Error correction up to the information-theoretic limit

Abstract

Ever since the birth of coding theory almost 60 years ago, researchers have been pursuing the elusive goal of constructing the "best codes," whose encoding introduces the minimum possible redundancy for the level of noise they can correct. In this article, we survey recent progress in list decoding that has led to efficient error-correction schemes with an optimal amount of redundancy, even against worst-case errors caused by a potentially malicious channel. To correct a proportion p (say 20%) of worst-case errors, these codes only need close to a proportion p of redundant symbols. The redundancy cannot possibly be any lower informationtheoretically. This new method holds the promise of correcting a factor of two more errors compared to the conventional algorithms currently in use in diverse everyday applications.

Unlinkable minutiae‐based fuzzy vault for multiple fingerprints

“…It is not the purpose of the present paper to provide comprehensive analyses and evaluations of Guruswami–Sudan algorithms; therefore we see [36]. However, in order to design a decoding mechanism, we describe some experiments that we conducted.…”

Codes That Achieve Capacity on Symmetric Channels

“…BEC(p i ). Let's denote this channel by BEC(p) 5 . In this setting we would like to analyze the probability that the MAP decoder is unable to decode the i-th bit and then try to get a bound on the probability of error for the block MAP decoder.…”

Distributed Object Store Principles of Operation The Case for Intelligent Storage

“…While there are means to gain greater storage efficiency without traditional RAID storage subsystems, such as erasure encoding [27], these methods are still relatively novel and therefore have not undergone the rigor of extensive customer use typified by RAID models. If the object store is to be used as the final home for object data, the means of data protection must be solid or it risks data loss.…”