Repair of Multiple Descriptions on Distributed Storage

TL;DR

This paper investigates how to efficiently repair distributed storage systems that use multiple descriptions, focusing on minimizing additional bits needed during server replacement while maintaining original distortion levels.

Contribution

It provides the optimal repair solution for two Gaussian servers and an achievable rate for general n-node systems, emphasizing the importance of designing codes with repair in mind.

Findings

Optimal repair solution for two Gaussian servers.

Achievable repair rate for general n-node systems.

Designing codes with repair considerations reduces repair rates.

Abstract

In multiple descriptions on distributed storage, a source is stored in a shared fashion on multiple servers. When a subset of servers are contacted, the source should be estimated with a certain maximum distortion depending on the number of servers. The problem considered in this paper is how to restore the system operation when one of the servers fail and a new server replaces it, that is, repair. The requirement is that the distortions in the restored system should be no more than in the original system. The question is how many extra bits are needed for repair. We find the optimum solution for a two server problem in the Gaussian case, and an achievable rate for general $n$ nodes. One conclusion is that it is necessary to design the multiple description codes with repair in mind; just using an existing multiple description code results in unnecessary high repair rates.