Some Key Problems in Network Error Correction Coding Theory

Abstract

This paper summarizes our recent works on network error correction codes. We study basic properties of linear network error correction codes in the single source multicast case. We define the minimum distance of a network error correction code which plays the same role as it does in classical coding theory. We construct MDS codes and give sufficient conditions for its existence. We propose basic decoding algorithms and analyze their performance. We propose an improved upper bound for the failure probability of random network code and use it to analyze the performance of randomized network error correction codes [9], [10]. We study the possibility of decoding beyond error correction capability. We propose a hybrid network error correction coding systems. An extensive performance analysis of this coding system is reported in a separate paper.