Algorithms for computation are a central part of both digital signal pro cessing and decoders for error-control codes and the central algorithms of the two subjects share many similarities. Each subject makes extensive use of the discrete Fourier transform, of convolutions, and of algorithms for the inversion of Toeplitz systems of equations. Digital signal processing is now an established subject in its own right; it no longer needs to be viewed as a digitized version of analog signal process ing. Algebraic structures are becoming more important to its development. Many of the techniques of digital signal processing are valid in any algebraic field, although in most cases at least part of the problem will naturally lie either in the real field or the complex field because that is where the data originate. In other cases the choice of field for computations may be up to the algorithm designer, who usually chooses the real field or the complex field because of familiarity with it or because it is suitable for the particular application. Still, it is appropriate to catalog the many algebraic fields in a way that is accessible to students of digital signal processing, in hopes of stimulating new applications to engineering tasks.

Digital Signal Processing: Applications to Communications and Algebraic Coding Theories discusses the design of computationally efficient digital signal processing algorithms over finite fields and the relation of these algorithms to algebraic error-correcting codes. The book provides chapters that cover such topics as signal processing techniques employed for modeling, synthesis, and analysis; systems of bilinear forms; efficient finite field algorithms; the design and study of long length cyclic convolutions and some preliminary results on their relation to linear codes; the study of the algebraic structure of the class of linear codes obtained from bilinear cyclic and aperiodic convolution algorithms over the finite field of interest; and the concept of a generalized hybrid Automatic- Repeat-Request (ARQ) scheme for adaptive error control in digital communication systems. Engineers, mathematicians, and computer scientists will find the text invaluable.

Codes, Curves, and Signals: Common Threads in Communications is a collection of seventeen contributions from leading researchers in communications. The book provides a representative cross-section of cutting edge contemporary research in the fields of algebraic curves and the associated decoding algorithms, the use of signal processing techniques in coding theory, and the application of information-theoretic methods in communications and signal processing. The book is organized into three parts: Curves and Codes, Codes and Signals, and Signals and Information. Codes, Curves, and Signals: Common Threads in Communications is a tribute to the broad and profound influence of Richard E. Blahut on the fields of algebraic coding, information theory, and digital signal processing. All the contributors have individually and collectively dedicated their work to R. E. Blahut. Codes, Curves, and Signals: Common Threads in Communications is an excellent reference for researchers and professionals.

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. More recently, broader applications have emerged, requiring quite sophisticated algebra - for example, the Alamouti scheme in MIMO communications is just Hamilton's quaternions in disguise and has spawned the use of PhD-level algebra to produce generalizations. Likewise, in the absence of credible alternatives, the industry has in many cases been forced to adopt elliptic curve cryptography. In addition, algebra has been successfully applied to problems in signal processing such as face recognition, biometrics, control design, and signal design for radar. This book introduces the reader to the algebra they need to appreciate these developments and to various problems solved by these techniques.

The need to transmit and store massive amounts of data reliably and without error is a vital part of modern communications systems. Error-correcting codes play a fundamental role in minimising data corruption caused by defects such as noise, interference, crosstalk and packet loss. This book provides an accessible introduction to the basic elements of algebraic codes, and discusses their use in a variety of applications. The author describes a range of important coding techniques, including Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. Throughout the book, mathematical theory is illustrated by reference to many practical examples. The book was first published in 2003 and is aimed at graduate students of electrical and computer engineering, and at practising engineers whose work involves communications or signal processing.

One of the most important key technologies for digital communication systems as well as storage media is coding theory. It provides a means to transmit information across time and space over noisy and unreliable communication channels. Coding Theory: Algorithms, Architectures and Applications provides a concise overview of channel coding theory and practice, as well as the accompanying signal processing architectures. The book is unique in presenting algorithms, architectures, and applications of coding theory in a unified framework. It covers the basics of coding theory before moving on to discuss algebraic linear block and cyclic codes, turbo codes and low density parity check codes and space-time codes. Coding Theory provides algorithms and architectures used for implementing coding and decoding strategies as well as coding schemes used in practice especially in communication systems. Feature of the book include: Unique presentation-like style for summarising main aspects Practical issues for implementation of coding techniques Sound theoretical approach to practical, relevant coding methodologies Covers standard coding schemes such as block and convolutional codes, coding schemes such as Turbo and LDPC codes, and space time codes currently in research, all covered in a common framework with respect to their applications. This book is ideal for postgraduate and undergraduate students of communication and information engineering, as well as computer science students. It will also be of use to engineers working in the industry who want to know more about the theoretical basics of coding theory and their application in currently relevant communication systems

DIGITAL SIGNAL PROCESSING Understand the future of signal processing with the latest edition of this groundbreaking text Signal processing is a key aspect of virtually all engineering fields. Digital techniques enormously expand the possible applications of signal processing, forming a part of not only conventional engineering projects but also data analysis and artificial intelligence. There are considerable challenges raised by these techniques, however, as the gulf between theory and practice can be wide; the successful integration of digital signal processing techniques requires engineers capable of bridging this gulf. For years, Digital Signal Processing has met this need with a comprehensive guide that consistently connects abstract theory with practical applications. Now fully updated to reflect the most recent developments in this crucial field, the tenth* edition of this seminal text promises to foster a broader understanding of signal processing among a new generation of engineers and researchers. Readers of the new edition of Digital Signal Processing will also find: Exercises at the end of each chapter to reinforce key concepts A new chapter covering digital signal processing for neural networks Handy structure beginning with undergraduate-level material before moving to more advanced concepts in the second half Digital Signal Processing is a must-own for students, researchers, and industry professionals in any of the hundreds of fields and subfields that make use of signal processing algorithms. *This is the English language translation of the French original Traitement Numérique du Signal 10th edition by Maurice Bellanger © Dunod 2022 and is the 4th edition in English.