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.