# An Optimal Linear Error Correcting Delivery Scheme for Coded Caching with Shared Caches

## TL;DR

This paper introduces an optimal linear error correcting delivery scheme for shared cache coded caching systems, providing a precise peak rate expression and an improved scheme for non-distinct demands.

## Contribution

It presents a new optimal linear error correcting delivery scheme for shared cache coded caching and derives the exact worst-case rate expression.

## Key findings

- Derived the exact worst-case rate for the scheme
- Proposed an improved delivery scheme for non-distinct demands
- Established the peak rate expression for the system

## Abstract

Classical coded caching setting avails each user to have one dedicated cache. This is generalized to a more general shared cache scheme and the exact expression for the worst case rate was derived in [E. Parrinello, A. Unsal, P. Elia, "Fundamental Limits of Caching in Heterogeneous Networks with Uncoded Prefetching," available on arXiv:1811.06247 [cs.IT], Nov. 2018]. For this case, an optimal linear error correcting delivery scheme is proposed and an expression for the peak rate is established for the same. Furthermore, a new delivery scheme is proposed, which gives an improved rate for the case when the demands are not distinct.