Decoding of parallel Reed-Solomon codes with applications to product and concatenated codes

Krachkovsky, V.Yu.; Lee, Yuan Xing

doi:10.1109/isit.1998.708636

Cited by 20 publications

(24 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A better bound on the decoding error probability was obtained by Kurzweil et al [20] and by Schmidt et al [29], [30]. See also Brown et al [5], Coppersmith and Sudan [6], Justesen et al [16], Krachkovsky and Lee [19], and Wachter-Zeh et al [34].…”

Section: B Related Workmentioning

confidence: 91%

Coding for combined block-symbol error correction

Roth

Vontobel

2013

2013 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

We design low-complexity error correction coding schemes for channels that introduce different types of errors and erasures: on the one hand, the proposed schemes can successfully deal with symbol errors and erasures, and, on the other hand, they can also successfully handle phased burst errors and erasures.Index Terms-Decoding, generalized Reed-Solomon (GRS) code, Feng-Tzeng algorithm, phased burst erasure, phased burst error, symbol erasure, symbol error.

show abstract

Section: B Related Workmentioning

confidence: 91%

Coding for combined block-symbol error correction

Roth

Vontobel

2013

2013 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

show abstract

“…11) as a p s -interleaved code and apply a probabilistic decoder (as e.g. analyzed in [25], [32], [33]). Note that this decoding method also corrects p s -phased burst errors.…”

Section: Probabilistic Decoding Up To Bound IIImentioning

confidence: 99%

Decoding of repeated-root cyclic codes up to new bounds on their minimum distance

Zeh

Ulmschneider

2015

Probl Inf Transm

View full text Add to dashboard Cite

The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code.Furthermore, we present a third technique for bounding the minimum Hamming distance based on the embedding of a given repeated-root cyclic code into a repeated-root cyclic product code. A second quadratic-time probabilistic burst error decoding procedure based on the third bound is outlined. Index TermsBound on the minimum distance, burst error, efficient decoding, folded code, repeated-root cyclic code, repeatedroot cyclic product code

show abstract

“…Interleaved Reed-Solomon (IRS) codes like considered in [14], [15], [16], [17], [18], [19], [20], and others are capable of correcting error patterns beyond half the minimum distance. Usually, IRS code constructions are homogeneous, i.e., they consist of l codewords of one single Reed-Solomon code.…”

Section: A Virtual Extension To An Interleaved Reed-solomon Codementioning

confidence: 99%

“…Usually, IRS code constructions are homogeneous, i.e., they consist of l codewords of one single Reed-Solomon code. However, as suggested in [15] and investigated in [20], we also can construct heterogeneous IRS codes by taking the l codewords from different Reed-Solomon codes with the same length but different dimensions. As shown in [20], decoding of both homogeneous and heterogeneous IRS codes can be performed very efficiently using multi-sequence shift-register synthesis.…”

Section: A Virtual Extension To An Interleaved Reed-solomon Codementioning

confidence: 99%

Syndrome Decoding of Reed–Solomon Codes Beyond Half the Minimum Distance Based on Shift-Register Synthesis

Schmidt

Sidorenko

Bossert

2010

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

In this paper, a new approach for decoding lowrate Reed-Solomon codes beyond half the minimum distance is considered and analyzed. Unlike the Sudan algorithm published in 1997, this new approach is based on multi-sequence shiftregister synthesis, which makes it easy to understand and simple to implement. The computational complexity of this shift-register based algorithm is of the same order as the complexity of the well-known Berlekamp-Massey algorithm. Moreover, the error correcting radius coincides with the error correcting radius of the original Sudan algorithm, and the practical decoding performance observed on a q-ary symmetric channel (QSC) is virtually identical to the decoding performance of the Sudan algorithm. Bounds for the failure and error probability as well as for the QSC decoding performance of the new algorithm are derived, and the performance is illustrated by means of examples.Index Terms-Reed-Solomon codes, decoding beyond half the minimum distance, Interleaved Reed-Solomon codes, multisequence shift-register synthesis,

show abstract

Decoding of parallel Reed-Solomon codes with applications to product and concatenated codes

Cited by 20 publications

References 1 publication

Coding for combined block-symbol error correction

Coding for combined block-symbol error correction

Decoding of repeated-root cyclic codes up to new bounds on their minimum distance

Syndrome Decoding of Reed–Solomon Codes Beyond Half the Minimum Distance Based on Shift-Register Synthesis

Contact Info

Product

Resources

About