Codes, Curves, and Signals: Common Threads in Communications

264 Pages·1998·8.671 MB·English

by  Tom Høholdt (auth.), Alexander Vardy (eds.)

CODES, CURVES, AND SIGNALS
Common Threads in Communications
The Kluwer International Series in
Engineering and Computer Science
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Consulting Editor
ROBERT G. GALLAGER
Other books in the series:
PERSPECTIVES IN SPREAD SPECTRUM, Amer A. Hassan, John E. Hershey, and Gary
J. Saulnier; ISBN: 0-7923-8265-X
WIRELESS PERSONAL COMMUNICATIONS: Advances in Coverage and Capacity, Jeffrey
H. Reed, Theodore S. Rappaport, Brian D. Woerner; ISBN: 0-7923-9788-6
ASYMPTOTIC COMBINATORIAL CODING THEORY, Volodia Blinovsky; ISBN:
0-7923-9988-9
PERSONAL AND WIRELESS COMMUNICATIONS: Digital Technology and Standards, Kun
II Park; ISBN: 0-7923-9727-4
WIRELESS INFORMATION NETWORKS: Architecture, Resource Managment, and Mobile
Data, Jack M. Holtzman; ISBN: 0-7923-9694-4
DIGITAL IMAGE COMPRESSION: Algorithms and Standards, Weidong Kou; ISBN:
0-7923-9626-X
CONTROL AND PERFORMANCE IN PACKET, CIRCUIT, AND ATM NETWORKS, XueDao Gu,
Kazem Sohraby and Dhadesugoor R. Vaman; ISBN: 0-7923-9625-1
DISCRETE STOCHASTIC PROCESSES, Robert G. Gallager; ISBN: 0-7923-9583-2
WIRELESS PERSONAL COMMUNICATIONS: Research Developments, Brian D. Woerner,
Theodore S. Rappaport and Jeffrey H. Reed; ISBN: 0-7923-9555-7
PLANNING AND ARCHITECTURAL DESIGN OF INTEGRATED SERVICES DIGITAL NETWORKS,
A. Nejat Ince, Dag Wilhelmsen and Bllent Sankur; ISBN: 0-7923-9554-9
WIRELESS INFRARED COMMUNICATIONS, John R. Barry; ISBN: 0-7923-9476-3
COMMUNICATIONS AND CRYPTOGRAPHY: Two sides 0/ One Tapestry, Richard E.
Blahut, Daniel J. Costello, Jr., Ueli Maurer and Thomas Mittelholzer; ISBN:
0-7923-9469-0
WIRELESS AND MOBILE COMMUNICATIONS, Jack M. Holtzman and David J. Goodman;
ISBN: 0-7923-9464-X
INTRODUCTION TO CONVOLUTIONAL CODES WITH APPLICATIONS, Ajay Dholakia; ISBN:
0-7923-9467-4
CODED-MODULATION TECHNIQUES FOR FADING CHANNELS, S. Hamidreza Jamali, and
Tho Le-Ngoc; ISBN: 0-7923-9421-6
WIRELESS PERSONAL COMMUNICATIONS: Trends and Challenges, Theodore S.
Rappaport, Brian D. Woerner, Jeffrey H. Reed; ISBN: 0-7923-9430-5
ELLIPTIC CURVE PUBLIC KEY CRYPTOSYSTEMS, Alfred Menezes; ISBN: 0-7923-9368-6
SATELLITE COMMUNICATIONS: Mobile and Fixed Services, Michael Miller, Branka
Vucetic and Les Berry; ISBN: 0-7923-9333-3
WIRELESS COMMUNICATIONS: Future Directions, Jack M. Holtzman and David J.
Goodman; ISBN: 0-7923-9316-3
DISCRETE-TIME MODELS FOR COMMUNICATION SYSTEMS INCLUDING ATM, Herwig Bruneel
and Byung G. Kim; ISBN: 0-7923-9292-2
APPLICATIONS OF FINITE FIELDS, Alfred J. Menezes, Ian F. Blake, Xu Hong Gao,
Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian; ISBN: 0-7923-9282-5
WIRELESS PERSONAL COMMUNICATIONS, Martin J. Feuerstein, Theodore S.
Rappaport; ISBN: 0-7923-9280-9
SEQUENCE DETECTION FOR HIGH-DENSITY STORAGE CHANNEL, Jaekyun Moon, L.
Richard Carley; ISBN: 0-7923-9264-7
DIGITAL SATELLITE COMMUNICATIONS SYSTEMS AND TECHNOLOGIES: Military and
Civil Applications, A. Nejat Ince; ISBN: 0-7923-9254-X
IMAGE AND TEXT COMPRESSION, James A. Storer; ISBN: 0-7923-9243-4
VECTOR QUANTIZATION AND SIGNAL COMPRESSION, Allen Gersho, Robert M. Gray;
ISBN: 0-7923-9181-0
CODES, CURVES, AND SIGNALS
Common Threads in Communications
Edited by
ALEXANDER V ARDY
Coordinated Science Laboratory
University of Illinois at Urbana-Champaign
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
ISBN 978-1-4613-7330-8 ISBN 978-1-4615-5121-8 (eBook)
DOI 10.1007/978-1-4615-5121-8
Library of Congress Cataloging-in-Publication Data
A C.I.P. Catalogue record for this book is available
from the Library of Congress.
Copyright © 1998 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1998
Softcover reprint ofthe hardcover 1st edition 1998
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC.
Printed on acid-free paper.
Dedicated to Richard E. Blahut
Contents
Foreword .................................................... ix
Acknowledgement ............................................. xiii
List of Contributors ........................................... xv
Part I: CURVES AND CODES
1. On (or in) the Blahut Footprint ................................. 3
TOMH0HOLDT
2. The Klein Quartic, the Fano Plane, and Curves Representing Designs ........ 9
RUUD PELLIKAAN
3. Improved Hermitian-like Codes over GF(4) ........................ 21
GUI-LIANG FENG AND THAMMAVARAPU R. N. RAo
4. The BM Algorithm and the BMS Algorithm ........................ 39
SHOJIRO SAKATA
5. Lee Weights of Zl4Z Codes from Elliptic Curves .................... 53
JosE FELIPE VOLOCH AND JUDY L. WALKER
6. Curves, Codes, and Cryptography ............................... 63
IAN F. BLAKE
Part ll: CODES AND SIGNALS
7. Transforms and Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
G. DAVID FORNEY, JR.
8. Spherical Codes Generated from Self-dual Association Schemes ........ 99
THOMAS ERICSON
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9. Codes and Ciphers: Fourier and Blahut ........................ 105
JAMES L. MASSEY
10. Bounds on Constrained Codes in One and Two Dimensions .......... 121
JORN JUSTESEN
11. Classification of Certain Tail-Biting
Generators for the Binary Golay Code ......................... 127
A. R. CALDERBANK, G. DAVID FORNEY, JR., AND ALEXANDER VARDY
12 On the Weight Distribution of Some Turbo-Like Codes ............. 155
DANIEL J. COSTELLO, JR. AND JIALI HE
Part ill: SIGNALS AND INFORMATION
13. Alternating Minimization Algorithms:
From Blahut-Arimoto to Expectation-Maximization ................ 173
JOSEPH A. 0' SULLIVAN
14. Information-Theoretic Reflections on PCM Voiceband Modems ....... 193
GOITFRIED UNGER BOECK
15. Some Wireless Networking Problems with a Theoretical Conscience ...... 201
ANTHONY EPHREMIDES
16. Bounds on the EffICiency of Two-Stage Group Testing .............. 213
TOBY BERGER AND JAMES W. MANDELL
17. Computational Imaging ..................................... 233
DAVID C. MUNSON, JR.
viii
Foreword
This book is a direct consequence of the broad and profound influence of
Richard E. Blahut on the fields of algebraic coding, information theory, and digital
signal processing. The book consists of seventeen chapters that provide a represen
tative cross-section of cutting-edge contemporary research in the fields of study to
which R.E. Blahut has contributed during his career. These include: codes defined
on algebraic curves and the associated decoding algorithms, the use of signal pro
cessing techniques in coding theory, and the application of information-theoretic meth
ods in communications and signal processing. The book is organized accordingly into
three parts, titled: Curves and Codes, Codes and Signals, and Signals and Infonnation.
The list of contributors to this volume (see p.xv) consists of21 researchers, from six coun
tries in North America, Europe, and Asia. All the authors have individually and collectively
dedicated their work to R.E. Blahut ---this book is thus testimony not only to the impact of
his scholarship, but also to the deep affection in which he is held around the world.
a .•••
Richard E. Blahut was born in 1937 in Orange, New Jersey. He received his B.Sc.
degree in electrical engineering from the Massachusetts Institute of Technology, M.Sc.
degree in physics from the Stevens Institute of Technology, and Ph.D. degree in elec
trical engineering from Cornell University.
He is now a Professor of Electrical and Computer Engineering at the University of
Illinois and a Research Professor in the Coordinated Science Laboratory. Previously,
he had served as a Courtesy Professor of Electrical Engineering at Cornell Univer
sity, where he taught from 1973 to 1994, and as a Consulting Professor at the South
China University of Technology. He has taught at Princeton University, the Swiss
Federal Institute of Technology, and the NATO Advanced Study Institute. In addi
tion to his numerous academic positions over the past 24 years, he was employed by
the Federal Systems Division of IBM from 1964 to 1994. At IBM, he had general
responsibility for the analysis and design of coherent signal processing systems, digital
communications systems, and statistical information processing systems. Early in
his career at IBM, he has pioneered the emitter location technology that is now used
in the U.S. Department of Defense surveillance systems. For this work, he was named
Fellow of the IBM Corporation in 1980. His direct contributions to industry also
include the development of error-control codes and decoders that protect both the
video-text data transmitted via the U.S. public broadcasting network and the mes
sages to the Tomahawk missile. He designed a damage-resistant bar code used by
the British Royal Mail, and developed error-control algorithms used in the data link
for the U.S. Navy's LAMPS helicopter.
R.E. Blahut is a Systems Consultant to the Information Optics Corporation, Issaquah,
Washington, where he is involved in the development ofthe first truly two-dimensional
ix
data storage device. Some of the challenging theory of two-dimensional recording sys
tems is examined in Chapter 10 of this volume, contributed by Jl'lrn Justesen.
For his paper Computation of channel capacity and rate distortion functions, he re
ceived the 1974 IEEE Information Theory Society best paper Award. The impact of
this work on our field is still felt today. Two chapters in this volume (Chapter 13 by
Joseph A. O'Sullivan and Chapter 14 by Gottfried Ungerboeck) relate to the well
known Blahut-Arimoto algorithm for computing the capacity of discrete channels.
During the years 1975--1985, Richard E. Blahut has championed the use of signal
processing techniques (in particular, Fourier transforms over a finite field) in alge
braic coding theory. His ideas turned out to be extremely productive. Three chapters
in this volume are devoted to Fourier transforms. Chapter 7 by G. David Forney, Jr.
extends the theory to transforms defined over abelian groups, Chapter 8 by Thomas Ericson
uses Fourier transforms to design spherical codes, and Chapter 9 by James L. Massey
examines applications of the Gunther-Blahut theorem (which relates the DFT to
linear complexity) in coding theory and cryptography.
Later in his career, R.E. Blahut became interested in codes defined on algebraic
curves. He pursued this subject with remarkable determination to explain the un
derlying mathematics on an elementary level. The paradigm of "algebraic-geom
etry codes without algebraic geometry" is universally attributed to R.E. Blahut.
The first six chapters in this volume relate to his work in this field.
These contributions notwithstanding, his major project of the past two decades
was a series of advanced textbooks and monographs in error-control coding, in
formation theory, and signal processing, including:
Theory and Practice of Error-Control Codes, Addison-Wesley, 1983
Fast Algorithmsfor Digital Signal Processing, Addison-Wesley, 1985
Principles and Practice of Information Theory, Addison-Wesley, 1987
Digital Transmission of Information, Addison-Wesley, 1990
Algebraic Methods of Signal Processing and Communication Coding,
Springer-Verlag, 1992.
These books were translated into several languages, and a generation of students
worldwide has been introduced to information theory and coding theory using this
material. There is more to come: R.E. Blahut is currently working on revisions to
some of his earlier textbooks, and on new books in the series. Byway of an advance
preview, Chapter 17 in this volume (contributed by David C. Munson, Jr.) relates to
Blahut's forthcoming book on remote surveillance.
R.E. Blahut served as President of the Information Theory Society of the IEEE in
1982, and as Editor-in-Chief ofthe IEEE TRANSACTIONS ON INFORMATION THEORY, from
x
1992 until 1995. Among other honors, he was named Fellow of the Institute ofElectrical
and Electronics Engineers in 1981, elected to membership in the National Academy of
Engineering in 1990, and received the IEEE Alexander Graham Bell medal in 1998.
• • •
As editor, I would like to conclude this foreword on a personal note. I feel fortunate
to have chosen coding theory and information theory as my field of research. It is
a field in which insights derived from theoretical investigation often have immedi
ate and far-reaching impact on technology and practice. The work ofR.E. Blahut has
exemplified this trait in the best possible way, throughout his career. Furthermore,
our field has inherent intellectual beauty that has always attracted the best and brightest
people to information theory, and we have been particularly lucky to have
Richard E. Blahut join our research community 30 years ago. His insights, his
philosophy, and his personality left an indelible mark on our field.
Alexander Vardy
Urbana, Illinois
xi