Zigzag Decodable codes: Linear-time erasure codes with applications to data storage

An erasure code is said to be k-reliable if it maps k source packets into n coded packets, and any k out of the n coded packets allow recovery of the original k source packets. Codes of k-reliability achieve the best reliability-storage tradeoff, which are useful for fault tolerance in data storage systems. Zigzag Decodable (ZD) codes are k-reliable erasure codes. Its encoding and decoding (per information bit) can be done in linear time, involving only XOR and bit-shift operations. Two classes of ZD codes are constructed, and compared with Cacuhy-RS codes, the state-of-the-art general-purpose MDS codes. Numerical results show that ZD codes outperform Cauchy-RS codes over a wide range of coding parameters.