Graftage Coding for Distributed Storage Systems

To achieve various tradeoffs between storage and repair bandwidth, this article proposes to construct exact repair codes by grafting two codes C-1 and C-2. By replacing certain nonzero entries in the generator matrix of C-1 by zero, the repair bandwidth of the resulting grafting part decreases. However, it may no longer keep the maximum-distance-separable (MDS) property. As a result, the grafted code C-2 takes these nonzero entries into account such that the entire graftage code can keep the MDS property. The relationship between the bandwidth reduction of C-1 and the file size of C-2 is derived to optimize graftage codes. Our analysis indicates that these graftage codes may provide better tradeoffs than space-sharing.