Adaptive erasure code based distributed storage systems

Consider the following scenario: A data storage service provider provides an erasure code based distributed storage system (DSS). For the same data, the service provider gives several options: an (ni, ki) erasure code based DSS for i = 1,2, …, m. The service provider charges differently for different options (say dollar Pi for an (ni, ki) erasure code based DSS for the data B of size |B|). A client had initially chosen for an (ni, ki) erasure code based DSS. At some point of time, the client wants to change for another option, say for an (nj, kj) erasure code based DSS for the same data, where 1≤ i, j ≤ m, i ≠ j. Thus, service provider would require to convert the (ni, ki) erasure code based DSS into an (nj, kj) erasure code based DSS. The service provider has the following problem: How to design an erasure code based DSS so that the conversion of an (ni, ki) erasure code based DSS into an (nj, kj) erasure code based DSS, for 1 ≤ i, j ≤ m, i ≠ j, can be done by downloading the minimum amount of data? In this paper, we present an adaptive coding scheme which requires to download the minimum amount of data while converting an (ni, ki) erasure code based DSS to an (nj, kj) erasure code based DSS, where 1 ≤ i, j ≤ m, i ≠ j.