Fundamental Limits of Coded Caching: The Memory Rate Pair (K-1-1/K, 1/(K-1))

TL;DR

This paper extends the understanding of fundamental limits in coded caching by proposing an optimal scheme for the (K, K) network and establishing its optimality with a new lower bound.

Contribution

It introduces a new optimal caching scheme for the (K, K) network and proves its optimality for the case of all users requesting distinct files.

Findings

Proposed a scheme with memory rate pair (K-1-1/K, 1/(K-1)).

Derived a new lower bound demonstrating the scheme's optimality.

Confirmed the scheme's optimality for demand where all users request distinct files.

Abstract

Maddah-Ali and Niesen, in a seminal paper, introduced the notion of coded caching. The exact nature of the fundamental limits in this context has remained elusive even as several approximate characterizations have been found. A new optimal scheme for the (3, 3) cache network, operating at the memory rate pair (5/3, 1/2) for the demand where all the users request for distinct files, was introduced recently to partially address this issue. In this paper, an extension of this scheme to the general (K, K) cache network, operating at the memory rate pair (K-1-1/K, 1/(K-1)), is proposed. A new lower bound is also derived which demonstrates the optimality of the proposed scheme for the demand where all the users request for distinct files.