Shared Cache Coded Caching Schemes Using Designs and Circuits of Matrices

TL;DR

This paper introduces a shared cache coded caching scheme that maintains a fixed subpacketization level regardless of the number of users or caches, using matrix-based designs and matroid circuits for efficient data delivery.

Contribution

The authors propose a novel SC-CC scheme with subpacketization independent of user and cache count, enabling flexible cache addition without re-encoding, using matrix and matroid-based constructions.

Findings

Achieves fixed subpacketization level for any number of caches and users.

Potentially reduces data transmission rate compared to existing schemes.

Supports adding new caches without redoing placement.

Abstract

In this paper, we study shared cache coded caching (SC-CC): a set of caches serves a larger set of users; each user access one cache, and a cache may serve many users. For this problem, under uncoded placement, Parrinello, \"Unsal, and Elia showed an optimal SC-CC scheme, in which the subpacketization level depends upon the number of caches. We show an SC-CC scheme where the subpacketization level does not directly depend upon the number of users or caches; any number of caches and users can be accommodated for a fixed subpacketization level. Furthermore, new caches can be added without re-doing the placement of the existing caches. We show that given an upper limit on the allowable subpacketization level, our SC-CC scheme may achieve a lesser rate than other relevant SC-CC schemes. Our scheme is constructed using matrices and designs. A matroid can be obtained from a matrix over a finite field; the placement of our scheme is decided by a design constructed from a matrix; the circuits of a matroid obtained from the matrix and the design is used to decide the delivery.