Mojette Transform Based Ldpc Erasure Correction Codes for Distributed Storage Systems

Abstract

Mojette Transform (MT) based erasure correction coding possesses extremely efficient encoding/decoding algorithms and demonstrate promising burst erasure recovery performance. MT codes are based on discrete geometry and provide redundancy through creating projections. Projections are made of smaller data structures called bins and are generated from a two dimensional convex-shaped data. For exact data recovery, only a subset of projections are needed by the decoder. We realize that the discrete geometry definition of MT erasure codes corresponds to creating structured/deterministic generator matrices. In this study, we show an alternative Low Density Parity Check (LDPC) code construction methodology through investigating parity check matrices of MT codes which shows sparseness as the blocklength of the code gets large. In a distributed storage setting, we also quantify the repair bandwidth and show that this novel interpretation can be used to facilitate bin-level local repairs.