Repair optimal erasure codes through hadamard designs

Dimitris S. Papailiopoulos, Alexandros G. Dimakis, Viveck R. Cadambe
2011 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
In distributed storage systems that employ erasure coding, the issue of minimizing the total communication required to exactly rebuild a storage node after a failure arises. This repair bandwidth depends on the structure of the storage code and the repair strategies used to restore the lost data. Designing high-rate maximum-distance separable (MDS) codes that achieve the optimum repair communication has been a well-known open problem. In this work, we use Hadamard matrices to construct the
more » ... construct the first explicit 2-parity MDS storage code with optimal repair properties for all single node failures, including the parity nodes. Our construction relies on a novel method of achieving perfect interference alignment over finite fields with a finite file size, or number of symbol extensions.
doi:10.1109/allerton.2011.6120328 dblp:conf/allerton/PapailiopoulosDC11 fatcat:2amv77rqvvbcrlbcmedrkrg3l4