Decoding of Reed Solomon Codes beyond the Error-Correction Bound

Decoding of Reed Solomon codes beyond the error-correction bound

Decoding interleaved Reed-Solomon codes beyond their joint error-correcting capability

A new probabilistic decoding algorithm for low-rate Interleaved Reed– Solomon (IRS) codes is presented. This approach increases the error correcting capability of IRS codes compared to other known approaches (e.g. joint decoding) with high probability. It is a generalization of well-known decoding approaches and its complexity is quadratic with the length of the code. Asymptotic parameters of t...

Title of dissertation: PERFORMANCE ANALYSIS OF ALGEBRAIC SOFT-DECISION DECODING OF REED-SOLOMON CODES

Title of dissertation: PERFORMANCE ANALYSIS OF ALGEBRAIC SOFT-DECISION DECODING OF REED-SOLOMON CODES Andrew Duggan, Masters of Science, 2006 Thesis directed by: Professor Alexander Barg Department of Electrical and Computer Engineering We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. An expres...

List Decoding of q - ary Reed - Muller Codes 1 )

The q-ary Reed-Muller codes RMq(u,m) of length n = q are a generalization of Reed-Solomon codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for Reed-Muller codes were given in [1] and [15]. The algorithm in [15] is an improvement of the algorithm ...

Code Constructions based on Reed-Solomon Codes

Reed–Solomon codes are a well–studied code class which fulfill the Singleton bound with equality. However, their length is limited to the size q of the underlying field Fq. In this paper we present a code construction which yields codes with lengths of factors of the field size. Furthermore a decoding algorithm beyond half the minimum distance is given and analyzed.

Efficient root-finding algorithm with application to list decoding of Algebraic-Geometric codes

A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance from the received vector, where can be greater than the error-correction bound. In [18], a list-decoding procedure for Reed–Solomon codes [19] was generalized to algebraic–geometric codes. A recent work [8] gives improved list decodings for Reed–Solomon codes and alg...