Memory-Rate Tradeoff for Caching with Uncoded Placement under Nonuniform File Popularity

TL;DR

This paper analyzes the tradeoff between memory and rate in caching systems with nonuniform file popularity, introducing bounds and showing the optimality of a modified caching scheme under uncoded placement.

Contribution

It provides new information-theoretic lower bounds and proves the optimality of the MCCS scheme for certain user scenarios with nonuniform popularity.

Findings

MCCS attains the lower bound for 2 users, proving optimality.

For multiple users, MCCS achieves the popularity-first-based lower bound.

Zero-padding causes a small gap in some cases, with minimal impact observed.

Abstract

For caching with nonuniform file popularity, we aim to characterize the memory-rate tradeoff under uncoded cache placement. We consider the recently proposed Modified Coded Caching Scheme (MCCS) with the optimized cache placement based on the popularity-first approach to minimize the average delivery rate. We introduce two information-theoretic lower bounds on the average rate for caching under uncoded placement. For $K = 2$ users, we show that the optimized MCCS attains the lower bound and is optimal for caching with uncoded placement. For general $K$ users with distinct file requests, the optimized MCCS attains the popularity-first-based lower bound. When there are redundant file requests among $K$ users, we show a possible gap between the optimized MCCS and the lower bounds, which is attributed to zero-padding commonly used for coded delivery. We analyze the impact of zero-padding and its limitation. Simulation study shows that the loss is very small in general and only exists in some limited cases.