Asymmetric Decentralized Caching With Coded Prefetching Under Nonuniform Requests

We investigate a basic decentralized caching network with coded prefetching under nonuniform requests and arbitrary file popularities, where a server containing $N$ files is connected to $K$ users, each with limited cache memory of $M$ files through a shared link. In the decentralized placement phase, the server encodes all files by the maximum distance separable (MDS) codes with different rates, and each user allocates different files with different cache weights, resulting in that each user randomly prefetches the coded subfiles with diverse sizes. In this context, the symmetric delivery in existing decentralized caching networks with coded prefetching cannot be directly applied. To address this problem, we develop an asymmetric delivery procedure for the decentralized caching network with arbitrary MDS code rates and cache weights. Furthermore, we characterize the expected normalized rate induced by the asymmetric delivery using the concept of user grouping and leader set. Following the proposed asymmetric delivery and rate analysis, we derive the exact rate–memory tradeoff for a decentralized two-user and two-file caching network and optimize cache weights to minimize the expected normalized rate. Finally, numerical results corroborate our analytical results in the two-user two-file caching scenario.