Rank-Metric Codes for Priority Encoding Transmission with Network Coding

2007 ◽  
Author(s):  
Danilo Silva ◽  
Frank R. Kschischang
Keyword(s):  
Network Coding ◽  
Rank Metric ◽  
Rank Metric Codes

scholarly journals Degenerate flag varieties in network coding

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ghislain Fourier ◽  
Gabriele Nebe
Keyword(s):  
Network Coding ◽  
Affine Space ◽  
Linear Subspace ◽  
Flag Varieties ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
Information Set ◽  
Degenerate Flag Varieties

<p style='text-indent:20px;'>Building upon the application of flags to network coding introduced in [<xref ref-type="bibr" rid="b6">6</xref>], we develop a variant of this coding technique that uses degenerate flags. The information set is a metric affine space isometric to the space of upper triangular matrices endowed with the flag rank metric. This suggests the development of a theory for flag rank metric codes in analogy to the rank metric codes used in linear subspace coding.</p>

On interleaved rank metric codes

2020 ◽  
Author(s):  
Vladimir Sidorenko ◽  
Wenhui Li ◽  
Gerhard Kramer
Keyword(s):  
Rank Metric ◽  
Rank Metric Codes

Secret Error-Correcting Network Coding against Eavesdropping and Pollution Attacks

2012 ◽  
Vol 457-458 ◽  
pp. 1499-1507 ◽  
Author(s):  
Si Guang Chen ◽  
Meng Wu ◽  
Wei Feng Lu
Keyword(s):  
Network Coding ◽  
Necessary Condition ◽  
Information Theoretic ◽  
Transmitted Information ◽  
Information Theoretic Security ◽  
Secret Communication ◽  
Pollution Attacks ◽  
Rank Metric Codes ◽  
Shared Secret ◽  
And Performance

In this work we consider the problem of designing a secret error-correcting network coding scheme against an adversary that can re-select the tapping links in different time slot and inject z erroneous packets into network. We first derive a necessary condition for keeping the transmitted information secret from the adversary, while the network is only subject to the eavesdropping attack. We then design an error-correcting scheme by combining the rank-metric codes with shared secret model, which can decode the transmitted information correctly provided a sufficiently large q. With that, a secret error-correcting network coding is proposed by combining this error-correcting scheme with secret communication. We show that under the requirement of communication can achieve a rate of packets. Moreover, it ensures that the communicated information is reliable and information-theoretic security from the adversary. In particular, the requirement of packet length is not as large as the required in [12]. Finally, the security and performance analyses illustrate the characteristics of our scheme.

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