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Linear network error correction coding
Guang X., Zhang Z., Springer Publishing Company, Incorporated, New York, NY, 2014. 107 pp. Type: Book (978-1-493905-87-4)
Date Reviewed: Dec 8 2014

Make a friend on Facebook, send an email to a friend or colleague, pay your credit card bills, or make a phone call--you are always using a computer network. They are the fundamental backbone of information and communications technology (ICT). They have come a long way and have a history of almost 70 years. But did you know that each node of the network is still either simply routing or replicating a data packet (store and forward)? A paradigm shift happened around 1999, when a new approach of network coding (NC) emerged. Any network has some source nodes (where information originates), some intermediate nodes (store and forward), and some sink nodes (final information destination). In NC, the information packets are mixed at the intermediate nodes. It is known that optimal information transmission can be achieved using NC. Over the last decade, NC has shown promise and applications in almost every scenario of computer networks. Suddenly, there are bursts of activities in this hot area and new research papers are coming out almost daily.

This short book on linear network error-correcting codes is a timely introductory review of a specific area of NC. The book considers the scenario when errors occur across the networks. That means some packets are corrupted. Since we are mixing the information at intermediate nodes, its effect is severe. Old techniques of classical coding theory do not work, so we need network error-correcting codes. Mainly, random errors, erasure errors, malicious attacks, and errors in headers have been considered.

The book focuses on acyclic networks (networks with no directed cycle) and single-source networks. It is divided into six chapters. Chapter 1 gives an overview of NC basic notations and terminology and ends with historical notes, which are quite useful. It also provides the basics of linear network coding. However, for beginners, it may be difficult to read chapter 1; it may require a second reading. Chapter 2 gives the basics of network error correction, showing how the idea of Hamming distance is useful in correcting network errors. It would have been nice to give at least a few examples; at present, this chapter is example free. A slightly different network error correction model is given in chapter 3, with its own idea of distance and weights. Chapter 4 generalizes well-known bounds of classical coding theory in network error correction, such as the Hamming bound and the Singleton bound. Chapter 4 ends with some construction algorithms of maximum distance separable (MDS) network error-correcting codes. Chapter 5 talks about random linear network error-correcting codes in a single section. For non-coherent network models (when the network topology and network code are unknown to the source and sink nodes) and for random linear network coding, the idea of subspace coding is considered in the last chapter. Using subspace distance, different coding theory bounds are described.

This short book could have been very useful for beginners if some missing examples had been provided. However, for subject experts, it does provide quick reading material on the main concepts in network error correction. Readers can quickly grasp the new research area and start working on problems of interest.

Reviewer:  Manish Gupta Review #: CR142989 (1503-0208)
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