# On the Optimality of Ali-Niesen Decentralized Coded Caching Scheme With and Without Error Correction

## TL;DR

This paper proves the optimality of the Ali-Niesen decentralized coded caching scheme for certain conditions and introduces an optimal error correction delivery scheme for error-prone shared links, enhancing reliability.

## Contribution

It establishes the optimality of the Ali-Niesen scheme for N ≥ K and proposes an optimal error correction method for unreliable links in decentralized caching.

## Key findings

- Ali-Niesen scheme is optimal for N ≥ K using index coding techniques.
- An optimal error correcting delivery scheme is developed for error-prone shared links.
- Expression for worst-case rate with finite errors is derived.

## Abstract

The decentralized coded caching was introduced in [M.~A. Maddah-Ali and U.~Niesen, `Decentralized coded caching attains order-optimal memory-rate tradeoff,' \emph{IEEE/ACM Trans. Networking}, vol.~23, no.~4, pp. 1029--1040, Aug. 2015] in which no coordination is required for the content placement. In this paper, with $N$ files and $K$ users, first it is shown that the decentralized coded caching scheme of Ali and Niesen is optimal for $N \geq K$ using techniques from index coding. Next the case when the shared link is error prone is considered. For this case, an optimal error correcting delivery scheme is proposed for coded caching problems with decentralized placement. Expression for the worst case rate is obtained when there are finite number of transmissions in error.