Describes various wavelet image coding systems that use set partitioning primarily, such as SBHP (Subband Block Hierarchical Partitioning), SPIHT, and EZBC (Embedded Zero-Block Coder).
The biggest challenge facing many game programmers is completing their game. Most game projects fizzle out, overwhelmed by the complexity of their own code. Game Programming Patterns tackles that exact problem. Based on years of experience in shipped AAA titles, this book collects proven patterns to untangle and optimize your game, organized as independent recipes so you can pick just the patterns you need. You will learn how to write a robust game loop, how to organize your entities using components, and take advantage of the CPUs cache to improve your performance. You'll dive deep into how scripting engines encode behavior, how quadtrees and other spatial partitions optimize your engine, and how other classic design patterns can be used in games.
Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a one-stop reference on the results and research activities of set partitions from 1500 A.D. to today. Each chapter gives historical perspectives and contrasts different approaches, including generating functions, kernel method, block decomposition method, generating tree, and Wilf equivalences. Methods and definitions are illustrated with worked examples and MapleTM code. End-of-chapter problems often draw on data from published papers and the author’s extensive research in this field. The text also explores research directions that extend the results discussed. C++ programs and output tables are listed in the appendices and available for download on the author’s web page.
''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--
The attitudes behind coded modulation mark a paradigm shift that occurred after 1975, which led to a major awakening of interest in coding theory and practice."--BOOK JACKET.
The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.
When the 50th anniversary of the birth of Information Theory was celebrated at the 1998 IEEE International Symposium on Informa tion Theory in Boston, there was a great deal of reflection on the the year 1993 as a critical year. As the years pass and more perspec tive is gained, it is a fairly safe bet that we will view 1993 as the year when the "early years" of error control coding came to an end. This was the year in which Berrou, Glavieux and Thitimajshima pre sented "Near Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes" at the International Conference on Communications in Geneva. In their presentation, Berrou et al. claimed that a combi nation of parallel concatenation and iterative decoding can provide reliable communications at a signal to noise ratio that is within a few tenths of a dB of the Shannon limit. Nearly fifty years of striving to achieve the promise of Shannon's noisy channel coding theorem had come to an end. The implications of this result were immediately apparent to all -coding gains on the order of 10 dB could be used to dramatically extend the range of communication receivers, increase data rates and services, or substantially reduce transmitter power levels. The 1993 ICC paper set in motion several research efforts that have permanently changed the way we look at error control coding.