by controlling the subpacketization size.

Contribution

It presents novel coded caching schemes with polynomial subpacketization for any system parameters, improving scalability over previous exponential schemes.

Findings

Achieves polynomial subpacketization $F=O(K^{n+1})$ for caching systems.

Provides explicit constructions for schemes with various cache sizes.

Demonstrates improved scalability and efficiency in coded caching.

Abstract

Consider a centralized caching network with a single server and $K$ users. The server has a database of $N$ files with each file being divided into $F$ packets ($F$ is known as subpacketization), and each user owns a local cache that can store $\frac{M}{N}$ fraction of the $N$ files. We construct a family of centralized coded caching schemes with polynomial subpacketization. Specifically, given $M$, $N$ and an integer $n\geq 0$, we construct a family of coded caching schemes for any $(K,M,N)$ caching system with $F=O(K^{n+1})$. More generally, for any $t\in\{1,2,\cdots,K-2\}$ and any integer $n$ such that $0\leq n\leq t$, we construct a coded caching scheme with $\frac{M}{N}=\frac{t}{K}$ and $F\leq K\binom{\left(1-\frac{M}{N}\right)K+n}{n}$.