Network Error Correction Model

In this chapter, we focus on the basic model of linear network error correction (LNEC). First, the basic network error correction model is established over linear network coding. And then, like classical coding theory, the distance between two received vectors at each sink node is proposed to characterize the discrepancy of these two vectors. In particular, the distance between two codewords is of importance in LNEC coding. We further define the weight of error vectors in order to measure their seriousness. In addition, similar to the minimum distance decoding principle for classical error-correcting codes, we can also apply the minimum distance decoding principle to LNEC codes at each sink node, but distinct distances used. For this decoding principle, it is shown that the minimum distance of a LNEC code at each sink node can fully characterize its error-detecting, error-correcting, and erasure-error-correcting capabilities with respect to the sink node.