Distributed systems, especially those providing cloud services, endeavor to construct sufficiently reliable storage in order to attract more customers. Generally, pure replication and erasure code are widely adopted in distributed systems to guarantee reliable data storage, yet both of them contain some deficiencies. Pure replication consumes too much extra storage and bandwidth, while erasure ...

Product codes are powerful codes that can be used to correct errors or recover erasures. The simplest form of a product code is that where every row and every column is terminated by a single parity bit, referred to as single parity check (SPC) product code. This code has a minimum distance of four and is thus guaranteed to recover all single, double, and triple erasure patterns. Judging the co...

This paper proposes a fountain coding system which has lower space decoding complexity and lower decoding erasure rate than the Raptor coding systems. The main idea of the proposed fountain code is employing shift and exclusive OR to generate the output packets. This technique is known as the zigzag decodable code, which is efficiently decoded by the zigzag decoder. In other words, we propose a...

Erasure codes are the means by which storage systems are typically made reliable. Recent high profile studies of disk failure and sector failures indicate that ever more fault tolerant erasure codes are needed. Many traditional RAID approaches, parity-check array codes (e.g.,EVENODD, RDP, and X-code), and MDS codes offer two and three disk fault tolerant schemes. There are also many novel erasu...

We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used e...

Erasure coding has attracted the attention of space research community due to its potential to present an alternative or complementary solution to ARQ schemes. Typically, erasure coding can enhance reliability and decrease delivery latency when long delays render ARQ-based solutions inefficient. In this paper, we explore the benefits of erasure coding for file transfers over space Delay Toleran...

HyFS is designed to employ erasure codes to build a highly available distributed file system. It implements a general framework to use any erasure code. Thus, by applying different erasure codes, HyFS offers high flexibility for customizations to meet various application requirements.

A new ensemble of low-density parity-check (LDPC) codes for correcting a solid burst erasure is proposed. This ensemble is an instance of a combined matrix ensemble obtained by concatenating some LDPC matrices. We derive a new bound on the critical minimum span ratio of stopping sets for the proposed code ensemble by modifying the bound for ordinary code ensemble. By calculating this bound, we ...

Proper data placement schemes based on erasure correcting code are one of the most important components for a highly available data storage system. A new class of Maximum Distance Separable (MDS) array codes is presented for correcting triple storage failures, which is an extension of the double-erasure-correcting EVENODD code and is called the HDD-EOD code. The encoding and decoding procedures...

In this paper, the minimum span of stopping sets of regular LDPC codes are defined and analyzed. The minimum span of an LDPC code is closely related to immunity to burst erasures when an LDPC code is decoded with belief propagation (BP) for erasure channels. The minimum span of stopping sets is the smallest span of a non-empty stopping set. If a single erasure burst of length shorter than the m...