Efficient decoding of interleaved linear block codes

Haslach, Christoph; Vinck, A. J. Han

doi:10.1109/isit.2000.866441

Cited by 8 publications

(10 citation statements)

References 3 publications

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“…We start with Theorem 2 below that generalizes the results of [24] and [14] to the case where the set of nonzero columns of the m × n error array E are not necessarily linearly independent. Note that this theorem was already stated (without proof) in the one-page abstract [15] for the error-only case (i.e., no block erasures). We include the proof of the theorem not just for the sake of completeness, but also because the proof technique will be useful in Section III as well.…”

Section: A Block Errors and Erasures With Rank Constraintsmentioning

confidence: 87%

“…The idea of exploiting the rank of the error array when decoding interleaved codes was presented by Metzner and Kapturowski in [24] and by Haslach and Vinck in [14], [15]. Therein, the code C is chosen to be a linear [n, k, d] code over F , and, clearly, any combination of block errors can be corrected as long as their number does not exceed (d − 1)/2.…”

Section: B Related Workmentioning

confidence: 99%

“…As pointed out in [15], when K is empty and the difference t − µ = |supp(E)| − rank(E) is assumed to be equal to some nonnegative integer b, then the decoding algorithm of [24] and [14] can be generalized into finding a subset U ⊆ n of size…”

Section: A Block Errors and Erasures With Rank Constraintsmentioning

confidence: 99%

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Coding for combined block-symbol error correction

Roth

Vontobel

2013

2013 IEEE International Symposium on Information Theory

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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.

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Section: A Block Errors and Erasures With Rank Constraintsmentioning

confidence: 87%

Section: B Related Workmentioning

confidence: 99%

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Coding for combined block-symbol error correction

Roth

Vontobel

2013

2013 IEEE International Symposium on Information Theory

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“…In [25], Haslach and Vinck generalized the algorithm of Metzner and Kapturowski to linearly dependent (Hamming-)error matrices. An interesting open question is whether our algorithm can also be generalized to such errors in the rank metric.…”

Section: B Open Problemsmentioning

confidence: 99%

Decoding High-Order Interleaved Rank-Metric Codes

Puchinger¹,

Renner²,

Wachter-Zeh³

2019

Preprint

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This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric. The new decoder is an adaption of the Hamming-metric decoder by Metzner and Kapturowski (1990) and guarantees to correct all rank errors of weight up to d − 2 whose rank over the large base field of the code equals the number of errors, where d is the minimum rank distance of the underlying code. In contrast to previously-known decoding algorithms, the new decoder works for any rank-metric code, not only Gabidulin codes. It is purely based on linear-algebraic computations, and has an explicit and easy-to-handle success condition. Furthermore, a lower bound on the decoding success probability for random errors of a given weight is derived. The relation of the new algorithm to existing interleaved decoders in the special case of Gabidulin codes is given.

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“…Unlike all decoders mentioned above, this decoder works with interleaved codes obtained from an arbitrary linear constituent code and guarantees to correct any error of weight up to d − 2 that has full rank, where d is the minimum distance of the constituent code. It was rediscovered in [5] and generalized in [27], [28].…”

Section: Introductionmentioning

confidence: 99%

Decoding of Interleaved Alternant Codes

Holzbaur¹,

Liu²,

Neri³

et al. 2020

Preprint

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Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon code, as described by Schmidt et al. This decoder may either fail to return a codeword, or it may miscorrect to an incorrect codeword, and good upper bounds on the fraction of error matrices for which these events occur are known.The decoding algorithm immediately applies to interleaved alternant codes as well, i.e., the subfield subcodes of interleaved Reed-Solomon codes, but the fraction of decodable error matrices differs, since the error is now restricted to a subfield. In this paper, we present new general lower and upper bounds on the fraction of error matrices decodable by Schmidt et al.'s decoding algorithm, thereby making it the only decoding algorithm for interleaved alternant codes for which such bounds are known.

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Efficient decoding of interleaved linear block codes

Cited by 8 publications

References 3 publications

Coding for combined block-symbol error correction

Coding for combined block-symbol error correction

Decoding High-Order Interleaved Rank-Metric Codes

Decoding of Interleaved Alternant Codes

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