We extend the framework for studying the stopping redundancy of a linear block code by introducing and analyzing the stopping redundancy hierarchy. The stopping redundancy hierarchy of a code represents a measure of the trade-off between performance and complexity of iteratively decoding a code used over the binary erasure channel. It is defined as an ordered list of positive integers in which ...

Low encoding/decoding complexity is essential for practical storage systems. This paper presents a new Maximum Distance Separable (MDS) array codes, called Triple-Star, for tolerating triple disk failures in Redundant Arrays of Inexpensive Disks (RAID) architecture. Triple-Star is an extension of the double-erasure-correcting Rotarycode and a modification of the generalized triple-erasure-corre...

It is shown that Pierce’s pulse-position modulation scheme with 2L pulse positions used on a self-noise-limited direct-detection optical communication channel results in a 2L-ary erasure channel that is equivalent to the parallel combination of L completelycorrelated binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff ...

As modern storage systems have grown in size and complexity, RAID-6 is poised to replace RAID-5 as the dominant form of RAID architectures due to its ability to protect against double disk failures. Many excellent erasure codes specially designed for RAID-6 have emerged in recent years. However, all of them have limitations. In this paper, we present a class of near perfect erasure codes for RA...

A message independence property and some new performance upper bounds are derived in this work for erasure, list and decision-feedback schemes with linear block codes transmitted over memoryless symmetric channels. Similarly to the classical work of Forney, this work is focused on the derivation of some Gallager-type bounds on the achievable tradeoffs for these coding schemes, where the main no...

A number of applications of Steiner triple systems (e.g. disk erasure codes) exist that require a special ordering of its blocks. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, and Gray codes are examples of listing elements of a combinatorial family in a specific manner, and Godbole invented the following generalization of these in 2010. 1-overlap cycles require a set of ...

This paper presents a survey on existing data transport reliability protocols in wireless sensor networks (WSNs). Most of the existing research employs retransmission mechanisms to achieve reliability, ignoring the use of redundancy schemes such as erasure codes to enhance event reliability. We review the data transport reliability schemes in terms of event and packet reliability using retransm...

We are investigating strategies for using replication to design and implement highly reliable peer-to-peer systems. In particular, we are comparing the use of whole object and blocking replication, and pursuing the use of erasure codes with blocking replication as a novel technique for achieving high reliability even for systems primarily composed of hosts with poor availability. In this paper,...

The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region an...

Redundancy is the basic technique to provide reliability in storage systems consisting of multiple components. A redundancy scheme defines how the redundant data are produced and maintained. The simplest redundancy scheme is replication, which however suffers from storage inefficiency. Another approach is erasure coding, which provides the same level of reliability as replication using a signif...