Update-Efficient Error-Correcting Product-Matrix Codes

Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the communication overhead for regeneration (called MBR). In this work, we propose new encoding schemes for error-correcting MSR and MBR codes that generalize our earlier results on error-correcting regenerating codes. General encoding schemes for product-matrix MSR and MBR codes are derived such that the encoder based on Reed-Solomon (RS) codes is no longer limited to the Vandermonde matrix proposed earlier. Furthermore, MSR codes and MBR codes with the least update complexity can be found. A decoding scheme is proposed that utilizes RS codes to perform data reconstruction for MSR codes. The proposed decoding scheme has better error correction capability and incurs least number of node accesses when errors are present. A new decoding scheme is also proposed for MBR codes that is more capable and can correct more error-patterns. Simulation results are presented that exhibit the superior performance of the proposed schemes.