Symmetry in Distributed Storage Systems

TL;DR

This paper introduces a new linear programming bound and a concatenation coding scheme for exact repair distributed storage systems, advancing understanding of their capacity and providing tools for stronger theoretical limits.

Contribution

It formulates a linear programming bound, proposes a concatenation coding scheme, and establishes new entropy equalities to improve capacity analysis of exact repair systems.

Findings

Concatenation coding scheme achieves any admissible rate.

New entropy equalities simplify bounds and strengthen converse results.

Linear programming bound formulated for exact repair systems.

Abstract

The max-flow outer bound is achievable by regenerating codes for functional repair distributed storage system. However, the capacity of exact repair distributed storage system is an open problem. In this paper, the linear programming bound for exact repair distributed storage systems is formulated. A notion of symmetrical sets for a set of random variables is given and equalities of joint entropies for certain subsets of random variables in a symmetrical set is established. Concatenation coding scheme for exact repair distributed storage systems is proposed and it is shown that concatenation coding scheme is sufficient to achieve any admissible rate for any exact repair distributed storage system. Equalities of certain joint entropies of random variables induced by concatenation scheme is shown. These equalities of joint entropies are new tools to simplify the linear programming bound and to obtain stronger converse results for exact repair distributed storage systems.