Repairing Reed-Solomon Codes With Multiple Erasures

Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the whole file to be reconstructed in order to recover a single erased codeword symbol. In a recent work, Guruswami and Wootters (STOC’16) proposed a single-erasure repair method for RS codes that achieves the optimal repair bandwidth amongst all linear encoding schemes. Their key idea is to recover the erased symbol by collecting a sufficiently large number of its traces, each of which can be constructed from a number of traces of other symbols. As all traces belong to a subfield of the defining field of the RS code and many of them are linearly dependent, the total repair bandwidth is significantly reduced compared to that of the naive repair scheme. We extend the trace collection technique to cope with multiple erasures.