Theory and Applications of Network Error Correction Coding

Network error correction coding (NEC) has attracted a lot of attention in recent years because of its potential usefulness in network communications. Several kinds of errors may occur in communication networks using network coding. This includes random errors, erasures, and errors caused by attacks from malicious nodes. The main goal of the theory of NEC is to deal with these errors efficiently. Two kinds of network models have been considered in network coding theory: coherent and noncoherent networks. A network is called coherent if network characteristics are known to senders and receivers, and called noncoherent if they are unknown. Although both scenarios are theoretically interesting, the noncoherent network model fits better to the requirements in most applications. So far, there are two lines of research in the theory of NEC. One approach follows the classical method by representing messages by sequences and the other approach uses the theory of rank metric codes for network error correction by representing messages by subspaces. Following both approaches, basic theories have been developed. This includes the formulation of channel models, the characterization of error correction/detection capabilities for various kinds of errors, the derivation of bounds for NECs, the study of existence and constructions of optimal codes, the development of encoding and decoding techniques, and the design of code suitable for real applications. In this paper, we summarize some important contributions in this research direction.