# Caching with Partial Adaptive Matching

## TL;DR

This paper investigates a caching strategy that combines partial adaptive matching with coding, analyzing its performance against theoretical bounds and proposing a hybrid scheme for improved efficiency.

## Contribution

It introduces a hybrid caching scheme that integrates adaptive matching and coding, providing a comprehensive analysis of its performance across different regimes.

## Key findings

- Hybrid scheme outperforms extremal schemes in most regimes
- Characterization of regimes where matching or coding is more effective
- Comparison with information-theoretic bounds shows near-optimal performance

## Abstract

We study the caching problem when we are allowed to match each user to one of a subset of caches after its request is revealed. We focus on non-uniformly popular content, specifically when the file popularities obey a Zipf distribution. We study two extremal schemes, one focusing on coded server transmissions while ignoring matching capabilities, and the other focusing on adaptive matching while ignoring potential coding opportunities. We derive the rates achieved by these schemes and characterize the regimes in which one outperforms the other. We also compare them to information-theoretic outer bounds, and finally propose a hybrid scheme that generalizes ideas from the two schemes and performs at least as well as either of them in most memory regimes.