In classical algebraic coding theory, the minimum distance of block code completely determines the ability of the code in terms of error correction/detection and erasure correction. We have obtained generalizations of these results for network codes.

In this paper, we extend our work in [4] which employed Partial Reed-Solomon (PRS) Codes at coding rates near channel capacity on a Binary Erasure Channel (BEC). We demonstrated that an appropriately designed PRS code outperforms the classical Reed-Solomon (RS) code for a performance criterion tailored for realtime applications. This paper extends this analysis for a general BEC with varying ch...

In this paper, we investigate erasure-resilient codes coming from Steiner 2-designs with block size k which can correct up to any k erasures. In view of applications it is desirable that such a code can also correct as many erasures of higher order as possible. Our main result is that the erasure-resilient code constructed from an affine space with block size q – a special Steiner 2-design – ca...

Erasure coding is a fundemental technique to prevent data loss in storage systems composed of multiple disks. Recently, there have been multiple open-source implementations of a variety of erasure codes. In this work, we present a comparison of the performance of various codes and implementations, concentrating on encoding and decoding. It is hard to draw overarching conclusions from a single p...

his Network error correction (NEC) helps to correct errors of a communication network by using the concept of network coding [1] and provides an alternative to the traditional link-by-link error correction. NEC is widely used in sensor networks and in video network broadcasting, where the network suffers from delay and energy constraints. This paper aims to design an Automatic Repeat Request (A...

Sector-Disk (SD) codes are erasure codes that address the mixed failure mode of current RAID systems. Rather than dedicate entire disks to erasure coding, as done in RAID-5, RAID-6 and Reed-Solomon coding, an SD code dedicates entire disks, plus individual sectors to erasure coding. The code then tolerates combinations of disk and sector errors, rather than solely disk errors. It has been an op...

SD codes are erasure codes that address the mixed failure mode of current RAID systems. Rather than dedicate entire disks to erasure coding, as done in RAID-5, RAID-6 and Reed-Solomon coding, an SD code dedicates entire disks, plus individual sectors to erasure coding. The code then tolerates combinations of disk and sector errors, rather than solely disk errors. It is been an open problem to c...

In 2007, Martinian and Trott presented codes for correcting a burst of erasures with a minimum decoding delay. Their construction employs [n, k] codes that can correct any burst of erasures (including wrap-around bursts) of length n− k. They raised the question if such [n, k] codes exist for all integers k and n with 1 ≤ k ≤ n and all fields (in particular, for the binary field). In this note, ...

Erasure codes play an important role in storage systems to prevent data loss. In this work, we study a class of erasure codes called Multi-Erasure Locally Recoverable Codes (ME-LRCs) for flash memory array. Compared to previous related works, we focus on the construction of ME-LRCs over small fields. We first develop upper and lower bounds on the minimum distance of MELRCs. These bounds explici...