Z Codes: General Systematic Erasure Codes with Optimal Repair Bandwidth and Storage for Distributed Storage Systems

Erasure codes are widely used in distributed storage systems to prevent data loss. Traditional erasure codes suffer from a typical repair-bandwidth problem in which the amount of data required to reconstruct the lost data, referred to as the repair bandwidth, is often far more than the theoretical minimum. While many novel erasure codes have been proposed in recent years to reduce the repair bandwidth, these codes either require extra storage capacity and computation overhead or are only applicable to some special cases. To address the weaknesses of the existing solutions to the repair-bandwidth problem, we propose Z Codes, a general family of codes capable of achieving the theoretical lower bound of repair bandwidth for a single data node failure. To the best of our knowledge, the Z codes are the first general systematic erasure codes that achieve optimal repair bandwidth under the minimum storage. Our in-memory performance evaluations of a 1-GB file indicate that Z codes have encoding and repairing speeds that are approximately equal to those of the Reed-Solomon (RS) codes, and their speed on the order of GB/s practically removes computation as a performance bottleneck.