Some Recent Progresses in Network Error Correction Coding Theory

In this talk, we summarize some of our recent works on network error correction coding theory. Our works mainly focus on issues related to the goal of pushing the theory of network error correction coding to applications. In (Zhen Zhang, 2006), we define the minimum distance of a linear network error correction code and prove that it plays the same role as it does in classical coding theory, we propose the concept of statistical decoding and develop a statistical algorithm for decoding packet network error correction codes. In (S. Yang et al.), we study the characterization of network error correction capabilities in the general case which includes nonlinear codes. In (H. Bali et al., 2007), 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. In (X. Yan et al.), we study the possibility of decoding network error correction codes beyond its error correction capability, and analyze the decoding complexity of statistical decoding algorithms. In (H. Bali and Z. Zhang), we propose some techniques for reducing overhead of network error correction coding. This is a key issue for pushing network error correction codes to applications. In (Zhen Zhang), we propose a hybrid network error correction coding systems combining both the network error correction codes in the space domain and the classical error correction codes in the time domain and analyze its performance.