Bandwidth Overhead-Free Data Reconstruction Scheme for Distributed Storage Code With Low Decoding Complexity

Abstract

The $(n,k)$ combination property (CP) is defined as follows: $k$ source packets are mapped into $n \geq k$ packets and any $k$ out of these $n$ packets are able to recover the information of the original $k$ packets. This $(n,k)$ CP is extensively needed by cloud storage service providers. Reed-Solomon (RS) codes possess CP at the cost of high encoding and decoding complexity for two reasons: operation over a large-size finite field and time-consuming matrix inversion operation. By operating within the binary field and by allowing only zigzag decoding at the decoder, binary zigzag decoding that possesses CP lowers the decoding complexity significantly. The drawback is that storage room overhead is needed. Corresponding to this storage room overhead, in the data reconstruction process, intuitively fetching $k$ whole stored packets will consume overhead bandwidth. In this paper, a data reconstruction scheme that is optimal in terms of bandwidth consumption is designed, where optimal means the bandwidth consumption is equal to the volume of data to be reconstructed, namely, no overhead bandwidth is needed. To do that, a universal method of fetching sub-packet is proposed, and its corresponding decoding method is also designed.