Multi-Version Coding - An Information Theoretic Perspective of Consistent Distributed Storage

In applications of distributed storage systems to distributed computing and implementation of key- value stores, the following property, usually referred to as consistency in computer science and engineering, is an important requirement: as the data stored changes, the latest version of the data must be accessible to a client that connects to the storage system. An information theoretic formulation called multi-version coding is introduced in the paper, in order to study storage costs of consistent distributed storage systems. Multi-version coding is characterized by {\nu} totally ordered versions of a message, and a storage system with n servers. At each server, values corresponding to an arbitrary subset of the {\nu} versions are received and encoded. For any subset of c servers in the storage system, the value corresponding to the latest common version, or a later version as per the total ordering, among the c servers is required to be decodable. An achievable multi-version code construction via linear coding and a converse result that shows that the construction is approximately tight, are provided. An implication of the converse is that there is an inevitable price, in terms of storage cost, to ensure consistency in distributed storage systems.
Comment: 30 Pages. Extended version of conference publications in ISIT 2014 and Allerton 2014. Revision adds a section, Section VII, and corrects minor typographical errors in the rest of the document