This book, written by experts from universities and major research laboratories, addresses the hot topic of network coding, a powerful scheme for information transmission in networks that yields near-optimal throughput. It introduces readers to this striking new approach to network coding, in which the network is not simply viewed as a mechanism for delivering packets, but rather an algebraic structure named the subspace, which these packets span. This leads to a new kind of coding theory, employing what are called subspace codes. The book presents selected, highly relevant advanced research output on: Subspace Codes and Rank Metric Codes; Finite Geometries and Subspace Designs; Application of Network Coding; Codes for Distributed Storage Systems. The outcomes reflect research conducted within the framework of the European COST Action IC1104: Random Network Coding and Designs over GF(q). Taken together, they offer communications engineers, R&D engineers, researchers and graduate students in Mathematics, Computer Science, and Electrical Engineering a comprehensive reference guide to the construction of optimal network codes, as well as efficient encoding and decoding schemes for a given network code.

Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.

Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, yet they are rarely covered in the graduate curricula. This book provides new researchers in academia and industry with informal introductions to the basic ideas of these topics, including pointers to further reading.

This book constitutes the proceedings of the 32nd International Workshop on Combinatorial Algorithms which was planned to take place in Ottawa, ON, Canada, in July 2021. Due to the COVID-19 pandemic the conference changed to a virtual format. The 38 full papers included in this book together with 2 invited talks were carefully reviewed and selected from 107 submissions. They focus on algorithms design for the myriad of combinatorial problems that underlie computer applications in science, engineering and business. Chapter “Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

The idea of this book comes from the observation that sensor networks represent a topic of interest from both theoretical and practical perspectives. The title und- lines that sensor networks offer the unique opportunity of clearly linking theory with practice. In fact, owing to their typical low-cost, academic researchers have the opportunity of implementing sensor network testbeds to check the validity of their theories, algorithms, protocols, etc., in reality. Likewise, a practitioner has the opportunity of understanding what are the principles behind the sensor networks under use and, thus, how to properly tune some accessible network parameters to improve the performance. On the basis of the observations above, the book has been structured in three parts:PartIisdenotedas“Theory,”sincethetopicsofits vechaptersareapparently “detached” from real scenarios; Part II is denoted as “Theory and Practice,” since the topics of its three chapters, altough theoretical, have a clear connection with speci c practical scenarios; Part III is denoted as “Practice,” since the topics of its ve chapters are clearly related to practical applications.

This book provides a consolidated view of the various network coding techniques to be implemented at the design of the wireless networks for improving its overall performance. It covers multiple sources communicating with multiple destinations via a common relay followed by network coded modulation schemes for multiple access relay channels. Performance of the distributed systems based on distributed convolutional codes with network coded modulation is covered including a two-way relay channel (TWRC). Two MIF protocols are proposed including derivation of signal-to-noise ratio (SNR) and development of threshold of the channel conditions of both. Features: Systematically investigates coding and modulation for wireless relay networks. Discusses how to apply lattice codes in implementing lossless communications and lossy source coding over a network. Focusses on theoretical approach for performance optimization. Includes various network coding strategies for different networks. Reviews relevant existing and ongoing research in optimization along with practical code design. This book aims at Researchers, Professionals and Graduate students in Networking, Communications, Information, Coding Theory, Theoretical Computer Science, Performance Analysis and Resource Optimization, Applied Discrete Mathematics, and Applied Probability.

This book constitutes the refereed proceedings of the 18th IMA International Conference on Cryptography and Coding, IMACC 2021, held in December 2021. Due to COVID 19 pandemic the conference was held virtually. The 14 papers presented were carefully reviewed and selected from 30 submissions. The conference focuses on a diverse set of topics both in cryptography and coding theory.

Network Coding Applications looks at how ideas from network coding can have an impact on a number of new applications. It explains what network coding is, explores what its benefits are, and how much it costs to design and operate networks implementing network coding

This Festschrift volume contains the proceedings of the conference Mathematical Methods in Computer Science, MMICS 2008, which was held during December 17-19, 2008, in Karlsruhe, Germany, in memory of Thomas Beth. The themes of the conference reflected the many interests of Thomas Beth. Although, these interests might seem diverse, mathematical methods and especially algebra as a language constituted the common denominator of all of his scientific achievements. The 12 contributed talks presented were carefully selected from 30 submissions and cover the topics cryptography, designs, quantum computing, algorithms, and coding theory. Furthermore, this volume contains two invited talks held at the conference. One focuses on the area of coding theory and symbolic computation, an area especially appreciated by Thomas Beth, because it combines algebra and algorithmics. The other one discusses quantum information, which again was a focus of Thomas Beth’s research.