On error control codes for random network coding

Abstract

The random network coding approach is an effective technique for linear network coding, however it is highly susceptible to errors and adversarial attacks. Recently Kotter and Kschischang introduced the operator channel, where the inputs and outputs are subspaces of a given vector space, showing that this is a natural transmission model in noncoherent random network coding. A suitable metric, defined for subspaces: d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> (U, V ) = dim U + dim V - 2 dim(U cap V), gives rise to the notion of codes capable of correcting different kinds of errors (like packet errors, erasures etc.) in noncoherent random network coding. In this paper we continue the study of coding for operator channels started. We consider codes correcting insertions/deletions (dimension enlargement and dimension reduction respectively). Bounds and constructions for those codes are presented.