Network Coding, Algebraic Coding, and Network Error Correction

This paper discusses the relation between network coding, (classical) algebraic coding, and network error correction. In the first part, we clarify the relation between network coding and algebraic coding. By showing that the Singleton bound in algebraic coding theory is a special case of the Maxflow Min-cut bound in network coding theory, we formally establish that linear multicast and its stronger versions are network generalizations of a maximum distance separation (MDS) code. In the second part, we first give an overview of network error correction, a paradigm for error correction on networks which can be regarded as an extension of classical point-to-point error correction. Then by means of an example, we show that an upper bound in terms of classical errorcorrecting codes is not tight even for a simple class of networks called regular networks. This illustrates the complexity involved in the construction of network error-correcting codes.