GMD-Based Erasure-and-Error Decoding of Lifted MRD Code for Network Error Correction

The Lifted MRD (Maximum Rank Distance) code was introduced by Silva et al. to correct link errors and erasures for network coding systems. It achieves the generalized asymptotic Singleton bound for network error correction codes, and was shown to be equivalent to the Koetter-Kschischang code. However, in wireless network coding, undetected link errors that occur early in the network may accumulate and propagate beyond the decoding capability of the Lifted MRD code at the destination node. In this paper, we address this problem by a few strategies: detect and track possible error packets as erasure packets as they propagate through the network, reverse the error propagation process at the destination node by exploiting knowledge of the erasure packet positions, and double the MRD decoding capability by using erasure-and-error decoding. Algorithms to implement the above strategies are designed for low network overhead and low computational complexity. Simulation results show that the proposed scheme significantly improves the reliability of network coding over unreliable wireless links.