Cache-Aided $K$-User Broadcast Channels with State Information at Receivers

TL;DR

This paper investigates a cache-aided broadcast scenario with time-varying erasure channels and receiver-only channel state information, providing bounds on achievable source rates and highlighting open problems in optimality gap closure.

Contribution

It characterizes the maximum source rate for 2-user and degraded K-user cases, and introduces a linear programming approach to bound achievable rates.

Findings

Characterized maximum source rate for 2-user case.

Provided upper bounds for caching strategies.

Developed a linear programming formulation to evaluate bounds.

Abstract

We study a $K$-user coded-caching broadcast problem in a joint source-channel coding framework. The transmitter observes a database of files that are being generated at a certain rate per channel use, and each user has a cache, which can store a fixed fraction of the generated symbols. In the delivery phase, the transmitter broadcasts a message so that the users can decode their desired files using the received signal and their cache content. The communication between the transmitter and the receivers happens over a (deterministic) \textit{time-varying} erasure broadcast channel, and the channel state information is only available to the users. We characterize the maximum achievable source rate for the $2$-user and the degraded $K$-user problems. We provide an upper bound for any caching strategy's achievable source rates. Finally, we present a linear programming formulation to show that the upper bound is not a sharp characterization. Closing the gap between the achievable rate and the optimum rate remains open.