Using Rank-Metric Codes for Error Correction in Random Network Coding

Abstract

It is shown that the error correction problem in random network coding is closely related to a generalized decoding problem for rank-metric codes. This result enables many of the rich tools devised for the rank metric to be naturally applied to random network coding. The generalized decoding problem introduced in this paper allows partial information about the error to be supplied. This partial information can be either in the form of erasures (knowledge of an error location but not its value) or deviations (knowledge of an error value but not its location). For Gabidulin codes, an efficient decoding algorithm is proposed that can correct e errors, mu erasures and v deviations, provided 2isin + mu + v les d - 1, where d is the minimum distance of the code.