Multishot codes for network coding: Bounds and a multilevel construction

Nóbrega, Roberto W.; Uchôa-Filho, Bartolomeu F.

doi:10.1109/isit.2009.5205750

Cited by 33 publications

(67 citation statements)

References 12 publications

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“…This work presented a bit more explicit multilevel construction of multishot codes for network coding than that introduced in [5]. A natural question arises: how good are the proposed codes?…”

Section: Discussionmentioning

confidence: 99%

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Multishot Codes for Network Coding Using Rank-Metric Codes

Nóbrega

Uchôa-Filho

2010

2010 Third IEEE International Workshop on Wireless Network Coding

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108

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The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a previous work we proposed a general construction of multishot codes for this channel based on the multilevel coding theory. Herein we apply this construction to the rank-metric space, obtaining multishot rank-metric codes which, by lifting, can be converted to codes for the aforementioned channel. We also adapt well-known encoding and decoding algorithms to the considered situation.

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Section: Discussionmentioning

confidence: 99%

“…For a simple example in which a multishot code is capable of detecting more errors when compared with the best one could do by simply repeating one-shot codes, we point the reader to [5].…”

Section: A Motivationmentioning

confidence: 99%

Multishot Codes for Network Coding Using Rank-Metric Codes

Nóbrega

Uchôa-Filho

2010

2010 Third IEEE International Workshop on Wireless Network Coding

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108

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“…The ball centered at V ∈ P(F m q ) n with radius r is defined as respectively. From [10] we know that the volume of B r (V) only depends on k = (dim V 1 , dim V 2 , ..., dim V n ) and…”

Section: B Sphere Packing Bound For General Lobcsmentioning

confidence: 99%

An upper bound on broadcast subspace codes

Pang¹,

Honold²

2011

2011 6th International ICST Conference on Communications and Networking in China (CHINACOM)

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“…Correction of link errors in multishot network coding (see Fig. 1) was first investigated in [24], [25]. As noted in these works, the ℓ-shot case can be treated as a 1-shot case with number of outgoing links at the source n = ℓn ′ .…”

Section: Introductionmentioning

confidence: 99%

“…To circumvent these issues, the authors of [24], [25] provide a multilevel construction that improves the error-correction capability of trivial concatenations of 1-shot Gabidulin codes, with lower decoding complexity than an ℓ-shot Gabidulin code, although without achieving the maximum secret message size.…”

Section: Introductionmentioning

confidence: 99%

Reliable and Secure Multishot Network Coding Using Linearized Reed-Solomon Codes

Martínez-Peñas

Kschischang

2019

IEEE Trans. Inform. Theory

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Multishot network coding is considered in a worstcase adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to t links, erase up to ρ packets, and wire-tap up to µ links, all throughout ℓ shots of a linearly-coded network. Assuming no knowledge of the underlying linear network code (in particular, the network topology and underlying linear code may be random and change with time), a coding scheme achieving zero-error communication and perfect secrecy is obtained based on linearized Reed-Solomon codes. The scheme achieves the maximum possible secret message size of ℓn ′ − 2t − ρ − µ packets for coherent communication, where n ′ is the number of outgoing links at the source, for any packet length m ≥ n ′ (largest possible range). By lifting this construction, coding schemes for non-coherent communication are obtained with information rates close to optimal for practical instances. The required field size is q m , where q > ℓ, thus q m ≈ ℓ n ′ , which is always smaller than that of a Gabidulin code tailored for ℓ shots, which would be at least 2 ℓn ′ . A Welch-Berlekamp sum-rank decoding algorithm for linearized Reed-Solomon codes is provided, having quadratic complexity in the total length n = ℓn ′ , and which can be adapted to handle not only errors, but also erasures, wiretap observations and non-coherent communication. Combined with the obtained field size, the given decoding complexity is of O(n ′4 ℓ 2 log(ℓ) 2 ) operations in F2, whereas the most efficient known decoding algorithm for a Gabidulin code has a complexity of O(n ′3.69 ℓ 3.69 log(ℓ) 2 ) operations in F2, assuming a multiplication in a finite field F costs about log(|F|) 2 operations in F2.

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Multishot codes for network coding: Bounds and a multilevel construction

Cited by 33 publications

References 12 publications

Multishot Codes for Network Coding Using Rank-Metric Codes

Multishot Codes for Network Coding Using Rank-Metric Codes

An upper bound on broadcast subspace codes

Reliable and Secure Multishot Network Coding Using Linearized Reed-Solomon Codes

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