New optimal trade-off point for coded caching systems with limited cache size

TL;DR

This paper introduces an optimal coded caching scheme for systems with N files, N users, and small cache size, achieving the best possible load with a simple linear coding approach.

Contribution

It proposes a new achievable scheme that is proven to be optimal for cache size M=1/(N-1) in N-user N-file systems, demonstrating the optimality of linear coding placement.

Findings

Achieves the known converse bound, proving optimality.

Uses a simple linear coding scheme with finite field operations.

Shows optimality for cache size M=1/(N-1) when N≥3.

Abstract

This paper presents a new achievable scheme for coded caching systems with $\mathsf{N}$ files, $\mathsf{K}=\mathsf{N}$ users, and cache size $\mathsf{M}=1/(\mathsf{N}-1)$. The scheme employs linear coding during the cache placement phase, and a three-stage transmissions designed to eliminate interference in the delivery phase. The achievable load meets a known converse bound, which impose no constraint on the cache placement, and is thus optimal. This new result, together with known inner and outer bounds, shows optimality of linear coding placement for $\mathsf{M} \leq 1/(\mathsf{N}-1)$ when $\mathsf{K}=\mathsf{N}\geq 3$. Interestingly and surprisingly, the proposed scheme is relatively simple but requires operations on a finite field of size at least 3.