Solomon W. Golomb

The field of information theory and coding has developed into a vibrant and dynamic discipline that has revolutionized all aspects of information handling, storage, and communication. It has transformed our understanding of information in areas as diverse as biology, linguistics, and philosophy. This highly readable text provides a clear exposition of the fundamentals of discrete information theory and coding. The authors present in-depth discussions of the implications, interpretations, and examples of these basic principles, covering subjects that include information measures, Shannon's channel capacity/coding theorems, and source and channel coding concepts. Focusing on the results of practical applications of the material, the book features the use of Secret Agent 00111, a recurring character who solves information problems for a living and provides a concrete context for abstract theories; thorough treatment of noiseless self-synchronizing codes not found in any other book; a clear explanation of the Lempel-Ziv algorithm; problem sets used successfully with students at the University of Southern California. This instructive resource is written for readers with a knowledge of basic calculus and the elementary concepts of discrete probability theory. Basic Concepts in Information Theory and Coding makes an excellent and accessible introduction to the field for researchers, professionals, and graduate-level students in communication systems, computer science, and electrical systems science.

Inspiring popular video games like Tetris while contributing to the study of combinotorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of polyominoes, incorporoting the most important recent developments. Deceptively simple, polyominoes are a collection of squares joined together along their edges. But how many different polyominoes can you make with 5 squares, 6 squares, n squares? If you have a set of pentominoes (shapes consisting of five squares) could you cover a rectangle with them? What would happen if you had cubes instead of squares? Could you pack a box with them? Posing problems and giving answers along the way, Golomb invites the reader to play with these mathematical structures and develop on understanding of their extraordinary properties. In this new edition, he addresses, for example, the properties of octominoes and enneominoes and the problem of how to cover a donut with polyominoes. An extensive bibliography has been included to guide the reader to other interesting mathematical conundrums and to more advanced mathematical theories of polyominoes. For professional mathematicians and amateurs seeking further challenge, the author offers a host of new problems that remain to be solved.

This book provides a comprehensive, up-to-date description of the methodologies and the application areas, throughout the range of digital communication, in which individual signals and sets of signals with favorable correlation properties play a central role. The necessary mathematical background is presented to explain how these signals are generated, and to show how they satisfy the appropriate correlation constraints. All the known methods to obtain balanced binary sequences with two-valued autocorrelation, many of them only recently discovered, are presented in depth. The authors treat important application areas including: Code Division Multiple Access (CDMA) signals, such as those already in widespread use for cell-phone communication, and planned for universal adoption in the various approaches to 'third-generation'(3G) cell-phone use; systems for coded radar and sonar signals; communication signals to minimize mutual interference ('cross-talk') in multi-user environments; and pseudo-random sequence generation for secure authentication and for stream cipher cryptology.