The Exact Rate Memory Tradeoff for Large Caches with Coded Placement

TL;DR

This paper advances the understanding of the exact rate-memory tradeoff in coded caching for large caches, providing new schemes and bounds that extend previous results to broader cache sizes.

Contribution

It introduces a new coded caching scheme and matching lower bounds, extending the exact rate-memory tradeoff characterization to larger cache sizes in the $(N,K)$ network.

Findings

Proposes a new coded caching scheme for certain cache sizes.

Derives matching lower bounds demonstrating scheme optimality.

Extends the known rate-memory tradeoff characterization to larger cache regimes.

Abstract

The idea of coded caching for content distribution networks was introduced by Maddah-Ali and Niesen, who considered the canonical $(N, K)$ cache network in which a server with $N$ files satisfy the demands of $K$ users (equipped with independent caches of size $M$ each). Among other results, their work provided a characterization of the exact rate memory tradeoff for the problem when $M\geq\frac{N}{K}(K-1)$. In this paper, we improve this result for large caches with $M\geq \frac{N}{K}(K-2)$. For the case $\big\lceil\frac{K+1}{2}\big\rceil\leq N \leq K$, we propose a new coded caching scheme, and derive a matching lower bound to show that the proposed scheme is optimal. This extends the characterization of the exact rate memory tradeoff to the case $M\geq \frac{N}{K}\Big(K-2+\frac{(K-2+1/N)}{(K-1)}\Big)$. For the case $1\leq N\leq \big\lceil\frac{K+1}{2}\big\rceil$, we derive a new lower bound, which demonstrates that the scheme proposed by Yu et al. is optimal and thus extend the characterization of the exact rate memory tradeoff to the case $M\geq \frac{N}{K}(K-2)$.