Titles i n This Series

14 Rober t Calderbank , G . Davi d Forney , Jr. , an d Nade r Moayeri , Editors , Codin g an d Quantization: DIMACS/IEEE Worksho p 13 Jin-Y i Cai, Editor, Advance s in Computational Complexit y Theory 12 Davi d S. Johnson an d Catherine C . McGeoch, Editors , Networ k Flow s and Matching : First DIMACS Implementation Challeng e 11 Larr y Finkelstein an d William M. Kantor, Editors, Group s and Computatio n 10 Joe l Friedman, Editor, Expandin g Graphs 9 Willia m T. Trotter, Editor, Plana r Graph s 8 Simo n Gindikin, Editor, Mathematica l Method s of Analysis of Biopolymer Sequence s 7 Lyl e A. McGeoch and Daniel D. Sleator, Editors, On-Lin e Algorithms 6 Jaco b E . Goodman , Richar d Pollack , an d Willia m Steiger , Editors , Discret e and Computational Geometry : Paper s from th e DIMACS Special Year 5 Fran k Hwang , Clyd e Monma, an d Fred Roberts, Editors , Reliabilit y o f Compute r an d Communication Network s 4 Pete r Gritzman n an d Bern d Sturmfels , Editors , Applie d Geometr y an d Discret e Mathematics, The Victor Klee Festschrif t 3 E . M. Clarke and R. P. Kurshan, Editors, Computer-Aide d Verificatio n '9 0 2 Joa n Feigenbaum and Michael Merritt, Editors, Distribute d Computin g and Cryptograph y 1 Willia m Cook and Paul D. Seymour, Editors, Polyhedra l Combinatoric s This page intentionally left blank https://doi.org/10.1090/dimacs/014 DIMACS Series in Discrete Mathematic s and Theoretical Computer Scienc e

Volume 1 4

Coding an d Quantization

DIMACS/IEEE Worksho p October 19-21 , 199 2

Robert Calderban k G. Davi d Forney , Jr . Nader Moayer i Editors

NSF Scienc e an d Technolog y Cente r in Discret e Mathematic s an d Theoretica l Compute r Scienc e A consortium o f Rutgers University , Princeto n University , AT&T Bel l Labs , Bellcor e

American Mathematical Societ y This Dimacs volume on codin g and quantization contain s papers fro m a workshop hel d at DIMAC S fro m Octobe r 1 9 to Octobe r 21 , 1992 , a s wel l a s tw o paper s tha t recor d results obtained i n discussion outsid e the forma l sessions . 1991 Mathematics Subject Classification. Primar y 94A05 , 94A29, 94B05, 94B10 , 94B12.

Library o f Congress Cataloging-in-Publication Dat a Workshop on Coding and Quantization (1992 : Princeton University ) Coding and quantization: DIMACS/IEE E Workshop, October 19-21 , 1992/Rober t Calderbank , G. David Forney, Jr., Nader Moayeri, editors. p. cm . — (DIMACS series in discrete mathematics and theoretical computer science; no. 14) On t.p.: "NS F Science and Technolog y Cente r i n Discrete Mathematic s an d Theoretical Com - puter Science, a consortium of Rutgers University, Princeton University, AT&T Bell Labs, Bellcore." Workshop co-sponsore d b y th e Cente r fo r Discret e Mathematic s an d Theoretica l Compute r Science (DIMACS) and the Information Theory Society of the Institute of Electrical and Electronics Engineers (IEEE). Includes bibliographical references . ISBN 0-8218-6603-6 (alk . paper) 1. Telecommunication systems—Congresses . 2 . Coding theory—Congresses . I . Calderbank , Robert, 1954 - . II . Forney, G. David. III . Moayeri, Nader, 1956 - . IV . NSF Science and Tech- nology Center in Discrete Mathematics and Theoretical Computer Science . V . DIMACS (Group ) VI. IEEE Information Theor y Society . VII . Title. VIII . Series. TK5102.5.W69 199 2 93-2928 3 621.382—dc20 CI P

Copying an d reprinting . Individua l reader s o f thi s publication , an d nonprofi t librarie s actin g fo r them, are permitted to make fair us e of the material, such as to copy an article for us e in teaching or research. Permissio n is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment o f the source is given. Republication, systemati c copying, or multiple reproduction o f any material in this publication (including abstracts ) i s permitte d onl y unde r licens e fro m th e America n Mathematica l Society . Requests for suc h permission shoul d be addressed to the Manager o f Editorial Services, American Mathematical Society , P.O . Bo x 6248, Providence, Rhod e Islan d 02940-6248 . Request s ca n als o be made by e-mail to reprint-permissionQmath. ams. org. The appearanc e o f th e cod e o n th e first pag e o f a n articl e i n thi s publicatio n indicate s th e copyright owner' s consen t fo r copyin g beyond tha t permitte d b y Section s 10 7 or 10 8 of the U.S. Copyright Law , provided that the fee of $1.00 plus $.25 per page for eac h copy be paid directly to the Copyrigh t Clearanc e Center , Inc. , 22 2 Rosewood Drive , Danvers, Massachusett s 01923 . Thi s consent doe s not exten d t o othe r kind s o f copying , suc h a s copyin g fo r genera l distribution , fo r advertising or promotional purposes , for creating new collective works, or for resale .

© Copyrigh t 199 3 by the American Mathematical Society . Al l rights reserved. The American Mathematical Societ y retains all rights except those granted to the United State s Government . Printed in the United State s of America. @ Th e paper used in this book is acid-free an d falls within the guidelines established to ensure permanence and durability . C> Printed o n recycle d paper . This volume was prepared b y the authors using A^S-T^K an d A^^S-IAT^K, the American Mathematical Society' s TgX macro systems. 10 9 8 7 6 5 4 3 2 1 9 8 97 96 95 94 93 Contents

Foreword i x

Preface

A. R . CALDERBANK , G . D . FORNEY , JR. , N . MOAYER I x i

Workshop Progra m xii i

Workshop Participant s xvi i

On the Dualit y o f Coding an d Quantizin g 1 G. D . FORNEY , JR . On Existenc e Proof s fo r Asymptoticall y Goo d 1 5 Euclidean-Space Grou p Code s H.-A. LOELIGE R

The Nordstrom-Robinso n Cod e i s the Binar y Imag e 1 9 of the Octacod e G. D . FORNEY , JR. , N . J . A . SLOANE , AN D M . D . TROT T

Generalized Thet a Function s fo r Lattic e Vecto r Quantizatio n 2 7 P. SOL E

Tree Structured Signa l Spac e Code s 3 3 C. F . BARNE S

The Othe r Asymptoti c Theor y o f Lossy Sourc e Codin g 5 5 D. L . NEUHOF F

Block-Constrained Quantization : Asymptoti c Analysi s 6 7 A. S . BALAMES H AN D D . L . NEUHOF F vi CONTENT S

Syndrome-Based V Q Codebooks 7 5 P. F . SWASZE K

Decoding Unde r Intege r Metri c Constraint s 8 3 E. ZEHAV I AN D J . SAL Z

The Optimalit y o f the Natural Binar y Cod e 9 5 S. W . MCLAUGHLIN , J . ASHLEY , AN D D . L . NEUHOF F

Multiple Descriptio n Scala r Quantize r Design : 10 3 Good Inde x Assignment s V. VAISHAMPAYA N

Structured Vecto r Quantizer s a s Generalize d Produc t Code s 11 1 W.-Y. CHA N AN D A . GERSH O

A New Construction o f Trellis-Coded Quantizer s 12 1 R. J . VA N DE R VLEUTE N AN D J . H . WEBE R

Trellis-Based Scalar-Vecto r Quantize r fo r Memoryles s 12 7 Sources R. LAROI A AN D N . FARVARDI N

Lattice-Structured Codebooks—Constructio n an d Implementatio n 13 7 for Memoryles s Source s M. V . EYUBOGL U AN D A . S . BALAMES H

Decoding o n a Finite Stat e Transitio n Diagra m Whil e 14 9 Avoiding a Sub-Diagra m L. FREDRICKSON , R . KARABED , P . SIEGEL , AN D H . THAPA R

Covering Properties o f Binary Convolutiona l Code s and 15 3 Lattice Quantizatio n o f Uniform Source s A. R . CALDERBANK , P . C . FISHBURN , AN D A . RABINOVIC H

A Markovian Metho d Commo n t o Bot h Quantizatio n an d 16 1 Decoding Usin g Convolutiona l Code s Y. LEVY , D . J . COSTELLO , JR. , AN D A . R . CALDERBAN K

Trellis Codes , Symboli c Dynamics , an d Isometrie s 16 7 C. HEEGAR D AN D E . J . ROSSI N CONTENTS vn

The Desig n o f Finite-State Machine s fo r Quantizatio n 17 5 Using Simulate d Annealin g E. E . KURUOGL U AN D E . AYANOGL U

The M-Algorithm , th e Failur e o f Reduced-State Sequenc e 18 5 Detection wit h Goo d Convolutiona l Codes , an d Som e Implications fo r Trelli s Codin g J. B . ANDERSO N AN D E . OFFE R

An Algebrai c Approac h t o Constructin g Convolutiona l Code s 18 9 from Quasi-Cycli c Code s Y. LEV Y AN D D . J . COSTELLO , JR .

Table-Driven Decodin g o f Convolutional Code s with Sof t Decisio n 19 9 H. KOORAPATY , D . L . BITZER , A . DHOLAKIA , AN D M . A . VOU K

Rotationally Invarian t Multileve l Code s 20 7 J. N . LIVINGSTO N

Constellations fo r Diversit y 21 5 K. J . KERPE Z

Bounded Expansio n Code s fo r Erro r Contro l 22 5 A. S . KHAYRALLA H

A Bound o n the Zero-Erro r Lis t Codin g Capacit y 23 5 E. ARIKA N

Geometric Vecto r Quantizatio n fo r Subband-Base d Vide o 24 3 Coding C. PODILCHU K AN D A . JACQUI N

Recursively Indexe d Differentia l Puls e Cod e Modulation 25 3 K. SAYOO D AN D S . N A This page intentionally left blank Foreword

This DIMAC S volum e o n codin g an d quantizatio n contain s paper s fro m a workshop hel d Octobe r 19-21 , 1992 , a s wel l a s tw o paper s tha t recor d result s obtained i n discussio n outsid e th e forma l sessions . Th e worksho p wa s cospon - sored b y DIMAC S an d IEE E (Informatio n Theor y Societ y o f th e Institut e o f Electrical an d Electronic s Engineers) . We especially than k th e worksho p organizers , Rober t Calderbank , G . Davi d Forney, Jr. , an d Nade r Moayeri , fo r organizin g thi s workshop , whic h brough t together s o many outstandin g participant s i n this field.

Fred Roberts , Actin g Directo r Robert Tarjan , Co-Directo r Diane Souvaine , Associat e Directo r This page intentionally left blank Preface

This volum e i s devote d t o th e Proceeding s o f the Worksho p o n Codin g an d Quantization. Thi s workshop was cosponsored b y the Center fo r Discrete Math - ematics and Theoretical Computer Scienc e (DIMACS) and the Information The - ory Societ y o f the Institute o f Electrical an d Electronic s Engineer s (IEEE) . Ap- proximately on e hundre d an d twent y researcher s attende d on e o r mor e day s o f the worksho p whic h too k plac e Octobe r 19-21 , 1992 . Abou t eight y percen t o f the attendees wer e from universit y engineering departments, with the remainde r from loca l industry an d governmen t organizations . W e begin thes e Proceeding s with a short perspectiv e o n the theme s o f the workshop . In 194 8 Shanno n develope d fundamenta l limit s o n th e efficienc y o f commu - nication ove r nois y channels . I t i s codin g tha t make s reliabl e communicatio n possible, an d discret e mathematic s i s centra l t o codin g theory . Multidimen - sional Euclidea n geometr y (especiall y lattic e theory ) an d finite stat e machine s are o f particular importanc e withi n codin g theory . Discrete mathematics has had a significant impac t on coded transmission ove r bandlimited channels; this is already an important subject, an d will become more so i n th e comin g years , wit h th e adven t o f bette r cellula r networks , persona l communications device s and th e wireles s office . A bandlimite d channe l suc h a s a telephon e channe l support s transmissio n only o f continuous function s tha t contai n no frequencies highe r than W Hz . Th e sampling theore m allow s u s t o replac e a continuou s bandlimite d functio n b y a discrete sequenc e o f it s sample s withou t an y los s o f information . No w signal s become simpl y vector s i n R N consistin g o f N consecutiv e samples . Typicall y these signal s are drawn fro m a finite dimensional lattice; the signal constellatio n consists o f al l lattic e point s tha t li e withi n som e regio n 1Z whose centroi d i s the origin . No w th e goa l i s to desig n a lo w complexit y signalin g schem e tha t maximizes th e minimu m square d distanc e d 2 betwee n distinc t signa l sequences . The powe r required to transmit a lattice point x i s ||x|| 2, and the figure o f merit for the signaling scheme is d2/P, wher e P i s the average transmitted signal power. Typically encoding i s accomplished through a finite state machine, and decodin g is accomplished b y dynami c programming . I t i s these technique s fro m discret e

XI Xll PREFACE mathematics that hav e made possible (i n the last 5 years) practical systems that approach th e Shanno n limi t o n Gaussia n nois e channels . It i s natural t o as k th e questio n wh y thes e development s too k ove r 4 0 year s to emerge . Par t o f the answe r i s that onl y recentl y ha s i t becom e possibl e t o do signal processing i n silicon at hig h speeds. No w that w e have that capabilit y there wil l be mor e opportunities fo r codin g theory . It i s important t o notic e tha t th e fields o f communicatio n an d quantizatio n are ver y closel y related . A signa l constellatio n bounde d b y a regio n 1Z can b e used to quantize source samples that fal l within 1Z. Here the goal is to distribut e quantization point s s o a s t o minimiz e mea n square d error . Th e focu s o f muc h recent wor k i s t o combin e transfor m technique s wit h quantizatio n scheme s i n order t o compress speec h an d images . It i s clear fro m eve n this brief introduction that th e theory o f communicatio n and that o f quantization overla p significantly, an d that man y fundamental ques - tions ar e o f centra l interes t t o researcher s i n bot h fields. However , i t wa s th e sense of the organizers that there had been little crosspollination between the two communities. Th e mai n goa l o f the worksho p wa s to promote mor e interaction . There wer e thirty-fiv e presentation s a t th e worksho p spannin g a wid e rang e o f topics, fro m th e difficult y o f compressing song s b y Suzann e Veg a fo r digita l au - dio broadcasting, to the Minkowski-Hlawka theorem in geometric number theory . The paper s tha t appea r i n thes e Proceeding s are , fo r th e mos t part , account s of these presentations . However , tw o o f the paper s (on e b y G . D . Forney , Jr. , N. J. A . Sloan e an d M . D. Trott, th e othe r b y Y. Levy , D. J. Costello , Jr., an d A. R . Calderbank ) recor d result s tha t wer e obtaine d i n discussio n outsid e th e formal sessions . Al l papers ar e i n final form . AT&T Bel l Laboratories contribute d t o the publicatio n o f these Proceeding s by providing technical support. Th e contributions wer e typeset i n DIMACS for - mat b y Susa n Pope , withou t who m w e would no t hav e attempte d thi s project . Thanks ar e als o du e t o Joa n Stort z fo r he r cheerfu l administrativ e assistance , and t o Pa t Toc i o f DIMAC S fo r he r organizationa l suppor t durin g th e work - shop. Finally , an d mos t important , w e woul d lik e t o than k th e author s o f th e outstanding article s assemble d here , and w e hope that yo u the reader wil l enjo y these Proceedings .

Organizing Committe e Robert Calderban k G. Davi d Forney , Jr . Nader Moayer i Joint DIMACS/IEE E Worksho p o n Coding an d Quantizatio n Rutgers University , Piscataway , NJ , US A October 19-21 , 199 2

Technical Progra m

Session I : LATTICES, DUALITY, AN D SHANNO N THEOR Y Monday Morning , 9:00-12:0 0 Chair: N.J.A . Sloan e 9:00-9:30 Ne w Lattices an d Design s — N.J.A. Sloane 9:30-9:50 Existenc e proof s fo r goo d Euclidean-spac e code s — A. Loeliger 9:50-10:10 Asymptoticall y optima l nois y channe l quantizatio n vi a rando m coding — K. Zeger and V. Manzella 10:10-10:30 BREA K 10:30-10:50 Dualit y betwee n packin g an d coverin g problem s fo r lattice s — G.D. Forney, Jr. 10:50-11:10 Generalize d theta functions fo r lattice vector quantization — P. Sole 11:10-11:30 A coding theorem for low-rate transform code s — D.F. Lyons and D.L. Neuhoff 11:30-12:00 Tree-structure d signa l space code s — C.F. Barnes

Session II : QUANTIZATIO N Monday Afternoon , 2:00-5:0 0 Chair: D.L . Neuhof f Part A : HIGH-RAT E THEOR Y 2:00-2:20 Th e other asymptotic theory of lossy source coding — D.L. Neuhoff 2:30-2:50 Block-constraine d quantizers : introductio n an d asymptoti c anal - ysis — A.S. Balamesh and D.L. Neuhoff 2:50-3:10 Syndrome-base d V Q codebooks — P.F. Swaszek

Xlll xiv WORKSHO P PROGRA M

3:10-3:30 BREA K Part B : FUNDAMENTAL S AN D COMBINE D SOURCE-CHANNE L CODIN G 3:30-4:00 Th e quantization proble m fo r code d system s — E. Zehavi 4:00-4:20 Th e optimalit y o f the natura l binar y cod e — S. W. McLaughlin, D.L. Neuhoff, and J. Ashley 4:20-4:40 Multiple-descriptio n scala r quantize r design : goo d inde x assign - ments — V. Vaishnampayan 4:40-5:00 Structure d vecto r quantizers a s generalized product code s — W.- Y. Chan and A. Gersho

Session III : TRELLIS-CODED QUANTIZATIO N Tuesday Morning , 9:00-12:0 0 Chair: T.R . Fische r 9:00-9:30 Pyrami d cubic lattice and trellis codes — T.R. Fischer and J. Pan 9:30-9:50 A new construction o f trellis-coded quantizers — R.J. van der Vleuten and J.H. Weber 9:50-10:10 Wavele t coding of images using trellis-coded quantization — P. Sri- ram and M. W. Marcellin 10:10-10:30 BREA K 10:30-11:00 Trellis-base d scalar-vector quantizer fo r memoryless sources — R. Laroia and N. Farvardin 11:00-11:20 Vecto r quantizatio n usin g lattic e an d trellis-bounde d codebook s — M.V. Eyuboglu and A. Balamesh 11:20-11:40 Bound s o n the size s o f const ant-weight coverin g code s — T. Et- zion, V.K. Wei and Z. Zhang

Session IV : FINITE-STATE MACHINE S Tuesday Afternoon , 2:00-3:3 0 Chair: A.R . Calderban k 2:00-2:30 Slidin g bloc k code s fo r finite-state machine s wit h forbidde n sub - machines — R. Karabed and P.H. Siegel 2:30-2:50 Coverin g properties o f convolutional codes and associated lattice s — A.R. Calderbank, P.C. Fishburn, and A. Rabinovich 2:50-3:10 Trelli s codes , symboli c dynamics , an d isometrie s — C Heegard and E. Rossin 3:10-3:30 Th e desig n o f finite-state machine s fo r quantizatio n usin g simu - lated annealin g — E. Ayanoglu and E.E. Kuroglu 3:30-3:50 BREA K 3:50-5:00 DISCUSSION S WORKSHOP PROGRAM x v

Session V : CODIN G APPLICATION S Wednesday Morning , 9:00-12:0 0 Chair: D.J . Costello , Jr . 9:00-9:30 Th e M-algorithm , th e failur e o f reduced-state sequenc e detectio n with goo d convolutiona l codes , an d som e implication s fo r trelli s coding — J.B. Anderson and E. Offer 9:30-9:50 A n algebrai c approac h t o constructin g convolutiona l code s fro m quasi-cyclic code s — Y. Levy and D.J. Costello, Jr. 9:50-10:10 Table-drive n decodin g o f convolutional code s wit h sof t decision s — H. Koorapaty, D.L. Bitzer, A. Dholokia, and M.A. Vouk 10:10-10:30 BREA K 10:30-10:50 Rotationall y invarian t multileve l code s — J.N. Livingston 10:50-11:10 Constellation s fo r diversit y — K. Kerpez 11:10-11:30 Bounded-expansio n code s fo r erro r contro l — A.S. Khayrallah 11:30-11:50 A bound o n zero-error lis t codin g capacity — E. Arikan

Session VI : QUANTIZATIO N APPLICATION S Wednesday Afternoon , 2:00-4:0 0 Chair: J . Johnsto n 2:00-2:30 Geometri c vector quantization fo r subband-based vide o coding — C. Podilchuk and A. Jacquin 2:30-2:50 Quantizatio n analysi s in multirate filte r bank s b y spectral theor y — C. W. Kok and S.H. Leung 2:50-3:10 Recursivel y indexed differential puls e code modulation — K. Say- ood and S. Na 3:10-3:30 BREA K 3:30-4:00 Quantizatio n wit h perceptual criteri a — J. Johnston This page intentionally left blank Workshop Participant s

Behnaam Aazhang , Ric e Univ., Houston , T X [email protected]

Jean-Pierre Adoul , Univ . o f Sherbrooke, Sherbrooke , CANAD A adoul@gel. usherb. ca

John B . Anderson, Rensselae r Poly . Inst. , Troy , N Y ander son@ecse. rpi. edu

Erdal Arikan , Bilken t Univ. , Ankara, TURKE Y [email protected]

Ender Ayanoglu , AT& T Bel l Labs, Holmdel, N J ender @ boole. at t. com

Ahmed S . Balamesh, Kin g Abdul-Aziz University , Jeddah , SAUD I ARABI A [email protected]

Christopher F . Barnes , Georgi a Inst , o f Tech., Atlanta, G A [email protected]

Sankar Basu , Steven s Inst, o f Tech., Hoboken , N J [email protected]

Gal Ben-David, Technion , Haifa , ISRAE L [email protected]

Donald L . Bitzer, Nort h Carolin a Stat e Univ. , Raleigh , N C [email protected]

Richard E . Blahut, IBM , Owego , N Y [email protected]

A. R . Calderbank , AT& T Bel l Labs, Murray Hill , N J [email protected]

XVll XV111 WORKSHOP PARTICIPANT S

C. V. Chakravarthy, Steven s Inst, o f Tech., Hoboken , N J [email protected]

Wai-Yip Chan , McGil l Univ. , Montreal , CANAD A [email protected]

Gerard J . Chang , Rutger s Univ. , Piscataway , N J [email protected]

Bing Chen , AT& T Bel l Labs, Murray Hill , N J [email protected]

King-Wai Chow , Princeton University , Princeton , N J kingchow@ee. princet on. edu

Sean Coffey , Th e Univ . o f Michigan, An n Arbor , M I scoffey@eecs. umich. edu

Daniel J. Costello , Jr., Univ . o f Notre Dame, Notr e Dame , I N [email protected]

Thomas M . Cover , Stanfor d Univ. , Stanford , C A [email protected]

Rene Cruz , Univ . o f California, Sa n Diego , C A [email protected]

David G . Daut, Rutger s Univ. , Piscataway , N J daut @caip. rut gers. edu

Ajay Dholakia , Nort h Carolin a Stat e Univ. , Raleigh , N C [email protected]

Anthony D . DiBiase, EkTRON Applie d Imaging , Bedford , M A [email protected] / [email protected] m

Wei Ding, Princeton University , Princeton , N J [email protected]

Steven C . Dzik , AT& T Imag e Solutions , Middletown , N J WORKSHOP PARTICIPANT S xix

Anthony Ephremides , Univ . o f Maryland, Colleg e Park, M D [email protected]

M. Vedat Eyuboglu , Motorol a Codex , Mansfield , M A vedat _eyuboglu@mcimail. com

Thomas R . Fischer , Washingto n Stat e Univ. , Pullman , W A fischer @eecs . wsu. edu

G. Davi d Forney , Jr., Motorol a Codex , Mansfield , M A [email protected]

Richard L . Frost, Brigha m Youn g Univ. Provo , U T [email protected]

Tom Fuja , Univ . o f Maryland, Colleg e Park, M D [email protected]

Ehud Gelblum , Columbi a Univ. , Ne w York, N Y gelblum@ct r. Columbia, edu

Jerry D . Gibson , Texa s A&M Univ. , Colleg e Station, T X [email protected]

Bruce Hajek , Univ . o f Illinois, Urbana, I L [email protected]

Chris Heegard , Cornel l Univ. , Ithaca, N Y [email protected]

Shay-Jan Huang , Univ . o f Maryland, Colleg e Park, M D [email protected]

Arnaud Jacquin , AT& T Bel l Labs, Murray Hill , N J j acquin@chit ra. at t. com

Branko Jelicic , Univ. o f Pennsylvania, Philadelphia , P A

Frederick Jelinek , IB M T.J. Watso n Res . Center , Yorktow n Heights , N Y [email protected] XX WORKSHOP PARTICIPANT S

Jim Johnston , AT& T Bel l Labs, Murray Hill , N J j j ©research. at t. com

Mark Kahrs , Rutgers Univ. , Piscataway , N J [email protected]

Rama Kalluri , Rutger s Univ. , Piscataway , N J

Razmik Karabed , IB M Almaden Res . Center , Sa n Jose, C A [email protected]

Kenneth J . Kerpez , Bellcore , Morristown, N J kerpez@aries. bellcore. com

Ali S . Khayrallah, Univ . o f Delaware, Newark , D E [email protected]

Ken Kishi , Princeton, N J

C. W. Kok , Cit y Polytechni c o f Hong Kong, HONG KON G [email protected]

Havish Koorapaty , Nort h Carolin a Stat e Univ. , Raleigh , N C [email protected]

Prank R . Kschischang , Univ . o f Toronto, Toronto , CANAD A [email protected]

P. Sarath Kumar , Univ . o f Pennsylvania, Philadelphia , P A

Rajiv Laroia , AT& T Bel l Labs, Murray Hill , NJ [email protected]

Cheng Chie h Lee , Univ. o f Maryland, Colleg e Park, M D [email protected]

Don H . Lee , IBM T.J. Watso n Res . Center , Yorktow n Heights , N Y [email protected]

Jungwoo Lee , Princeton Univ. , Princeton, N J j unglee@ee. pr incet on. edu WORKSHOP PARTICIPANT S xxi

Yannick Levy , Univ. o f Notre Dame, Notre Dame, I N [email protected]

Pascal Ligdas , Univ . o f Maryland, Colleg e Park, M D [email protected]

Shu Lin , Univ . o f Hawaii, Honolulu , H I [email protected]

Jay N . Livingston, Texa s AkM Univ. , Colleg e Station, T X [email protected]

Hans-Andrea Loeliger , Linkopin g Univ. , Linkoping , SWEDE N [email protected]

Minsky Lou , AT& T Bel l Labs, Murray Hill , N J ml@ulysses. at t. com

Daniel F. Lyons , Mitre Corp. , McLean , V A [email protected]

Michael W. Marcellin , Univ . o f Arizona, Tucson , A Z [email protected]

James Mazo , AT&T Bel l Labs, Murray Hill , N J

Steven W. McLaughlin , Rocheste r Inst , o f Tech., Rochester , N Y s wmeee@r it vax. isc. r it. edu

Nader Mehravari , IBM , Owego , N Y nader @owgvmO. vnet. ibm. com

Laurence B. Milstein, Univ . o f California , Sa n Diego , C A [email protected]

Nader Moayeri , Rutgers University , Piscataway , N J moayer i@ winlab. r ut gers. edu

Nader Mohsenian , Princeto n Univ. , Princeton, N J [email protected] XXII WORKSHOP PARTICIPANT S

David L . Neuhoff , Th e Univ . o f Michigan, An n Arbor, M I neuhoff@eecs. umich. edu

Antonio Ortega , Columbi a Univ. , Ne w York, N Y [email protected]

Nam Phamdo , Univ . o f Maryland, Colleg e Park, M D [email protected]

Christine Podilchuk , AT& T Bel l Labs, Murray Hill , N J [email protected]

H. Vincent Poor , Princeto n Univ. , Princeton, N J [email protected]

Mohendra Pratap , AT& T Imag e Solutions , Middletown , N J

Asya Rabinovich , Stanfor d University , Stanford , C A asya@play fair. st anfor d. edu

M. V. Raganath, AT& T Imag e Solutions , Middletown , N J

Kannan Ramchandran , Columbi a Univ. , Ne w York, N Y kannan@ct r. Columbia, edu

Ramesh Rao , Univ. o f California, Sa n Diego , C A [email protected]

Eric Rossin , Cornel l Univ. , Ithaca, N Y [email protected]

Summit Roy , Univ. o f Pennsylvania, Philadelphia , P A r oy @pender. ee. upenn. edu

Noel Rozario, GE Astro Space , Princeton, N J

Burt Saltzberg , AT& T Bel l Labs, Middletown, N J

Khalid Sayood , Univ . o f Nebraska, Lincoln , N E [email protected] / [email protected] u WORKSHOP PARTICIPANT S xxin

Stuart C . Schwartz , Princeton University , Princeton , N J [email protected]

Mutsumu Serizawa , Rutger s Univ. , Piscataway , N J serizawa@ winlab. rut gers. edu

Homayoun Shahri , AT& T Bel l Labs, Murray Hill , N J hsa@uly sses. at t. com

Talal Shamoon , Cornel l Univ. , Ithaca, N Y t alal@ee. Cornell. edu

Vincent Shaw , LS I International, Marlboro , N J

Nagabhushana Sindhushayana , Cornel l Univ. , Ithaca, N Y bhushan@ee. Cornell. edu

Paul H . Siegel , IBM Almaden Res . Center , Sa n Jose , C A siegelph@ almaden. ibm. com

Neil J. A . Sloane , AT&T Bel l Labs, Murray Hill , N J [email protected]

Jakov Snyders , Ne w Jersey Inst , o f Tech., Newark , N J [email protected]

Patrick Sole , CNRS, Valbonne, FRANC E [email protected]

Peter F . Swaszek , Univ . o f Rhode Island , Kingston , R I [email protected]

I. Emre Telatar , AT& T Bel l Labs, Murray Hill , N J [email protected]

Steven A . Tretter, Univ . o f Maryland, Colleg e Park, M D [email protected]

Mitchell D . Trott, Mass . Inst , o f Technology, Cambridge , M A [email protected] XXIV WORKSHOP PARTICIPANT S

David N . Tse, Mass. Inst , o f Technology, Cambridge , M A dnt se@lids. mit. edu

Vinay Vaishampayan , Texa s A&M Univ. , Colleg e Station, T X [email protected]

Rene J. va n de r Vleuten, Delf t Univ . o f Tech., Delft , Th e NETHERLAND S rene@duteinm. et. tudelft. nl

Sridhar Vembu , Princeton University , Princeton , N J [email protected]

Sergio Verdu, Princeto n Univ. , Princeton, N J verdu@pr incet on. edu

Victor K . Wei , Bellcore, Morristown, N J [email protected]

Aaron D . Wyner, AT& T Bel l Labs, Murray Hill , N J ad w@resear ch. at t. com

Jian Yang , Univ. o f Pennsylvania, Philadelphia , P A

Xiancheng Yuan, PictureTel Corp. , Danvers, M A [email protected]

Rami Zamir , Tel-Avi v Univ. , Tel-Aviv , ISRAE L [email protected]

Kenneth A . Zeger , Univ . o f Illinois, Urbana, I L zeger @ai. mit. edu

Ephraim Zehavi , Technion , Haifa , Israe l ezehavi@ee .technion .ac.il