MDS codes are erasure-correcting codes that can correct the maximum number of erasures for a given number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in the code, the original information can be recovered. However, it was shown that in order to recover a single symbol erasure, only a fraction of 1/...

This manuscript comprises a tutorial on traditional erasure codes and their applications to networked distributed storage systems (NDSS), followed by a survey of novel code families tailor made for better repairability in NDSS.

Recently, erasure networks have received significant attention in the literature [1–7] as they are used to model both wireless and wireline packet-switched networks. Many packetswitched data networks like wireless mesh networks [8–10], the Internet [11–13], and Peerto-peer networks [14] can be modeled as erasure networks. The reason is that each packet contains an internal error detection code,...

Practical storage systems often adopt erasure codes to tolerate device failures and sector failures, both of which are prevalent in the field. However, traditional erasure codes employ device-level redundancy to protect against sector failures, and hence incur significant space overhead. Recent sector-disk (SD) codes are available only for limited configurations due to the relatively strict ass...

The array erasure code, an ideal method for fault tolerance in storage systems, however, is obstructed by its impossibility to set the fault tolerant ability according to dynamic application environment for practical purpose. In view of this, this paper presents a new class of array erasure codes, with the greatest contribution to the array codes which can be obtained according to the preset nu...

Erasure coding is widely used for massive storage in data centers to achieve high fault tolerance and low storage redundancy. Since the cross-rack communication cost is often high, it is critical to design erasure codes that minimize the cross-rack repair bandwidth during failure repair. In this paper, we analyze the optimal trade-off between storage redundancy and cross-rack repair bandwidth s...

This paper considers the problem of perfectly secure communication on a modified version of Wyner’s wiretap channel II where both the main and wiretapper’s channels have some erasures. A secret message is to be encoded into n channel symbols and transmitted. The main channel is such that the legitimate receiver receives the transmitted codeword with exactly n− ν erasures, where the positions of...

A new error correcting scheme is introduced in this paper. The scheme is based on a novel array code which is called Generalized E code (GE for short). GE code is a kind of erasure code with long length of codewords and low complexity of encoding/decoding. So it is very compatible to satisfy the characteristic of Color-PDF417, which is a 3-d extension of widespread using 2-d barcode PDF417. The...