On adaptive (functional MSR code based) distributed storage systems

Suppose that a data storage service provider implements a functional MSR code based distributed storage system (DSS). Consider a scenario where the service provider has implemented an (n₁, k₁, B, d₁, t₁) functional MSR code based DSS, where B is the file that is stored. At a later point of time, due to certain considerations (such as storage cost, download bandwidth to repair failed nodes etc.), the service provider wants to convert this (n₁, k₁, B, d₁, t₁) functional MSR code based DSS to an (n₂, k₂, B, d₂, t₂) functional MSR code based DSS. The service provider wants to perform this conversion at the lowest possible cost, i.e., by downloading the minimum amount of data. The question is: How should one design an (n₁, k₁, B, d₁, t₁) functional MSR code based DSS so that it requires minimum download to convert the DSS to an (n₂, k₂, B, d₂, t₂) functional MSR code based DSS? In this paper, we propose a coding scheme which requires the minimum download while converting an (n₁, k₁, B, d₁, t₁) functional MSR code based DSS to an (n₂, k₂, B, d₂, t₂) functional MSR code based DSS.