Beyond routing via Network Coding: An overview of fundamental information-theoretic results

Since the pioneering research work of Ahlswede et al. in 2000, Network Coding (NC) has rapidly emerged as a major research area in electrical engineering and computer science due to its wide applicability to communication through real networks. The many contributions available in the literature to date, ranging from pure theoretical studies on fundamental limits to practical experimentations in real-world environments, offer a clear evidence that the shift in paradigm envisaged by NC might revolutionize the way we manage, operate, and understand the organization of networks. NC allows intermediate nodes of communication networks to combine the information received from multiple links for subsequent transmissions, and offer a powerful and efficient generalization to network information delivery via routing, where network nodes simply store and forward data, and processing is only accomplished at the end nodes. In this paper, we have a twofold objective: i) first, we summarize fundamental information-theoretic results, which, since their publication, have been representing the foundation for all subsequent research in this field, and ii) then, we introduce and summarize the latest results related to the analysis, design, and optimization of the so-called network error correction coding problem, which is instrumental for the effective use of NC over lossy, e.g., wireless networks.