Error Correction Capability of Random Network Error Correction Codes

In this paper, we study the error correction capability of random linear network error correction codes (Z. Zhang, 2006). We derive bounds on the probability mass function of the minimum distance of a random network error correction code and the field size required for the existence of a network error correction code with a given degradation, which is the difference between the highest possible minimum distance in the Singleton bound and the minimum distance of the code. The main tool that we use to study these problems is an improved bound on the failure probability of random linear network codes that at one or more sinks, the source messages are not decodable. This problem was originally studied in T. Ho et al. (2006).