A Secretive Coded Caching for Shared Cache Systems using PDAs

TL;DR

This paper introduces a new secretive coded caching scheme for shared cache systems using PDA constructions, reducing subpacketization levels and achieving order-optimal transmission rates while ensuring user file secrecy.

Contribution

It proposes a novel PDA-based procedure for secretive caching, lowering subpacketization and recovering existing schemes, with proven order-optimality.

Findings

Reduced subpacketization levels compared to existing schemes

The scheme is order-optimal in transmission rate

Existing schemes can be recovered using the new procedure

Abstract

This paper considers the secretive coded caching problem with shared caches in which no user must have access to the files that it did not demand. In a shared cache network, the users are served by a smaller number of helper caches and each user is connected to exactly one helper cache. To ensure the secrecy constraint in shared cache networks, each user is required to have an individual cache of at least unit file size. For this setting, a secretive coded caching scheme was proposed recently in the literature (\enquote{Secretive Coded Caching with Shared Caches}, in \textit{IEEE Communications Letters}, 2021), and it requires a subpacketization level which is in the exponential order of the number of helper caches. By utilizing the PDA constructions, we propose a procedure to obtain new secretive coded caching schemes for shared caches with reduced subpacketization levels. We also show that the existing secretive coded caching scheme for shared caches can be recovered using our procedure. Furthermore, we derive a lower bound on the secretive transmission rate using cut-set arguments and demonstrate the order-optimality of the proposed secretive coded caching scheme.