Over the last 50 years there have been an increasing number of applications of algebraic tools to solve problems in communications, in particular in the fields of error-control codes and cryptography.
Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared t
This is the concluding volume of the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, and this fact has been acknowledged here with the inclusion of an additional chapter on applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.
Originally published in 1998, Multiuser Detection provides a comprehensive treatment of the subject of multiuser digital communications. Multiuser detection is one of the most important areas in modern communications technology, and this self-contained book covers the whole field, starting with simple examples and progressing to complex applications. The author begins with a review of multiaccess communications, dealing in particular with code division multiple access (CDMA) channels. He then discusses simple and optimum approaches for demodulating CDMA channels, and deals with decorrelating and non-decorrelating linear multiuser detection schemes. He also covers in detail more advanced topics such as decision-driven multiuser detection, noncoherent multiuser detection, and array processing. The only prerequisites assumed are undergraduate-level probability, linear algebra, and digital communications. The book contains over 240 exercises.
The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommun
Based on time-tested course material, this authoritative text examines the key topics, advanced mathematical concepts, and novel analytical tools needed to understand modern communication and radar systems. It covers computational linear algebra theory, VLSI systolic algorithms and designs, practical aspects of chaos theory, and applications in beamforming and array processing, and uses a variety of CDMA codes, as well as acoustic sensing and beamforming algorithms to illustrate key concepts. Classical topics such as spectral analysis are also covered, and each chapter includes a wealth of homework problems. This is an invaluable text for graduate students in electrical and computer engineering, and an essential reference for practitioners in communications and radar engineering.
