Composite extension finite fields for distributed storage erasure coding

Distributed storage systems aim at providing reliable access to data that is spread across multiple nodes typically at different physical locations to provide better data safety and/or improve the data access speed. By using an erasure code and spreading coded fragments of the data onto the nodes, faster and more reliable access to the data can be guaranteed. By using Random Linear Network Coding (RLNC) the important problem of replacing fragments from failed nodes becomes significantly simpler, since the unique receding operation can be utilized for functional repair. However, the coding throughput of RLNC codes is significantly reduced when high block decoding probability is required, because large finite fields must be used. This paper introduces the design of a code aimed at storage applications. The design utilizes composite extension finite fields to provide a strong and fast code, meaning a low block decoding failure probability and a high coding throughput. The gain in terms of reduced computational complexity is highest when the number of fragments per block is large, which is the case that brings the biggest advantages but is also more challenging. The design maintains full compatibility with traditional RLNC codes and includes a simple way to perform recoding.