Proceedings ArticleDOI
Improved decoding of Reed-Solomon and algebraic-geometric codes
Venkatesan Guruswami,Madhu Sudan +1 more
- pp 28-37
TLDR
An improved list decoding algorithm for decoding Reed-Solomon codes and alternant codes and algebraic-geometric codes is presented, including a solution to a weighted curve fitting problem, which is of use in soft-decision decoding algorithms for Reed- Solomon codes.Abstract:
Given an error-correcting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding Reed-Solomon codes. The list decoding problem for Reed-Solomon codes reduces to the following "curve-fitting" problem over a field F: Given n points {(x/sub i/.y/sub i/)}/sub i=1//sup n/, x/sub i/,y/sub i//spl isin/F, and a degree parameter k and error parameter e, find all univariate polynomials p of degree at most k such that y/sub i/=p(x/sub i/) for all but at most e values of i/spl isin/{1....,n}. We give an algorithm that solves this problem for e 1/3, where the result yields the first asymptotic improvement in four decades. The algorithm generalizes to solve the list decoding problem for other algebraic codes, specifically alternant codes (a class of codes including BCH codes) and algebraic-geometric codes. In both cases, we obtain a list decoding algorithm that corrects up to n-/spl radic/(n-d-) errors, where n is the block length and d' is the designed distance of the code. The improvement for the case of algebraic-geometric codes extends the methods of Shokrollahi and Wasserman (1998) and improves upon their bound for every choice of n and d'. We also present some other consequences of our algorithm including a solution to a weighted curve fitting problem, which is of use in soft-decision decoding algorithms for Reed-Solomon codes.read more
Citations
More filters
Book ChapterDOI
Fuzzy extractors: How to generate strong keys from biometrics and other noisy data
TL;DR: This work provides formal definitions and efficient secure techniques for turning biometric information into keys usable for any cryptographic application, and reliably and securely authenticating biometric data.
Proceedings ArticleDOI
A fuzzy commitment scheme
Ari Juels,Martin Wattenberg +1 more
TL;DR: Because the fuzzy commitment scheme is tolerant of error, it is capable of protecting biometric data just as conventional cryptographic techniques, like hash functions, are used to protect alphanumeric passwords.
Proceedings ArticleDOI
A fuzzy vault scheme
Ari Juels,Madhu Sudan +1 more
TL;DR: In this article, the authors describe a fuzzy vault construction that allows Alice to place a secret value /spl kappa/ in a secure vault and lock it using an unordered set A of elements from some public universe U. If Bob tries to "unlock" the vault using B, he obtains the secret value if B is close to A, i.e., only if A and B overlap substantially.
Book ChapterDOI
Polynomial reconstruction based cryptography
Aggelos Kiayias,Moti Yung +1 more
TL;DR: A short overview of recent works on the problem of Decoding Reed Solomon Codes (aka Polynomial Reconstruction) and the novel applications that were enabled due to this development.
Journal ArticleDOI
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data
TL;DR: In this article, the authors provide formal definitions and efficient secure techniques for turning noisy information into keys usable for any cryptographic application, and, in particular, reliably and securely authenticating biometric data.
References
More filters
Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Book
Algebraic Coding Theory
TL;DR: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
Book
A Course in Computational Algebraic Number Theory
TL;DR: The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.
Book
Algebraic Function Fields and Codes
TL;DR: This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded and contains numerous exercises that help the reader to understand the basic material.
Book
Theory and practice of error control codes
TL;DR: To understand the theoretical framework upon which error-control codes are built and then Algebraic Codes for Data Transmission by Richard E. Blahut, needed, several examples to illustrate the performance of the approximation scheme in practice are needed.