# Fundamental Limits of Coded Caching: From Uncoded Prefetching to Coded Prefetching

## TL;DR

This paper establishes a connection between uncoded and coded prefetching schemes in multiuser caching, introducing a general scheme that improves the understanding of the fundamental memory-rate tradeoff.

## Contribution

It unifies two major classes of caching schemes, providing a new general scheme that achieves previously unknown tradeoff points.

## Key findings

- A new general caching scheme that bridges uncoded and coded prefetching.
- Explicit examples demonstrating improved memory-rate tradeoff points.
- A rigorous analysis yielding a new inner bound to the caching tradeoff.

## Abstract

In order to characterize the fundamental limit of the tradeoff between the amount of cache memory and the delivery transmission rate of multiuser caching systems, various coding schemes have been proposed in the literature. These schemes can largely be categorized into two classes, namely uncoded prefetching schemes and coded prefetching schemes. While uncoded prefetching schemes in general offer order-wise optimal performance, coded prefetching schemes often have better performance at the low cache memory regime. The significant differences in the coding components between the two classes may leave the impression that they are largely unrelated. In this work, we provide a connection between the uncoded prefetching scheme proposed by Maddah Ali and Niesen (and its improved version by Yu et al) and the coded prefetching scheme proposed by Tian and Chen. A critical observation is first given where a coding component in the Tian-Chen scheme can be replaced by a binary .code, which enables us to view the two schemes as the extremes of a more general scheme. An explicit example is given to show that the intermediate operating points of this general scheme can in fact provide new memory-rate tradeoff points previously not known to be achievable in the literature. This new general coding scheme is then presented and analyzed rigorously, which yields a new inner bound to the memory-rate tradeoff for the caching problem.