A Secretive Coded Caching for Shared Cache Systems using PDAs

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 ("Secretive Coded Caching with Shared Caches", in 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.

Coded Caching for Two-Dimensional Multi-Access Networks

“…In order to reduce the subpacketization, the authors in [6] proposed to characterize the placement and delivery phases in a single array, referred to as Placement Delivery Array (PDA), where the MN scheme can be characterized by a special PDA (referred to as MN PDA) [6]. By using the PDA, various caching schemes were constructed, e.g., [6]- [17]. Furthermore, the authors in [18] pointed out that other coded caching schemes based on combinatorial design in [12], [13], [18]- [21] can be also represented by appropriate PDAs.…”

“…. , Bt defined in(17), correspond to t different user-retrieve arrays of the (K2, L, M2, N ) 1D MACC problem in the horizontal projection.…”