Communications in Information and Systems
Volume 6 (2006)
Network Error Correction, I: Basic Concepts and Upper Bounds
Pages: 19 – 35
Error correction in existing point-to-point communication networks is done on a link-by-link basis, which is referred to in this paper as classical error correction. Inspired by network coding, we introduce in this two-part paper a new paradigm called network error correction. The theory thus developed subsumes classical algebraic coding theory as a special case. In Part I, we discuss the basic concepts and prove the network generalizations of the Hamming bound and the Singleton bound in classical algebraic coding theory. By studying a few elementary examples, the relation between network error correction and classical error correction is investigated.
Network coding; multicast; error correction; algebraic coding; Hamming bound; Singleton bound
2010 Mathematics Subject Classification
Primary 94B60. Secondary 94A05.