The 2005 IEEE International Symposium on Information Theory, Adelaide, Australia
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Minimax Redundancy for Markov Chains with Large State Space
Minimax redundancy for Markov chains with large state space Kedar Shriram Tatwawadi, Jiantao Jiao, Tsachy Weissman May 8, 2018 Abstract For any Markov source, there exist universal codes whose normalized codelength approaches the Shannon limit asymptotically as the number of samples goes to infinity. This paper inves- tigates how fast the gap between the normalized codelength of the “best” universal compressor and the Shannon limit (i.e. the compression redundancy) vanishes non-asymptotically in terms of the alphabet size and mixing time of the Markov source. We show that, for Markov sources (2+c) whose relaxation time is at least 1 + √k , where k is the state space size (and c> 0 is a con- stant), the phase transition for the number of samples required to achieve vanishing compression redundancy is precisely Θ(k2). 1 Introduction For any data source that can be modeled as a stationary ergodic stochastic process, it is well known in the literature of universal compression that there exist compression algorithms without any knowledge of the source distribution, such that its performance can approach the fundamental limit of the source, also known as the Shannon entropy, as the number of observations tends to infinity. The existence of universal data compressors has spurred a huge wave of research around it. A large fraction of practical lossless compressors are based on the Lempel–Ziv algorithms [ZL77, ZL78] and their variants, and the normalized codelength of a universal source code is also widely used to measure the compressibility of the source, which is based on the idea that the normalized codelength is “close” to the true entropy rate given a moderate number of samples. -
Digital Communication Systems 2.2 Optimal Source Coding
Digital Communication Systems EES 452 Asst. Prof. Dr. Prapun Suksompong [email protected] 2. Source Coding 2.2 Optimal Source Coding: Huffman Coding: Origin, Recipe, MATLAB Implementation 1 Examples of Prefix Codes Nonsingular Fixed-Length Code Shannon–Fano code Huffman Code 2 Prof. Robert Fano (1917-2016) Shannon Award (1976 ) Shannon–Fano Code Proposed in Shannon’s “A Mathematical Theory of Communication” in 1948 The method was attributed to Fano, who later published it as a technical report. Fano, R.M. (1949). “The transmission of information”. Technical Report No. 65. Cambridge (Mass.), USA: Research Laboratory of Electronics at MIT. Should not be confused with Shannon coding, the coding method used to prove Shannon's noiseless coding theorem, or with Shannon–Fano–Elias coding (also known as Elias coding), the precursor to arithmetic coding. 3 Claude E. Shannon Award Claude E. Shannon (1972) Elwyn R. Berlekamp (1993) Sergio Verdu (2007) David S. Slepian (1974) Aaron D. Wyner (1994) Robert M. Gray (2008) Robert M. Fano (1976) G. David Forney, Jr. (1995) Jorma Rissanen (2009) Peter Elias (1977) Imre Csiszár (1996) Te Sun Han (2010) Mark S. Pinsker (1978) Jacob Ziv (1997) Shlomo Shamai (Shitz) (2011) Jacob Wolfowitz (1979) Neil J. A. Sloane (1998) Abbas El Gamal (2012) W. Wesley Peterson (1981) Tadao Kasami (1999) Katalin Marton (2013) Irving S. Reed (1982) Thomas Kailath (2000) János Körner (2014) Robert G. Gallager (1983) Jack KeilWolf (2001) Arthur Robert Calderbank (2015) Solomon W. Golomb (1985) Toby Berger (2002) Alexander S. Holevo (2016) William L. Root (1986) Lloyd R. Welch (2003) David Tse (2017) James L. -
Principles of Communications ECS 332
Principles of Communications ECS 332 Asst. Prof. Dr. Prapun Suksompong (ผศ.ดร.ประพันธ ์ สขสมปองุ ) [email protected] 1. Intro to Communication Systems Office Hours: Check Google Calendar on the course website. Dr.Prapun’s Office: 6th floor of Sirindhralai building, 1 BKD 2 Remark 1 If the downloaded file crashed your device/browser, try another one posted on the course website: 3 Remark 2 There is also three more sections from the Appendices of the lecture notes: 4 Shannon's insight 5 “The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.” Shannon, Claude. A Mathematical Theory Of Communication. (1948) 6 Shannon: Father of the Info. Age Documentary Co-produced by the Jacobs School, UCSD- TV, and the California Institute for Telecommunic ations and Information Technology 7 [http://www.uctv.tv/shows/Claude-Shannon-Father-of-the-Information-Age-6090] [http://www.youtube.com/watch?v=z2Whj_nL-x8] C. E. Shannon (1916-2001) Hello. I'm Claude Shannon a mathematician here at the Bell Telephone laboratories He didn't create the compact disc, the fax machine, digital wireless telephones Or mp3 files, but in 1948 Claude Shannon paved the way for all of them with the Basic theory underlying digital communications and storage he called it 8 information theory. C. E. Shannon (1916-2001) 9 https://www.youtube.com/watch?v=47ag2sXRDeU C. E. Shannon (1916-2001) One of the most influential minds of the 20th century yet when he died on February 24, 2001, Shannon was virtually unknown to the public at large 10 C. -
Vector Quantization and Signal Compression the Kluwer International Series in Engineering and Computer Science
VECTOR QUANTIZATION AND SIGNAL COMPRESSION THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE COMMUNICATIONS AND INFORMATION THEORY Consulting Editor: Robert Gallager Other books in the series: Digital Communication. Edward A. Lee, David G. Messerschmitt ISBN: 0-89838-274-2 An Introduction to Cryptolog)'. Henk c.A. van Tilborg ISBN: 0-89838-271-8 Finite Fields for Computer Scientists and Engineers. Robert J. McEliece ISBN: 0-89838-191-6 An Introduction to Error Correcting Codes With Applications. Scott A. Vanstone and Paul C. van Oorschot ISBN: 0-7923-9017-2 Source Coding Theory.. Robert M. Gray ISBN: 0-7923-9048-2 Switching and TraffIC Theory for Integrated BroadbandNetworks. Joseph Y. Hui ISBN: 0-7923-9061-X Advances in Speech Coding, Bishnu Atal, Vladimir Cuperman and Allen Gersho ISBN: 0-7923-9091-1 Coding: An Algorithmic Approach, John B. Anderson and Seshadri Mohan ISBN: 0-7923-9210-8 Third Generation Wireless Information Networks, edited by Sanjiv Nanda and David J. Goodman ISBN: 0-7923-9128-3 VECTOR QUANTIZATION AND SIGNAL COMPRESSION by Allen Gersho University of California, Santa Barbara Robert M. Gray Stanford University ..... SPRINGER SCIENCE+BUSINESS" MEDIA, LLC Library of Congress Cataloging-in-Publication Data Gersho, A1len. Vector quantization and signal compression / by Allen Gersho, Robert M. Gray. p. cm. -- (K1uwer international series in engineering and computer science ; SECS 159) Includes bibliographical references and index. ISBN 978-1-4613-6612-6 ISBN 978-1-4615-3626-0 (eBook) DOI 10.1007/978-1-4615-3626-0 1. Signal processing--Digital techniques. 2. Data compression (Telecommunication) 3. Coding theory. 1. Gray, Robert M., 1943- . -
IEEE Information Theory Society Newsletter
IEEE Information Theory Society Newsletter Vol. 59, No. 3, September 2009 Editor: Tracey Ho ISSN 1059-2362 Optimal Estimation XXX Shannon lecture, presented in 2009 in Seoul, South Korea (extended abstract) J. Rissanen 1 Prologue 2 Modeling Problem The fi rst quest for optimal estimation by Fisher, [2], Cramer, The modeling problem begins with a set of observed data 5 5 5 c 6 Rao and others, [1], dates back to over half a century and has Y yt:t 1, 2, , n , often together with other so-called 5 51 c26 changed remarkably little. The covariance of the estimated pa- explanatory data Y, X yt, x1,t, x2,t, . The objective is rameters was taken as the quality measure of estimators, for to learn properties in Y expressed by a set of distributions which the main result, the Cramer-Rao inequality, sets a lower as models bound. It is reached by the maximum likelihood (ML) estima- 5 1 u 26 tor for a restricted subclass of models and asymptotically for f Y|Xs; , s . a wider class. The covariance, which is just one property of u5u c u models, is too weak a measure to permit extension to estima- Here s is a structure parameter and 1, , k1s2 real- valued tion of the number of parameters, which is handled by various parameters, whose number depends on the structure. The ad hoc criteria too numerous to list here. structure is simply a subset of the models. Typically it is used to indicate the most important variables in X. (The traditional Soon after I had studied Shannon’s formal defi nition of in- name for the set of models is ‘likelihood function’ although no formation in random variables and his other remarkable per- such concept exists in probability theory.) formance bounds for communication, [4], I wanted to apply them to other fi elds – in particular to estimation and statis- The most important problem is the selection of the model tics in general. -
Andrew Viterbi
Andrew Viterbi Interview conducted by Joel West, PhD December 15, 2006 Interview conducted by Joel West, PhD on December 15, 2006 Andrew Viterbi Dr. Andrew J. Viterbi, Ph.D. serves as President of the Viterbi Group LLC and Co- founded it in 2000. Dr. Viterbi co-founded Continuous Computing Corp. and served as its Chief Technology Officer from July 1985 to July 1996. From July 1983 to April 1985, he served as the Senior Vice President and Chief Scientist of M/A-COM Inc. In July 1985, he co-founded QUALCOMM Inc., where Dr. Viterbi served as the Vice Chairman until 2000 and as the Chief Technical Officer until 1996. Under his leadership, QUALCOMM received international recognition for innovative technology in the areas of digital wireless communication systems and products based on Code Division Multiple Access (CDMA) technologies. From October 1968 to April 1985, he held various Executive positions at LINKABIT (M/A-COM LINKABIT after August 1980) and served as the President of the M/A-COM LINKABIT. In 1968, Dr. Viterbi Co-founded LINKABIT Corp., where he served as an Executive Vice President and later as the President in the early 1980's. Dr. Viterbi served as an Advisor at Avalon Ventures. He served as the Vice-Chairman of Continuous Computing Corp. since July 1985. During most of his period of service with LINKABIT, Dr. Viterbi served as the Vice-Chairman and a Director. He has been a Director of Link_A_Media Devices Corporation since August 2010. He serves as a Director of Continuous Computing Corp., Motorola Mobility Holdings, Inc., QUALCOMM Flarion Technologies, Inc., The International Engineering Consortium and Samsung Semiconductor Israel R&D Center Ltd. -
Information Theory and Statistics: a Tutorial
Foundations and Trends™ in Communications and Information Theory Volume 1 Issue 4, 2004 Editorial Board Editor-in-Chief: Sergio Verdú Department of Electrical Engineering Princeton University Princeton, New Jersey 08544, USA [email protected] Editors Venkat Anantharam (Berkeley) Amos Lapidoth (ETH Zurich) Ezio Biglieri (Torino) Bob McEliece (Caltech) Giuseppe Caire (Eurecom) Neri Merhav (Technion) Roger Cheng (Hong Kong) David Neuhoff (Michigan) K.C. Chen (Taipei) Alon Orlitsky (San Diego) Daniel Costello (NotreDame) Vincent Poor (Princeton) Thomas Cover (Stanford) Kannan Ramchandran (Berkeley) Anthony Ephremides (Maryland) Bixio Rimoldi (EPFL) Andrea Goldsmith (Stanford) Shlomo Shamai (Technion) Dave Forney (MIT) Amin Shokrollahi (EPFL) Georgios Giannakis (Minnesota) Gadiel Seroussi (HP-Palo Alto) Joachim Hagenauer (Munich) Wojciech Szpankowski (Purdue) Te Sun Han (Tokyo) Vahid Tarokh (Harvard) Babak Hassibi (Caltech) David Tse (Berkeley) Michael Honig (Northwestern) Ruediger Urbanke (EPFL) Johannes Huber (Erlangen) Steve Wicker (GeorgiaTech) Hideki Imai (Tokyo) Raymond Yeung (Hong Kong) Rodney Kennedy (Canberra) Bin Yu (Berkeley) Sanjeev Kulkarni (Princeton) Editorial Scope Foundations and Trends™ in Communications and Information Theory will publish survey and tutorial articles in the following topics: • Coded modulation • Multiuser detection • Coding theory and practice • Multiuser information theory • Communication complexity • Optical communication channels • Communication system design • Pattern recognition and learning • Cryptology -
IEEE Information Theory Society Newsletter
IEEE Information Theory Society Newsletter Vol. 63, No. 3, September 2013 Editor: Tara Javidi ISSN 1059-2362 Editorial committee: Ioannis Kontoyiannis, Giuseppe Caire, Meir Feder, Tracey Ho, Joerg Kliewer, Anand Sarwate, Andy Singer, and Sergio Verdú Annual Awards Announced The main annual awards of the • 2013 IEEE Jack Keil Wolf ISIT IEEE Information Theory Society Student Paper Awards were were announced at the 2013 ISIT selected and announced at in Istanbul this summer. the banquet of the Istanbul • The 2014 Claude E. Shannon Symposium. The winners were Award goes to János Körner. the following: He will give the Shannon Lecture at the 2014 ISIT in 1) Mohammad H. Yassaee, for Hawaii. the paper “A Technique for Deriving One-Shot Achiev - • The 2013 Claude E. Shannon ability Results in Network Award was given to Katalin János Körner Daniel Costello Information Theory”, co- Marton in Istanbul. Katalin authored with Mohammad presented her Shannon R. Aref and Amin A. Gohari Lecture on the Wednesday of the Symposium. If you wish to see her slides again or were unable to attend, a copy of 2) Mansoor I. Yousefi, for the paper “Integrable the slides have been posted on our Society website. Communication Channels and the Nonlinear Fourier Transform”, co-authored with Frank. R. Kschischang • The 2013 Aaron D. Wyner Distinguished Service Award goes to Daniel J. Costello. • Several members of our community became IEEE Fellows or received IEEE Medals, please see our web- • The 2013 IT Society Paper Award was given to Shrinivas site for more information: www.itsoc.org/honors Kudekar, Tom Richardson, and Rüdiger Urbanke for their paper “Threshold Saturation via Spatial Coupling: The Claude E. -
Itnl0908.Pdf
itNL0908.qxd 8/13/08 8:34 AM Page 1 IEEE Information Theory Society Newsletter Vol. 58, No. 3, September 2008 Editor: Daniela Tuninetti ISSN 1059-2362 Annual IT Awards Announced The principal annual awards of the Information Theory Society of the U.S. National Academy of Engineering (2007 to date). He were announced at the Toronto ISIT. The 2009 Shannon Award will be General Co-Chair of the 2009 ISIT in Seoul. goes to Jorma Rissanen. The 2008 Wyner Award goes to Vincent Poor. The winners of the 2008 IT Paper Award are two 2006 IT The Information Theory Society Paper Award is given annually Transactions papers on compressed sensing by David Donoho to an outstanding publication in the fields of interest to the and by Emmanuel Candes and Terence Tao, respectively (with Society appearing anywhere during the preceding two calendar acknowledgment of an earlier paper by Candes, Romberg and years. The winners of the 2008 award are "Compressed sensing," Tao). The winner of the 2008 Joint IT/ComSoc Paper Award is a by David Donoho, which appeared in the April 2006 IEEE Communications Transactions paper on Accumulate-Repeat- Transactions on Information Theory, and "Near-optimal signal Accumulate Codes by Aliazam Abbasfar, Dariush Divsalar and recovery from random projections: universal encoding strate- Kung Yao. Three student authors of ISIT papers received ISIT gies," by Emmanuel Candes and Terence Tao, which appeared Student Paper Awards: Paul Cuff of Stanford, Satish Korada of in the December 2006 Transactions. These two overlapping EPFL, and Yury Polyanskiy of Princeton. Finally, the 2008 papers are the foundations of the exciting new field of com- Chapter of the Year Award was presented to the Kitchener- pressed sensing. -
Ieee Information Theory Society
IEEE INFORMATION THEORY SOCIETY The Information Theory Society is an organization, within the framework of the IEEE, of members with principal professional interests in information theory. All members of the IEEE are eligible for membership in the Society and will receive this TRANSACTIONS upon payment of the annual Society membership fee of $30.00. For information on joining, write to the IEEE at the address below. Member copies of Transactions/Journals are for personal use only. BOARD OF GOVERNORS President Secretary Treasurer Transactions Editor Conference Committee Chair GIUSEPPE CAIRE NATASHA DEVROYE NIHAR JINDAL HELMUT BÖLCSKEI BRUCE HAJEK EE Dept. Dept. ECE Dept. Elec. Eng. Comp. Sci. Dept. IT & EE Dept. EECS and Univ. of Southern California Univ. of Illinois Univ. of Minnesota ETH Zurich Coordinated Science Lab. Los Angeles, CA 90089 USA Chicago, IL 60607 USA Minneapolis, MN 55455 USA Zurich, Switzerland Univ. of Illinois Urbana, IL 61801 USA First Vice President Second Vice President Junior Past President Senior Past President MURIEL MÉDARD GERHARD KRAMER FRANK R. KSCHISCHANG ANDREA J. GOLDSMITH HELMUT BÖLCSKEI (2011) ALEX GRANT (2011) MURIEL MÉDARD (2012) EMINA SOLJANIN (2011) MARTIN BOSSERT (2012) ROLF JOHANNESSON (2012) PRAKASH NARAYAN (2012) DAVID TSE (2013) MAX H. M. COSTA (2012) GERHARD KRAMER (2011) L. PING (2012) ALEXANDER VARDY (2013) MICHELLE EFFROS (2013) J. NICHOLAS LANEMAN (2013) AMIN SHOKROLLAHI (2013) SERGIO VERDÚ (2011) ABBAS EL GAMAL (2011) HANS-ANDREA LOELIGER (2012) PAUL SIEGEL (2011) EMANUELE VITERBO (2013) IEEE TRANSACTIONS ON INFORMATION THEORY HELMUT BÖLCSKEI, Editor-in-Chief Executive Editorial Board G. DAVID FORNEY,JR.SHLOMO SHAMAI (SHITZ)ALEXANDER VARDY SERGIO VERDÚ CYRIL MÉASSON, Publications Editor PREDRAG SPASOJEVIc´, Publications Editor ERDAL ARIKAN ELZA ERKIP NAVIN KASHYAP DANIEL P. -
2010 Roster (V: Indicates Voting Member of Bog)
IEEE Information Theory Society 2010 Roster (v: indicates voting member of BoG) Officers Frank Kschischang President v Giuseppe Caire First Vice President v Muriel M´edard Second Vice President v Aria Nosratinia Secretary v Nihar Jindal Treasurer v Andrea Goldsmith Junior Past President v Dave Forney Senior Past President v Governors Until End of Alexander Barg 2010 v Dan Costello 2010 v Michelle Effros 2010 v Amin Shokrollahi 2010 v Ken Zeger 2010 v Helmut B¨olcskei 2011 v Abbas El Gamal 2011 v Alex Grant 2011 v Gerhard Kramer 2011 v Paul Siegel 2011 v Emina Soljanin 2011 v Sergio Verd´u 2011 v Martin Bossert 2012 v Max Costa 2012 v Rolf Johannesson 2012 v Ping Li 2012 v Hans-Andrea Loeliger 2012 v Prakash Narayan 2012 v Other Voting Members of BoG Ezio Biglieri IT Transactions Editor-in-Chief v Bruce Hajek Chair, Conference Committee v total number of voting members: 27 quorum: 14 1 Standing Committees Awards Giuseppe Caire Chair, ex officio 1st VP Muriel M´edard ex officio 2nd VP Alexander Barg new Max Costa new Elza Erkip new Ping Li new Andi Loeliger new Ueli Maurer continuing En-hui Yang continuing Hirosuke Yamamoto new Ram Zamir continuing Aaron D. Wyner Award Selection Frank Kschischang Chair, ex officio President Giuseppe Caire ex officio 1st VP Andrea Goldsmith ex officio Junior PP Dick Blahut new Jack Wolf new Claude E. Shannon Award Selection Frank Kschischang Chair, ex officio President Giuseppe Caire ex officio 1st VP Muriel M´edard ex officio 2nd VP Imre Csisz`ar continuing Bob Gray continuing Abbas El Gamal new Bob Gallager new Conference -
Reflections on Compressed Sensing, by E
itNL1208.qxd 11/26/08 9:09 AM Page 1 IEEE Information Theory Society Newsletter Vol. 58, No. 4, December 2008 Editor: Daniela Tuninetti ISSN 1059-2362 Source Coding and Simulation XXIX Shannon Lecture, presented at the 2008 IEEE International Symposium on Information Theory, Toronto Canada Robert M. Gray Prologue Source coding/compression/quantization A unique aspect of the Shannon Lecture is the daunting fact that the lecturer has a year to prepare for (obsess over?) a single lec- source reproduction ture. The experience begins with the comfort of a seemingly infi- { } - bits- - Xn encoder decoder {Xˆn} nite time horizon and ends with a relativity-like speedup of time as the date approaches. I early on adopted a few guidelines: I had (1) a great excuse to review my more than four decades of Simulation/synthesis/fake process information theoretic activity and historical threads extending simulation even further back, (2) a strong desire to avoid repeating the top- - - ics and content I had worn thin during 2006–07 as an interconti- random bits coder {X˜n} nental itinerant lecturer for the Signal Processing Society, (3) an equally strong desire to revive some of my favorite topics from the mid 1970s—my most active and focused period doing Figure 1: Source coding and simulation. unadulterated information theory, and (4) a strong wish to add something new taking advantage of hindsight and experience, The goal of source coding [1] is to communicate or transmit preferably a new twist on some old ideas that had not been pre- the source through a constrained, discrete, noiseless com- viously fully exploited.