# Optimal Cache Placement for Modified Coded Caching with Arbitrary Cache Size

## TL;DR

This paper derives the optimal cache placement for the modified coded caching scheme with arbitrary cache sizes, minimizing delivery rate and providing a closed-form solution that generalizes existing schemes.

## Contribution

It formulates the cache placement as a linear programming problem and derives a closed-form optimal solution for MCCS with any cache size, extending previous specific-cache solutions.

## Key findings

- Optimal cache placement minimizes average delivery rate.
- Closed-form solution generalizes existing cache schemes.
- Caching gain varies with user population and cache patterns.

## Abstract

We consider content caching between a service provider and multiple cache-enabled users, using the recently proposed modified coded caching scheme (MCCS) that provides an improved delivery strategy for random user requests. We develop the optimal cache placement solution for the MCCS with arbitrary cache size by formulating the cache placement as an optimization problem to minimize the average rate during the delivery phase under random user requests. Through reformulation, we show that the problem is a linear programming problem. By exploring the properties in the caching constraints, we obtain the optimal cache placement solution in closed-form. We verify that the existing cache placement scheme obtained at specific cache sizes is a special case of our solution. Numerical studies show how the caching gain changes as the user population increases, as a result of different cache placement patterns.