Convolutional codes in rank metric with application to random network coding

Antonia Wachter-Zeh, Markus Stinner, Vladimir Sidorenko

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a noncoherent multishot network, where the unknown and time-variant network is used several times. In order to create dependence between the different shots, particular convolutional codes in rank metric are used. These codes are so-called (partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one. First, distance measures for convolutional codes in rank metric are shown and two constructions of (P)UM codes in rank metric based on the generator matrices of maximum rank distance codes are presented. Second, an efficient error-erasure decoding algorithm for these codes is presented. Its guaranteed decoding radius is derived and its complexity is bounded. Finally, it is shown how to apply these codes for error correction in random linear and affine network coding.

Original languageEnglish
Article number7090997
Pages (from-to)3199-3213
Number of pages15
JournalIEEE Transactions on Information Theory
Volume61
Issue number6
DOIs
Publication statusPublished - 1 Jun 2015
Externally publishedYes

Keywords

  • (partial) unit memory codes
  • convolutional codes
  • Gabidulin codes
  • network coding
  • rank-metric codes

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