ε-MSR Codes with Small Sub-packetization

Minimum storage regenerating (MSR) codes form a special class of maximum distance separable (MDS) codes by providing mechanisms for exact regeneration of a single code block in their codewords by downloading the minimum amount of information from the remaining code blocks. As a result, the MSR codes find application to distributed storage systems to enable node repairs with the optimal repair bandwidth. However, the construction of exact-repairable MSR codes requires working with a large sub-packetization level, which restricts the employment of these codes in practice. This paper explores exact-repairable MDS codes that significantly reduce the required sub-packetization level by achieving slightly suboptimal repair bandwidth as compared to the MSR codes. This paper presents a general approach to combine an MSR code with large sub-packetization level with a code with large enough minimum distance to construct exact-repairable MDS codes with small sub-packetization level and near-optimal repair bandwidth. For a given number of parity blocks, the codes constructed using this approach have their sub-packetization level scaling logarithmically with the code length. In addition, the obtained codes require field size linear in the code length and ensure load balancing among the intact code blocks in terms of the information downloaded from these blocks during a node repair.