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

Abstract

The problem of error control in random network coding is considered, and a formulation of the problem is given in terms of rank-metric codes. This formulation allows many of the tools developed for rank-metric codes to be applied to random network coding. A random network code induces a generalized decoding problem for rank-metric codes in which the channel may supply partial information about the error in the form of erasures (knowledge of an error location not its values) and deviations (knowledge of an error value but not its location).