A Rank-Metric Approach to Error Control in Random Network Coding

The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of KÖtter and Kschischang. A large class of constant-dimension subspace codes is investigated. It is shown that codes in this class can be easily constructed from rank-metric codes, while preserving their distance properties. Moreover, it is shown that minimum distance decoding of such subspace codes can be reformulated as a generalized decoding problem for rank-metric codes where partial information about the error is available. This partial information may be in the form of erasures (knowledge of an error location but not its value) and deviations (knowledge…

• CD
  Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
• NS
  Natural Sciences and Engineering Research Council of Canada