Digital Communication Systems ECS 452
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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. -
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. -
Sharp Threshold Rates for Random Codes∗
Sharp threshold rates for random codes∗ Venkatesan Guruswami1, Jonathan Mosheiff1, Nicolas Resch2, Shashwat Silas3, and Mary Wootters3 1Carnegie Mellon University 2Centrum Wiskunde en Informatica 3Stanford University September 11, 2020 Abstract Suppose that P is a property that may be satisfied by a random code C ⊂ Σn. For example, for some p 2 (0; 1), P might be the property that there exist three elements of C that lie in some Hamming ball of radius pn. We say that R∗ is the threshold rate for P if a random code of rate R∗ + " is very likely to satisfy P, while a random code of rate R∗ − " is very unlikely to satisfy P. While random codes are well-studied in coding theory, even the threshold rates for relatively simple properties like the one above are not well understood. We characterize threshold rates for a rich class of properties. These properties, like the example above, are defined by the inclusion of specific sets of codewords which are also suitably \symmetric." For properties in this class, we show that the threshold rate is in fact equal to the lower bound that a simple first-moment calculation obtains. Our techniques not only pin down the threshold rate for the property P above, they give sharp bounds on the threshold rate for list-recovery in several parameter regimes, as well as an efficient algorithm for estimating the threshold rates for list-recovery in general. arXiv:2009.04553v1 [cs.IT] 9 Sep 2020 ∗SS and MW are partially funded by NSF-CAREER grant CCF-1844628, NSF-BSF grant CCF-1814629, and a Sloan Research Fellowship. -
SHANNON SYMPOSIUM and STATUE DEDICATION at UCSD
SHANNON SYMPOSIUM and STATUE DEDICATION at UCSD At 2 PM on October 16, 2001, a statue of Claude Elwood Shannon, the Father of Information Theory who died earlier this year, will be dedicated in the lobby of the Center for Magnetic Recording Research (CMRR) at the University of California-San Diego. The bronze plaque at the base of this statue will read: CLAUDE ELWOOD SHANNON 1916-2001 Father of Information Theory His formulation of the mathematical theory of communication provided the foundation for the development of data storage and transmission systems that launched the information age. Dedicated October 16, 2001 Eugene Daub, Sculptor There is no fee for attending the dedication but if you plan to attend, please fill out that portion of the attached registration form. In conjunction with and prior to this dedication, 15 world-renowned experts on information theory will give technical presentations at a Shannon Symposium to be held in the auditorium of CMRR on October 15th and the morning of October 16th. The program for this Symposium is as follows: Monday Oct. 15th Monday Oct. 15th Tuesday Oct. 16th 9 AM to 12 PM 2 PM to 5 PM 9 AM to 12 PM Toby Berger G. David Forney Jr. Solomon Golomb Paul Siegel Edward vanderMeulen Elwyn Berlekamp Jacob Ziv Robert Lucky Shu Lin David Neuhoff Ian Blake Neal Sloane Thomas Cover Andrew Viterbi Robert McEliece If you are interested in attending the Shannon Symposium please fill out the corresponding portion of the attached registration form and mail it in as early as possible since seating is very limited. -
Reflections on ``Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes
Reflections on \Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes" Venkatesan Guruswami∗ Madhu Sudany March 2002 n A t-error-correcting code over a q-ary alphabet Fq is a set C ⊆ Fq such that for any received n vector r 2 Fq there is at most one vector c 2 C that lies within a Hamming distance of t from r. The minimum distance of the code C is the minimum Hamming distance between any pair of distinct vectors c1; c2 2 C. In his seminal work introducing these concepts, Hamming pointed out that a code of minimum distance 2t + 1 is a t-error-correcting code. It also pointed out the obvious fact that such a code is not a t0-error-correcting code for any t0 > t. We conclude that a code can correct half as many errors as its distance and no more. The mathematical correctness of the above statements are indisputable, yet the interpretation is quite debatable. If a message encoded with a t-error-correcting code ends up getting corrupted in t0 > t places, the decoder may simply throw it hands up in the air and cite the above paragraph. Or, in an alternate notion of decoding, called list decoding, proposed in the late 1950s by Elias [10] and Wozencraft [43], the decoder could try to output a list of codewords within distance t0 of the received vector. If t0 is not much larger than t and the errors are caused by a probabilistic (non-malicious) channel, then most likely this list would have only one element | the transmitted codeword. -
Admissibility Properties of Gilbert's Encoding for Unknown Source
216 IEEE TRANSACTIONS ONINFORMATION THEORY,JANLJARY 1912 Admissibility Properties of Gilbert’s Encoding for Unknown We now wish to show that U*(b) minimizes Source Probabilities E{U@,P) I x1,x2,. .,X”h (7) THOMAS M. COVER the expected average code length conditioned on the data, if in fact p is drawn according to a Dirichlet prior distribution with parameters ,&), defined by the density function Abstract-Huffman coding provides optimal source encoding for (&A,. events of specified source probabilities. Gilbert has proposed a scheme &dPl,PZ,. ,PN) = C&J,,. .,a,)p;1-‘p;i-‘. .p;N-l, for source encoding when these source probabilities are imperfectly known. This correspondence shows that Gilbert’s scheme is a Bayes pi 1 0, zpp1 = 1, I* r 1, (8) scheme against a certain natural prior distribution on the source where C(1i,. J,) is a suitable normalization constant. This follows probabilities. Consequently, since this prior distribution has nonzero from application of Bayes’ rule, from which it follows that the posterior mass everywhere, Gilbert’s scheme is admissible in the sense that no distribution of p given X is again a Dirichlet distribution, this time source encoding has lower average code length for every choice of source with parameters Izl + nl, given by probabilities. APP,,P2,. ‘,PN I x1,x2,. .9X”) I. INTRODUCTION = C(Il + n1, a2 + Q,‘. ., a&l + nN)p;‘+“‘-‘p:2+“2-1.. ., CODINGFOR KNOWN~ ++Q- 1 Consider the random variable X, where Pr {X = xi} = pi, i = PN 3 p*ro,zppi=1. (9) 1,2,. ,N,pi 2 0, Xpi = 1. -
Andrew J. and Erna Viterbi Family Archives, 1905-20070335
http://oac.cdlib.org/findaid/ark:/13030/kt7199r7h1 Online items available Finding Aid for the Andrew J. and Erna Viterbi Family Archives, 1905-20070335 A Guide to the Collection Finding aid prepared by Michael Hooks, Viterbi Family Archivist The Andrew and Erna Viterbi School of Engineering, University of Southern California (USC) First Edition USC Libraries Special Collections Doheny Memorial Library 206 3550 Trousdale Parkway Los Angeles, California, 90089-0189 213-740-5900 [email protected] 2008 University Archives of the University of Southern California Finding Aid for the Andrew J. and Erna 0335 1 Viterbi Family Archives, 1905-20070335 Title: Andrew J. and Erna Viterbi Family Archives Date (inclusive): 1905-2007 Collection number: 0335 creator: Viterbi, Erna Finci creator: Viterbi, Andrew J. Physical Description: 20.0 Linear feet47 document cases, 1 small box, 1 oversize box35000 digital objects Location: University Archives row A Contributing Institution: USC Libraries Special Collections Doheny Memorial Library 206 3550 Trousdale Parkway Los Angeles, California, 90089-0189 Language of Material: English Language of Material: The bulk of the materials are written in English, however other languages are represented as well. These additional languages include Chinese, French, German, Hebrew, Italian, and Japanese. Conditions Governing Access note There are materials within the archives that are marked confidential or proprietary, or that contain information that is obviously confidential. Examples of the latter include letters of references and recommendations for employment, promotions, and awards; nominations for awards and honors; resumes of colleagues of Dr. Viterbi; and grade reports of students in Dr. Viterbi's classes at the University of California, Los Angeles, and the University of California, San Diego. -
Awards Program
Award Selection Committee Chairs Frontiers in Education Conference Benjamin J. Dasher Best Paper Award ........................................................... Diane Rover Helen Plants Award ........................................................................................ Elizabeth Eschenbach Ronald J. Schmitz Award ............................................................................... Robert Hofinger ASEE Electrical and Computer Engineering Division Hewlett-Packard Frederick Emmons Terman Award ..................................... Jeffrey Andrews IEEE Education Society IEEE William E. Sayle Award for Achievement in Education ....................... Susan Conry IEEE Transactions on Education Theodore Bachman Award ........................ Susan Lord Chapter Achievement Award ......................................................................... Kai Pan Mark Distinguished Chapter Leadership Award ...................................................... Trond Clausen and Emmanuel Gonzalez Distinguished Member Award ........................................................................ Victor Nelson Edwin C. Jones, Jr. Meritorious Service Award .............................................. Susan Lord Hewlett-Packard/Harriett B. Rigas Award ..................................................... Joanne Bechta Dugan Mac Van Valkenburg Early Career Teaching Award... ................................... S. Hossein Mousavinezhad Student Leadership Award ............................................................................. -
IEEE Information Theory Society Newsletter
IEEE Information Theory Society Newsletter Vol. 66, No. 4, December 2016 Editor: Michael Langberg ISSN 1059-2362 Editorial committee: Frank Kschischang, Giuseppe Caire, Meir Feder, Tracey Ho, Joerg Kliewer, Parham Noorzad, Anand Sarwate, Andy Singer, and Sergio Verdú President’s Column Alon Orlitsky One should never start with a cliche. So let me that would bring and curate information the- end with one: where did 2016 go? It seems like oretic lectures for large audiences. yesterday that I wrote my first column, and it’s already time to reflect on a year gone by? • Jeff Andrews and Elza Erkip are heading a BoG ad-hoc committee exploring the cre- And a remarkable year it was! Each of earth’s ation of a new publication connecting corners and all of life’s walks were abuzz with information theory to other topics and activity and change, and information theory communities, with two main formats con- followed suit. Adding to our society’s regu- sidered: a special topics journal, and a larly hectic conference meeting/publication popular magazine. calendar, we also celebrated Shannon’s 100th anniversary with fifty worldwide centennials, • Christina Fragouli and Anna Scaglione are numerous write-ups in major journals and co-authoring a children’s book on informa- magazines, and a coveted Google Doodle on tion theory, the first chapter is completed Shannon’s birthday. For the last time let me and the rest are expected next year. thank Christina Fragouli and Rudi Urbanke for co-chairing the hyperactive Centennials Committee. As the holidays ushered in, twelve-shy-one society members received jolly good tidings. -
Uwaterloo Latex Thesis Template
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Waterloo's Institutional Repository On Causal Video Coding with Possible Loss of the First Encoded Frame by Mahshad Eslamifar A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Applied Science in Electrical and Computer Engineering Waterloo, Ontario, Canada, 2013 c Mahshad Eslamifar 2013 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract Multiple Description Coding (MDC) was first formulated by A. Gersho and H. Witsen- hausen as a way to improve the robustness of telephony links to outages. Lots of studies have been done in this area up to now. Another application of MDC is the transmission of an image in different descriptions. If because of the link outage during transmission, any one of the descriptions fails, the image could still be reconstructed with some quality at the decoder side. In video coding, inter prediction is a way to reduce temporal redundancy. From an information theoretical point of view, one can model inter prediction with Causal Video Coding (CVC). If because of link outage, we lose any I-frame, how can we recon- struct the corresponding P- or B-frames at the decoder? In this thesis, we are interested in answering this question and we call this scenario as causal video coding with possible loss of the first encoded frame and we denote it by CVC-PL as PL stands for possible loss. -
Human Space Flight
HUMAN SPACE FLIGHT APOLLO 50 YEARS ON 2019 ANNUAL MEETING October 6-7, 2019 Washington, DC NATIONAL ACADEMY OF ENGINEERING 2019 ANNUAL MEETING October 6–7, 2019 Washington, DC CONTENTS Sunday, October 6 Public Program . 2 Chair’s Remarks . 2 President’s Address . 4 Induction Ceremony . 5 Awards Program. 5 Plenary Session . .10 Monday, October 7 Business Session . .12 Public Forum . .12 Reception & Dinner Dance . .17 Section Meetings . .18 General Information Meeting Services . 18 Section Meetings . 18 Registration . 19 Shuttle Bus Service . 19 Guest Tour Bus Service . .19 Guest Program . .20 Section Chairs . 21 NAS Building Map . .22 Area Map . 23 2018 Honor Roll of Donors . 24 Cover photo credit: William Anders/NASA/AP, Dec. 24, 1968 10:00 am–4:00 pm Registration NAS 120 10:30 am–11:45 am Brunch Buffet West Lawn 10:30 am–11:45 am Planned Giving in the Current Tax Environment Members’ Room (advance registration required; brunch included) Led by Alan L. Cates, JD Partner, Husch Blackwell Alan L. Cates focuses his practice on trust and estate issues and related private wealth matters and frequently presents on financial topics such as taxation, estate planning, business succession planning and probate and trust issues across the country. With decades of comprehensive legal experience, he has guided individuals and their businesses in estate planning and business succession planning. Additionally, he has represented individual and institutional executors and trustees in all sorts of litigation matters, both as defense counsel and in initiating action. He has also represented taxpayers in administrative proceedings and in courtrooms, and provided critical services to tax-exempt organizations.