Algebraic list-decoding on the operator channel

Mahdavifar, Hessam; Vardy, Alexander

doi:10.1109/isit.2010.5513656

Cited by 32 publications

(64 citation statements)

References 7 publications

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“…It also shows directly, rather than evading the questions and avoiding them, that the errors in network coding are really very dense. Mahdavifar and Vardy [9] generates Silva and Kschischang code about list decoding. It shows that for any L, the list-…”

Section: Existing Error-correcting Methods In Network Codingmentioning

confidence: 99%

“…Therefore, it is also inefficient. Based on [9,23], this improves the list model and achieves a much bigger decoding radius C k -1 where C is the max flow min cut and k is the size of information. Guruswami and Sudan [24] can correct C Á ð1−…”

Section: Existing Error-correcting Methods In Network Codingmentioning

confidence: 99%

“…They cannot correct errors beyond d min /2 = (C − k)/2 < C/2 where (C, k) is MDS linear block code with code length C and information length k. Only a few studies refer to the assumption that the number of errors in network coding is bigger than C/2. They are list coding in network coding [8,9] homomorphic signatures [10]. However, homomorphic signatures based on cryptographic approaches can correct the propagated error which equals C. However, cryptographic approaches have great complexity, and it is completely impractical in NEC [10].…”

Section: The Tough Problem About Error Propagation In Network Codingmentioning

confidence: 99%

“…The fourth is the list decoding. The representative work is [9]. Mahdavifar and Vardy [9] generate Silva and Kschischang code to list decoding.…”

Section: The Potential Viable Solutionsmentioning

confidence: 99%

“…The representative work is [9]. Mahdavifar and Vardy [9] generate Silva and Kschischang code to list decoding. Especially what deserves to be mentioned most is that there are also list decoding methods based on rank distance [8] and Hamming distance [34,35].…”

Section: The Potential Viable Solutionsmentioning

confidence: 99%

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The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

Zhang

Cai

Zhang

et al. 2018

J Wireless Com Network

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The network coding can spread a single original error over the whole network. The simulation shows that the propagated error mostly all the time pollute just 100% of the received packets at the sink if Hamming distance is adopted. If subspace codes are adopted, usually the propagated error will not pollute 100% of the received packets in the sense of subspace distance. However, it also usually pollutes 90% of received packets which is a high error ratio. Even if the rank code and the subspace code are adopted, these existing schemes based on traditional block codes can correct corrupted errors no more than C/2 because of the limitation of the block coding where C is the max flow min cut. It is an agent to find a dense error correction method in random network coding. List decoding of subspace codes can correct C k -1 errors where k is the size of information. When C k is big, many errors in the sense of subspace distance can be corrected. However, the solution of list decoding is not unique. John Wright proposed a dense error correction technique based on L1 minimization, which can recover nearly 100% of the corrupted observations. In our proposal, the original packets are coded with John Wright's coding matrix, and then, the coded message is coded again with subspace codes. In the sink, the decoding procedures about list decoding of subspace codes and John Wright's scheme are performed. At last, the unique solution is achieved even though there are dense propagated errors in random network coding.

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Section: Existing Error-correcting Methods In Network Codingmentioning

confidence: 99%

Section: Existing Error-correcting Methods In Network Codingmentioning

confidence: 99%

Section: The Tough Problem About Error Propagation In Network Codingmentioning

confidence: 99%

“…The fourth is the list decoding. The representative work is [9]. Mahdavifar and Vardy [9] generate Silva and Kschischang code to list decoding.…”

Section: The Potential Viable Solutionsmentioning

confidence: 99%

Section: The Potential Viable Solutionsmentioning

confidence: 99%

See 3 more Smart Citations

The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

Zhang

Cai

Zhang

et al. 2018

J Wireless Com Network

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On the geometry of balls in the Grassmannian and list decoding of lifted Gabidulin codes

Rosenthal

Silberstein

Trautmann

2014

Des. Codes Cryptogr.

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The finite Grassmannian G q (k, n) is defined as the set of all k-dimensional subspaces of the ambient space F n q . Subsets of the finite Grassmannian are called constant dimension codes and have recently found an application in random network coding. In this setting codewords from G q (k, n) are sent through a network channel and, since errors may occur during transmission, the received words can possibly lie in G q (k ′ , n), where k ′ = k.In this paper, we study the balls in G q (k, n) with center that is not necessarily in G q (k, n). We describe the balls with respect to two different metrics, namely the subspace and the injection metric. Moreover, we use two different techniques for describing these balls, one is the Plücker embedding of G q (k, n), and the second one is a rational parametrization of the matrix representation of the codewords.With these results, we consider the problem of list decoding a certain family of constant dimension codes, called lifted Gabidulin codes. We describe a way of representing these codes by linear equations in either the matrix representation or a subset of the Plücker coordinates. The union of these equations and the linear and bilinear equations which arise from the description of the ball of a given radius provides an explicit description of the list of codewords with distance less than or equal to the given radius from the received word.

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Efficient Error Control Decoder Architectures for Noncoherent Random Linear Network Coding

Lin

Xie

Yan

2013

J Sign Process Syst

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Algebraic list-decoding on the operator channel

Cited by 32 publications

References 7 publications

The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

On the geometry of balls in the Grassmannian and list decoding of lifted Gabidulin codes

Efficient Error Control Decoder Architectures for Noncoherent Random Linear Network Coding

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