Generalized Pyramid Codes for Versioned Data in Distributed Storage Networks

A distributed storage framework called sparsity exploiting coding (SEC) was recently proposed for storing multiple versions of data object, wherein the objects are stored in a differential manner in order to reduce the I/O reads when retrieving multiple versions. It was shown that the design of erasure codes for the SEC framework requires Cauchy-matrix-based maximum distance separable (MDS) codes, which, however, do not enjoy the locally repairable property during the repair process. In this letter, we study the suitability of generalized pyramid codes (GPCs), a well-known class of locally repairable codes, to the SEC framework, and analyze their capability to retrieve multiple versions with few I/O reads. We show that GPCs can retrieve correlated multiple versions with fewer I/O reads than the overall object size, however, requiring more I/O reads than that by Cauchy-matrix-based MDS codes. This penalty in the I/O reads comes at the advantage of availing the locally repairable property in the SEC framework. We also show that GPCs require fewer I/O reads than the optimal locally repairable codes, in some cases.