by Raymond W Yeung, Shuo-Yen Robert Li (The Chinese University of Hong Kong, Hong Kong), Ning Cai (Xidian University, China) & Zhen Zhang (University of South California, USA)

NETWORK CODING THEORY

Network Coding Theory provides a tutorial on the basic of network coding theory. It presents the material in a transparent manner without unnecessarily presenting all the results in their full generality.
Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory.

The tutorial is divided into two parts. Part I is devoted to network coding for the transmission from a single source node to other nodes in the network. Part II deals with the problem under the more general circumstances when there are multiple source nodes each intending to transmit to a different set of destination nodes.

Network Coding Theory presents a unified framework for understanding the basic notions and fundamental results in network coding. It will be of interest to students, researchers and practitioners working in networking research.

Published by Now Publishers and marketed by World Scientific

Contents:

Introduction
Acyclic Networks
Cyclic Networks
Network Coding and Algebraic Coding
Acknowledgements
References

Readership: Postgraduates and professionals.

148pp Pub. date: Jun 2006
ISBN 978-1-933019-24-6(pbk)
1-933019-24-7(pbk)

by Robert M Gray (Stanford University, USA)

TOEPLITZ AND CIRCULANT MATRICES
A Review

Toeplitz and Circulant Matrices: A Review derives in a tutorial manner the fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.
Toeplitz and Circulant Matrices: A Review is written for students and practicing engineers in an accessible manner bringing this important topic to a wider audience.

Published by Now Publishers and marketed by World Scientific

Contents:

Introduction
The Asymptotic Behavior of Matrices
Circulant Matrices
Toeplitz Matrices
Matrix Operations on Toeplitz Matrices
Applications to Stochastic Time Series
Acknowledgements
References
Updates

Readership: Postgraduates and professionals.

84pp Pub. date: Dec 2005
ISBN 978-1-933019-23-9(pbk)
1-933019-23-9(pbk)

by Mung Chiang (Princeton University, USA)

GEOMETRIC PROGRAMMING FOR COMMUNICATION SYSTEMS

Recently Geometric Programming has been applied to study a variety of problems in the analysis and design of communication systems from information theory and queuing theory to signal processing and network protocols.
Geometric Programming for Communication Systems begins its comprehensive treatment of the subject by providing an in-depth tutorial on the theory, algorithms, and modeling methods of Geometric Programming. It then gives a systematic survey of the applications of Geometric Programming to the study of communication systems. It collects in one place various published results in this area, which are currently scattered in several books and many research papers, as well as to date unpublished results.

Geometric Programming for Communication Systems is intended for researchers and students who wish to have a comprehensive starting point for understanding the theory and applications of geometric programming in communication systems.

Published by Now Publishers and marketed by World Scientific

Contents:

Introduction
Geometric Programming
Applications in Communication Systems
Why is Geometric Programming Useful for Communication Systems
History of Geometric Programming
Some Proofs
Acknowledgements
References

Readership: Postgraduates and professionals.

154pp Pub. date: Jul 2005
ISBN 978-1-933019-09-3(pbk)
1-933019-09-3(pbk)

by Imre Csiszar (Renyi Institute of Mathematics, Hungary)
& Paul C Shields (University of Toledo, USA)

INFORMATION THEORY AND STATISTICS
A Tutorial

Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory.
The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.

Published by Now Publishers and marketed by World Scientific

Contents:

Preface
Preliminaries
Large Deviations, Hypothesis Testing
I-Projections
f-Divergence and Contingency Tables
Iterative Algorithms
Universal Coding
Redundancy Bounds Redundancy and the MDL Principle
Appendix: A Summary of Process Concepts
Historical Notes
References

Readership: Postgraduates and professionals.

115pp Pub. date: Dec 2004
ISBN 978-1-933019-05-5(pbk)
1-933019-05-0(pbk)


by Emanuele Viterbo (Politecnico di Torino, Italy)
& Frederique Oggier (Ecole Polytechnique Federale de Lausanne, Switzerland)

ALGEBRAIC NUMBER THEORY
AND CODE DESIGN FOR RAYLEIGH FADING CHANNELS

Algebraic number theory is gaining an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems.
Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been developed in the last ten years and many explicit code constructions based on algebraic number theory are now available.

Algebraic Number Theory and Code Design for Rayleigh Fading Channels provides an overview of algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory.

The basic facts of this mathematical field are illustrated by many examples and by the use of computer algebra freeware in order to make it more accessible to a large audience. This makes the book suitable for use by students and researchers in both mathematics and communications.

Published by Now Publishers and marketed by World Scientific

Contents:

Introduction
The Communication Problem
Some Lattice Theory
The Sphere Decoder
First Concepts in Algebraic Number Theory
Ideal Lattices
Rotated-Lattices Codes
Other Applications and Conclusions
References

Readership: Postgraduates and professionals.

88pp Pub. date: Dec 2004
ISBN 978-1-933019-07-9(pbk)
1-933019-07-7(pbk)

Mariano Giaquinta and Domenico Mucci

Maps into manifolds and currents: area and W1,2-, W1/2-, BV-energies

This volume deals with the problem of characterizing the limit points of sequences of smooth maps from the unit ball of Rn with values into a smooth boundaryless Riemannian manifold and with equibounded gintegral energiesh. After surveying some known results about Cartesian currents and graphs with finite area and finite boundary area, we do characterize, as in the title, weak limits of sequences of smooth maps with equibounded W1,2-, W1/2-, or BV-energies


Mariano Giaquinta and Domenico Mucci, Maps into manifolds and currents: area and W1,2-, W1/2-, BV-energies. Pisa, Edizioni della Normale 2006, ISBN 88-7642-158-0, pp. 409,