ELEC3028 Digital Transmission Overview & Information Theory. Example 1


 Kory Patterson
 3 years ago
 Views:
Transcription
1 Example. A source emits symbols i, i 6, in the BCD format with probabilities P( i ) as given in Table, at a rate R s = 9.6 kbaud (baud=symbol/second). State (i) the information rate and (ii) the data rate of the source. 2. Apply ShannonFano coding to the source signal characterised in Table. Are there any disadvantages in the resulting code words? 3. What is the original symbol sequence of the Shannon Fano coded signal ? 4. What is the data rate of the signal after ShannonFano coding? What compression factor has been achieved? i Table. P( i ) BCD word A B C D E F Derive the coding efficiency of both the uncoded BCD signal as well as the ShannonFano coded signal. 6. Repeat parts 2 to 5 but this time with Huffman coding. 72
2 Example  Solution. (i) Entropy of source: 6 H = P( i ) log 2 P( i ) = 0.30 log log log i= 0.5 log log log = = bits/symbol Information rate: R = H R s = [bits/symbol] 9600 [symbols/s] = 9750 [bits/s] (ii) Data rate = 3 [bits/symbol] 9600 [symbols/s] = [bits/s] 2. ShannonFano coding: P() I (bits) steps code E A D B F C Disadvantage: the rare code words have maximum possible length of q = 6 = 5, and a buffer of 5 bit is required. 73
3 3. ShannonFano encoded sequence: = DEFEEEDADE 4. Average code word length: Data rate: Compression factor: d = = 2. [bits/symbol] 5. Coding efficiency before ShannonFano: d R s = = 2060 [bits/s] 3 [bits] d [bits] = 3 2. =.4286 CE = information rate data rate = = 68.58% Coding efficiency after ShannonFano: CE = information rate data rate == = 97.97% Hence ShannonFano coding brought the coding efficiency close to 00%. 6. Huffman coding: 74
4 P() steps code E 0.4 A D B F C step 3 step 4 step 5 E 0.40 E 0.40 ADBFC A 0.30 A E 0.40 D DBFC 0.30 BFC 0.5 step step 2 E 0.40 E 0.40 A 0.30 A 0.30 D 0.5 D 0.5 B 0.0 B F FC 0.05 C 0.02 Same disadvantage as ShannonFano: the rare code words have maximum possible length of q = 6 = 5, and a buffer of 5 bit is required = EEAEEEEAAEEDEEA The same data rate and the same compression factor achieved as ShannonFano coding. The coding efficiency of the Huffman coding is identical to that of ShannonFano coding. 75
5 Example 2. Considering the binary symmetric channel (BSC) shown in the figure: P( 0 ) = p P( ) = p 0 p e p e p e P(Y ) p e Y 0 Y P(Y 0 ) From the definition of mutual information, I(, Y ) = i P( i, Y ) log 2 P( i Y ) P( i ) [bits/symbol] derive both (i) a formula relating I(, Y ), the source entropy H(), and the average information lost per symbol H( Y ), and (ii) a formula relating I(, Y ), the destination entropy H(Y ), and the error entropy H(Y ). 2. State and ustify the relation (>,<,=,, or ) between H( Y ) and H(Y ). 3. Considering the BSC in Figure, we now have p = 4 and a channel error probability p e = 0. Calculate all probabilities P( i, Y ) and P( i Y ), and derive the numerical value for the mutual information I(, Y ). 76
6 Example 2  Solution. (i) Relating to source entropy and average information lost: I(, Y ) = i = i = i = i P( i, Y ) log 2 P( i Y ) P( i ) P( i, Y ) log 2 P( i ) i P( i, Y ) A log 2 P( i ) P(Y ) P( i ) log 2 P( i ) i! P( i Y ) log 2 P( i Y ) P( i, Y ) log 2 P( i Y ) P(Y ) I( Y ) = H() H( Y ) (ii) Bayes rule : P( i Y ) P( i ) = P( i, Y ) P( i ) P(Y ) = P(Y i ) P(Y ) 77
7 Hence, relating to destination entropy and error entropy: P(Y i ) I(, Y ) = P( i, Y ) log 2 P(Y ) i i P(Y, i ) log 2 P(Y i ) = i P(Y, i ) log 2 P(Y ) = H(Y ) H(Y ) 2. Unless p e = 0.5 or for equiprobable source symbols, the symbols Y at the destination are more balanced, hence H(Y ) H(). Therefore, H(Y ) H( Y ). 3. Joint probabilities: Destination total probabilities: P( 0, Y 0 ) = P( 0 ) P(Y 0 0 ) = = P( 0, Y ) = P( 0 ) P(Y 0 ) = 4 0 = P(, Y 0 ) = P( ) P(Y 0 ) = = P(, Y ) = P( ) P(Y ) = = P(Y 0 ) = P( 0 ) P(Y 0 0 ) + P( ) P(Y 0 ) = =
8 P(Y ) = P( 0 ) P(Y 0 ) + P( ) P(Y ) = = 0.7 Conditional probabilities: P( 0 Y 0 ) = P( 0, Y 0 ) = P(Y 0 ) 0.3 = 0.75 Mutual information: P( 0 Y ) = P( 0, Y ) P(Y ) P( Y 0 ) = P(, Y 0 ) P(Y 0 ) P( Y ) = P(, Y ) P(Y ) I(, Y ) = P( 0, Y 0 ) log 2 P(Y 0 0 ) P(Y 0 ) +P(, Y 0 ) log 2 P(Y 0 ) P(Y 0 ) = = = = 0.25 = = P( 0, Y ) log 2 P(Y 0 ) P(Y ) + P(, Y ) log 2 P(Y ) P(Y ) = = [bits/symbol] 79
9 Example 3 A digital communication system uses a 4ary signalling scheme. Assume that 4 symbols 3,,,3 are chosen with probabilities 8, 4, 2, 8, respectively. The channel is an ideal channel with AWGN, the transmission rate is 2 Mbaud (2 0 6 symbols/s), and the channel signal to noise ratio is known to be 5.. Determine the source information rate. 2. If you are able to employ some capacityapproaching errorcorrection coding technique and would like to achieve errorfree transmission, what is the minimum channel bandwidth required? 80
10 Example 3  Solution. Source entropy: H = 2 8 log log log 2 2 = 7 4 [bits/symbol] Source information rate: R = H R s = = 3.5 [Mbits/s] 2. To be able to achieve errorfree transmission ( R C = B log 2 + S ) P N P B log 2 ( + 5) Thus B [MHz] 8
11 Example 4 A predictive source encoder generates a bit stream, and it is known that the probability of a bit taking the value 0 is P(0) = p = The bit stream is then encoded by a run length encoder (RLC) with a codeword length of n = 5 bits.. Determine the compression ratio of the RLC. 2. Find the encoder input patterns that produce the following encoder output cordwords What is the encoder input sequence of the RLC coded signal ? 82
12 Example 4  Solution. Codeword length after RLC is n = 5 bits, and average codeword length d before RLC with N = 2 n N d = (l + ) p l ( p) + N p N = pn p Compression ratio l=0 d n = pn n( p) = = RLC table {z } {z } {z } {z } {z } the encoder input sequence 00 0 {z } {z 0000} 30 83
Coded modulation: What is it?
Coded modulation So far: Binary coding Binary modulation Will send R information bits/symbol (spectral efficiency = R) Constant transmission rate: Requires bandwidth expansion by a factor 1/R Until 1976:
More informationName: Shu Xiong ID:
Homework #1 Report Multimedia Data Compression EE669 2013Spring Name: Shu Xiong ID: 3432757160 Email: shuxiong@usc.edu Content Problem1: Writing Questions... 2 Huffman Coding... 2 LempelZiv Coding...
More informationEntropy and Mutual Information
ENCYCLOPEDIA OF COGNITIVE SCIENCE 2000 Macmillan Reference Ltd Information Theory information, entropy, communication, coding, bit, learning Ghahramani, Zoubin Zoubin Ghahramani University College London
More informationFUNDAMENTALS of INFORMATION THEORY and CODING DESIGN
DISCRETE "ICS AND ITS APPLICATIONS Series Editor KENNETH H. ROSEN FUNDAMENTALS of INFORMATION THEORY and CODING DESIGN Roberto Togneri Christopher J.S. desilva CHAPMAN & HALL/CRC A CRC Press Company Boca
More informationChap 3 Huffman Coding
Chap 3 Huffman Coding 3.1 Overview 3.2 The Huffman Coding Algorithm 3.4 Adaptive Huffman Coding 3.5 Golomb Codes 3.6 Rice Codes 3.7 Tunstall Codes 3.8 Applications of Huffman Coding 1 3.2 The Huffman Coding
More informationChapter 1 Introduction
Chapter 1 Introduction 1. Shannon s Information Theory 2. Source Coding theorem 3. Channel Coding Theory 4. Information Capacity Theorem 5. Introduction to Error Control Coding Appendix A : Historical
More informationReading.. IMAGE COMPRESSION I IMAGE COMPRESSION. Image compression. Data Redundancy. Lossy vs Lossless Compression. Chapter 8.
Reading.. IMAGE COMPRESSION I Week VIII Feb 25 Chapter 8 Sections 8.1, 8.2 8.3 (selected topics) 8.4 (Huffman, runlength, lossless predictive) 8.5 (lossy predictive, transform coding basics) 8.6 Image
More informationShannon and HuffmanType Coders
Shannon and HuffmanType Coders A useful class of coders that satisfy the Kraft's inequality in an efficient manner are called Huffmantype coders. To understand the philosophy of obtaining these codes,
More informationImage Compression through DCT and Huffman Coding Technique
International Journal of Current Engineering and Technology EISSN 2277 4106, PISSN 2347 5161 2015 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Research Article Rahul
More informationPrinciples of Image Compression
Principles of Image Compression Catania 03/04/2008 Arcangelo Bruna Overview Image Compression is the Image Data Elaboration branch dedicated to the image data representation It analyzes the techniques
More informationWhat s The Difference Between Bit Rate And Baud Rate?
What s The Difference Between Bit Rate And Baud Rate? Apr. 27, 2012 Lou Frenzel Electronic Design Serialdata speed is usually stated in terms of bit rate. However, another oftquoted measure of speed is
More informationcharacter E T A S R I O D frequency
Data Compression Data compression is any process by which a digital (e.g. electronic) file may be transformed to another ( compressed ) file, such that the original file may be fully recovered from the
More informationCompression techniques
Compression techniques David Bařina February 22, 2013 David Bařina Compression techniques February 22, 2013 1 / 37 Contents 1 Terminology 2 Simple techniques 3 Entropy coding 4 Dictionary methods 5 Conclusion
More informationINTRODUCTION TO CODING THEORY: BASIC CODES AND SHANNON S THEOREM
INTRODUCTION TO CODING THEORY: BASIC CODES AND SHANNON S THEOREM SIDDHARTHA BISWAS Abstract. Coding theory originated in the late 1940 s and took its roots in engineering. However, it has developed and
More informationInformation, Entropy, and Coding
Chapter 8 Information, Entropy, and Coding 8. The Need for Data Compression To motivate the material in this chapter, we first consider various data sources and some estimates for the amount of data associated
More informationImage Compression. Topics
Image Compression October 2010 Topics Redundancy Image information Fidelity Huffman coding Arithmetic coding Golomb code LZW coding Run Length Encoding Bit plane coding 1 Why do we need compression? Data
More informationHuffman Coding. National Chiao Tung University ChunJen Tsai 10/2/2014
Huffman Coding National Chiao Tung University ChunJen Tsai 10/2/2014 Huffman Codes Optimum prefix code developed by D. Huffman in a class assignment Construction of Huffman codes is based on two ideas:
More informationAlmost every lossy compression system contains a lossless compression system
Lossless compression in lossy compression systems Almost every lossy compression system contains a lossless compression system Lossy compression system Transform Quantizer Lossless Encoder Lossless Decoder
More informationDigital Video Broadcasting By Satellite
Digital Video Broadcasting By Satellite Matthew C. Valenti Lane Department of Computer Science and Electrical Engineering West Virginia University U.S.A. Apr. 2, 2012 ( Lane Department LDPCof Codes Computer
More informationCoding and decoding with convolutional codes. The Viterbi Algor
Coding and decoding with convolutional codes. The Viterbi Algorithm. 8 Block codes: main ideas Principles st point of view: infinite length block code nd point of view: convolutions Some examples Repetition
More informationDigital Modulation. David Tipper. Department of Information Science and Telecommunications University of Pittsburgh. Typical Communication System
Digital Modulation David Tipper Associate Professor Department of Information Science and Telecommunications University of Pittsburgh http://www.tele.pitt.edu/tipper.html Typical Communication System Source
More informationVLSM (CIDR) Subnet Calculator. IP address classes
VLSM (CIDR) Subnet Calculator Variable Length Subnet Masking is a technique that allows network administrators to divide an IP address space to subnets of different sizes, unlike simple samesize subnetting.
More informationInformation Theory and Coding SYLLABUS
SYLLABUS Subject Code : IA Marks : 25 No. of Lecture Hrs/Week : 04 Exam Hours : 03 Total no. of Lecture Hrs. : 52 Exam Marks : 00 PART  A Unit : Information Theory: Introduction, Measure of information,
More informationModule 6. Channel Coding. Version 2 ECE IIT, Kharagpur
Module 6 Channel Coding Lesson 35 Convolutional Codes After reading this lesson, you will learn about Basic concepts of Convolutional Codes; State Diagram Representation; Tree Diagram Representation; Trellis
More informationand the bitplane representing the second most significant bits is and the bitplane representing the least significant bits is
1 7. BITPLANE GENERATION The integer wavelet transform (IWT) is transformed into bitplanes before coding. The sign bitplane is generated based on the polarity of elements of the transform. The absolute
More informationCompression for IR. Lecture 5. Lecture 5 Information Retrieval 1
Compression for IR Lecture 5 Lecture 5 Information Retrieval 1 IR System Layout Lexicon (w, *occ) Occurrences (d, f t,d ) Locations (d, *pos) Documents 2 Why Use Compression? More storage inverted file
More informationAn Introduction to Information Theory
An Introduction to Information Theory Carlton Downey November 12, 2013 INTRODUCTION Today s recitation will be an introduction to Information Theory Information theory studies the quantification of Information
More informationModule 3. Data Link control. Version 2 CSE IIT, Kharagpur
Module 3 Data Link control Lesson 2 Error Detection and Correction Special Instructional Objectives: On completion of this lesson, the student will be able to: Explain the need for error detection and
More informationLecture slides prepared by Dr Lawrie Brown for Data and Computer Communications, 8/e, by William Stallings, Chapter 6 Digital Data
Lecture slides prepared by Dr Lawrie Brown (UNSW@ADFA) for Data and Computer Communications, 8/e, by William Stallings, Chapter 6 Digital Data Communications Techniques. 1 This quote from the start of
More informationLec 03 Entropy and Coding II Hoffman and Golomb Coding
Outline CS/EE 559 / ENG 4 Special Topics (Class Ids: 784, 785, 783) Lecture ReCap Hoffman Coding Golomb Coding and JPEG Lossless Coding Lec 3 Entropy and Coding II Hoffman and Golomb Coding Zhu Li Z. Li
More informationEnergy and Bandwidth Efficiency in Wireless Networks. Changhun Bae Wayne Stark University of Michigan
Energy and Bandwidth Efficiency in Wireless Networks Changhun Bae Wayne Stark University of Michigan Outline Introduction/Background Device/Physical Layer/Network Layer Models Performance Measure Numerical
More informationCHANNEL. 1 Fast encoding of information. 2 Easy transmission of encoded messages. 3 Fast decoding of received messages.
CHAPTER : Basics of coding theory ABSTRACT Part I Basics of coding theory Coding theory  theory of error correcting codes  is one of the most interesting and applied part of mathematics and informatics.
More informationTeaching Convolutional Coding using MATLAB in Communication Systems Course. Abstract
Section T3C2 Teaching Convolutional Coding using MATLAB in Communication Systems Course Davoud Arasteh Department of Electronic Engineering Technology, LA 70813, USA Abstract Convolutional codes are channel
More informationA New Digital Communications Course Enhanced by PCBased Design Projects*
Int. J. Engng Ed. Vol. 16, No. 6, pp. 553±559, 2000 0949149X/91 $3.00+0.00 Printed in Great Britain. # 2000 TEMPUS Publications. A New Digital Communications Course Enhanced by PCBased Design Projects*
More informationPolarization codes and the rate of polarization
Polarization codes and the rate of polarization Erdal Arıkan, Emre Telatar Bilkent U., EPFL Sept 10, 2008 Channel Polarization Given a binary input DMC W, i.i.d. uniformly distributed inputs (X 1,...,
More informationReview of Number Systems The study of number systems is important from the viewpoint of understanding how data are represented before they can be processed by any digital system including a computer. Different
More informationNonData Aided Carrier Offset Compensation for SDR Implementation
NonData Aided Carrier Offset Compensation for SDR Implementation Anders Riis Jensen 1, Niels Terp Kjeldgaard Jørgensen 1 Kim Laugesen 1, Yannick Le Moullec 1,2 1 Department of Electronic Systems, 2 Center
More informationChapter 3: Digital Audio Processing and Data Compression
Chapter 3: Digital Audio Processing and Review of number system 2 s complement sign and magnitude binary The MSB of a data word is reserved as a sign bit, 0 is positive, 1 is negative. The rest of the
More informationQuantization. Yao Wang Polytechnic University, Brooklyn, NY11201
Quantization Yao Wang Polytechnic University, Brooklyn, NY11201 http://eeweb.poly.edu/~yao Outline Review the three process of A to D conversion Quantization Uniform Nonuniform Mulaw Demo on quantization
More informationInformation Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture  17 ShannonFanoElias Coding and Introduction to Arithmetic Coding
More informationSampling Theorem Notes. Recall: That a time sampled signal is like taking a snap shot or picture of signal periodically.
Sampling Theorem We will show that a band limited signal can be reconstructed exactly from its discrete time samples. Recall: That a time sampled signal is like taking a snap shot or picture of signal
More information(continued on page 20) Field Strength (db mv/m) VCCI FCC Class A FTZ1046 VDEB MAC MAC. EN Class B PMI PMD PMI PMD PHY PHY
A physical layer has been developed for demand priority local area networks that accommodates different cable types by means of different physical medium dependent (PMD) sublayers. The major goal was to
More informationMIMO CHANNEL CAPACITY
MIMO CHANNEL CAPACITY Ochi Laboratory Nguyen Dang Khoa (D1) 1 Contents Introduction Review of information theory Fixed MIMO channel Fading MIMO channel Summary and Conclusions 2 1. Introduction The use
More informationMultimedia Communications. Huffman Coding
Multimedia Communications Huffman Coding Optimal codes Suppose that a i > w i C + is an encoding scheme for a source alphabet A={a 1,, a N }. Suppose that the source letter a 1,, a N occur with relative
More informationSample Solution to Problem Set 1
College of Computer & Information Science Spring 21 Northeastern University Handout 3 CS 671: Wireless Networks 19 February 21 Sample Solution to Problem Set 1 1. (1 points) Applying lowpass and bandpass
More informationToken Ring and. Fiber Distributed Data Interface (FDDI) Networks: Token Ring and FDDI 1
Token Ring and Fiber Distributed Data Interface (FDDI) Networks: Token Ring and FDDI 1 IEEE 802.5 Token Ring Proposed in 1969 and initially referred to as a Newhall ring. Token ring :: a number of stations
More informationCapacity Limits of MIMO Channels
Tutorial and 4G Systems Capacity Limits of MIMO Channels Markku Juntti Contents 1. Introduction. Review of information theory 3. Fixed MIMO channels 4. Fading MIMO channels 5. Summary and Conclusions References
More informationCS263: Wireless Communications and Sensor Networks
CS263: Wireless Communications and Sensor Networks Matt Welsh Lecture 2: RF Basics and Signal Encoding September 22, 2005 2005 Matt Welsh Harvard University 1 Today's Lecture Basics of wireless communications
More informationPublic Switched Telephone System
Public Switched Telephone System Structure of the Telephone System The Local Loop: Modems, ADSL Structure of the Telephone System (a) Fullyinterconnected network. (b) Centralized switch. (c) Twolevel
More informationArithmetic Coding: Introduction
Data Compression Arithmetic coding Arithmetic Coding: Introduction Allows using fractional parts of bits!! Used in PPM, JPEG/MPEG (as option), Bzip More time costly than Huffman, but integer implementation
More informationInverted Indexes Compressed Inverted Indexes. Indexing and Searching, Modern Information Retrieval, Addison Wesley, 2010 p. 40
Inverted Indexes Compressed Inverted Indexes Indexing and Searching, Modern Information Retrieval, Addison Wesley, 2010 p. 40 Compressed Inverted Indexes It is possible to combine index compression and
More informationSignal Compression Survey of the lectures Hints for exam
Signal Compression Survey of the lectures Hints for exam Chapter 1 Use one statement to define the three basic signal compression problems. Answer: (1) designing a good code for an independent source;
More informationThe ISO/OSI Reference Model
The ISO/OSI Reference Model The Model Functionality of Layers Example Networks The OSI Model Basic principles of layered architecture: Each layer means different layer of abstraction Each layer should
More informationParametric Comparison of H.264 with Existing Video Standards
Parametric Comparison of H.264 with Existing Video Standards Sumit Bhardwaj Department of Electronics and Communication Engineering Amity School of Engineering, Noida, Uttar Pradesh,INDIA Jyoti Bhardwaj
More information802.11A  OFDM PHY CODING AND INTERLEAVING. Fernando H. Gregorio. Helsinki University of Technology
802.11A  OFDM PHY CODING AND INTERLEAVING Fernando H. Gregorio Helsinki University of Technology Signal Processing Laboratory, POB 3000, FIN02015 HUT, Finland Email:gregorio@wooster.hut.fi 1. INTRODUCTION
More informationBinary Codes for Nonuniform
Binary Codes for Nonuniform Sources (dcc2005) Alistair Moffat and Vo Ngoc Anh Presented by: Palak Mehta 11202006 Basic Concept: In many applications of compression, decoding speed is at least as important
More informationLab Session 4. Review. Outline. May 18, Image and video encoding: A big picture
Outline Lab Session 4 May 18, 2009 Review Manual Exercises Comparing coding performance of different codes: Shannon code, ShannonFano code, Huffman code (and Tunstall code *) MATLAB Exercises Working
More information5 Capacity of wireless channels
CHAPTER 5 Capacity of wireless channels In the previous two chapters, we studied specific techniques for communication over wireless channels. In particular, Chapter 3 is centered on the pointtopoint
More informationA software for learning Information Theory basics with emphasis on Entropy of. Spanish. Fabio G. Guerrero, Member, IEEE and Lucio A.
A software for learning Information Theory basics with emphasis on Entropy of Spanish Fabio G. Guerrero, Member, IEEE and Lucio A. Pérez Abstract In this paper, a tutorial software to learn Information
More informationCHAPTER 10 Linear TimeInvariant (LTI) Models for Communication Channels
MIT 6.02 DRAFT Lecture Notes Fall 2011 (Last update: November 5, 2011) Comments, questions or bug reports? Please contact verghese at mit.edu CHAPTER 10 Linear TimeInvariant (LTI) Models for Communication
More informationDo not turn this page over until instructed to do so by the Senior Invigilator.
CARDIFF UNIVERSITY EXAMINATION PAPER Academic Year: 2014/2015 Examination Period: Examination Paper Number: Examination Paper Title: Duration: Autumn CM3106 Solutions Multimedia Solutions 2 hours Do not
More informationA Methodology and the Tool for Testing SpaceWire Routing Switches Session: SpaceWire test and verification
A Methodology and the Tool for Testing SpaceWire Routing Switches Session: SpaceWire test and verification Elena Suvorova SaintPetersburg University of Aerospace Instrumentation. 67, B. Morskaya, Saint
More informationCommunications Systems Laboratory. Department of Electrical Engineering. University of Virginia. Charlottesville, VA 22903
Turbo Trellis Coded Modulation W. J. Blackert y and S. G. Wilson Communications Systems Laboratory Department of Electrical Engineering University of Virginia Charlottesville, VA 22903 Abstract Turbo codes
More informationExercises with solutions (1)
Exercises with solutions (). Investigate the relationship between independence and correlation. (a) Two random variables X and Y are said to be correlated if and only if their covariance C XY is not equal
More informationVoiceis analog in character and moves in the form of waves. 3important wavecharacteristics:
Voice Transmission Basic Concepts Voiceis analog in character and moves in the form of waves. 3important wavecharacteristics: Amplitude Frequency Phase Voice Digitization in the POTS Traditional
More informationLecture 18 October 30
EECS 290S: Network Information Flow Fall 2008 Lecture 18 October 30 Lecturer: Anant Sahai and David Tse Scribe: Changho Suh In this lecture, we studied two types of onetomany channels: (1) compound channels
More informationCSC 310: Information Theory
CSC 310: Information Theory University of Toronto, Fall 2011 Instructor: Radford M. Neal Week 2 What s Needed for a Theory of (Lossless) Data Compression? A context for the problem. What are we trying
More informationMultiplexing, Circuit Switching and Packet Switching. Circuit Switching
Multiplexing, Circuit Switching and Packet Switching Circuit Switching Old telephone technology For each connection, physical switches are set in the telephone network to create a physical circuit That
More informationInformation Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture  14 NonBinary Huffman Code and Other Codes In the last class we
More informationDigital vs. Analog Transmission Nyquist and Shannon Laws
1 Digital vs. Analog Transmission Nyquist and Shannon Laws Required reading: Garcia 3.1 to 3.5 CSE 3213, Fall 2010 Instructor: N. Vlajic Transmission Impairments 2 Transmission / Signal Impairments caused
More informationManaging HighSpeed Clocks
Managing HighSpeed s & Greg Steinke Director, Component Applications Managing HighSpeed s Higher System Performance Requires Innovative ing Schemes What Are The Possibilities? HighSpeed ing Schemes
More informationBits, Bytes, and Codes
Bits, Bytes, and Codes Telecommunications 1 Peter Mathys Black and White Image Suppose we want to draw a B&W image on a computer screen. We first subdivide the screen into small rectangles or squares called
More informationEnhancing HighSpeed Telecommunications Networks with FEC
White Paper Enhancing HighSpeed Telecommunications Networks with FEC As the demand for highbandwidth telecommunications channels increases, service providers and equipment manufacturers must deliver
More informationSignaltoNoise, CarriertoNoise, EbNo on Signal Quality Ratios. by Wolfgang Damm, WTG
SignaltoNoise, CarriertoNoise, EbNo on Signal Quality Ratios by Wolfgang Damm, WTG Agenda Signal Measurement Environment Ratios: S/N, C/N, C/No, C/I, EbNo Shannon Limit Error Correction BER & Coding
More informationImage Transmission over IEEE 802.15.4 and ZigBee Networks
MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com Image Transmission over IEEE 802.15.4 and ZigBee Networks Georgiy Pekhteryev, Zafer Sahinoglu, Philip Orlik, and Ghulam Bhatti TR2005030 May
More informationFast Ethernet and Gigabit Ethernet. Networks: Fast Ethernet 1
Fast Ethernet and Gigabit Ethernet Networks: Fast Ethernet 1 Fast Ethernet (100BASET) How to achieve 100 Mbps capacity? MII LLC MAC Convergence Sublayer Media Independent Interface Media Dependent Sublayer
More informationLezione 6 Communications Blockset
Corso di Tecniche CAD per le Telecomunicazioni A.A. 20072008 Lezione 6 Communications Blockset Ing. Marco GALEAZZI 1 What Is Communications Blockset? Communications Blockset extends Simulink with a comprehensive
More information0L[HG6LJQDO&LUFXLWVDQG6\VWHPV 0RGHP7HFKQLTXHV. The Modem as an example of a mixed signal system
0L[HG6LJQDO&LUFXLWVDQG6\VWHPV 0RGHP7HFKQLTXHV The Modem as an example of a mixed signal system Mixed Signal Circuits and Systems, A.J.M. van Tuijl, IC Ontwerpkunde, sheet 8.1 ['6/[[['LJLWDO6XEVFULEHU/LQH2YHUYLHZ
More informationIntroduction to Learning & Decision Trees
Artificial Intelligence: Representation and Problem Solving 538 April 0, 2007 Introduction to Learning & Decision Trees Learning and Decision Trees to learning What is learning?  more than just memorizing
More informationDATA SECURITY USING PRIVATE KEY ENCRYPTION SYSTEM BASED ON ARITHMETIC CODING
DATA SECURITY USING PRIVATE KEY ENCRYPTION SYSTEM BASED ON ARITHMETIC CODING Ajit Singh 1 and Rimple Gilhotra 2 Department of Computer Science & Engineering and Information Technology BPS Mahila Vishwavidyalaya,
More informationTCOM 370 NOTES 994 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS
TCOM 370 NOTES 994 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS 1. Bandwidth: The bandwidth of a communication link, or in general any system, was loosely defined as the width of
More informationCS413: Computer Networks
CS413: Computer Networks 2005 Fall Term Midterm Exam Solution Student ID: Name: Problem No. Marks Your Marks 1 16 2 5 3 5 4 7 5 4 6 7 7 3 8 3 Total 50 1 [Marking schemes are given in blue color and the
More informationAdvanced Computer Networks (CSL858) Vinay Ribeiro
Advanced Computer Networks (CSL858) Vinay Ribeiro Goals of Course Develop a strong understanding of network technologies from the physical to application layer design choices strengths and weaknesses Get
More informationPhysical Layer Part 2. Data Encoding Techniques. Networks: Data Encoding 1
Physical Layer Part 2 Data Encoding Techniques Networks: Data Encoding 1 Analog and Digital Transmissions Figure 223.The use of both analog and digital transmissions for a computer to computer call. Conversion
More informationCS/ECE 438: Communication Networks for Computers Spring 2014 Midterm Study Guide
CS/ECE 438: Communication Networks for Computers Spring 2014 Midterm Study Guide 1. Channel Rates and Shared Media You are entrusted with the design of a network to interconnect a set of geographically
More informationLargeScale IP Traceback in HighSpeed Internet
2004 IEEE Symposium on Security and Privacy LargeScale IP Traceback in HighSpeed Internet Jun (Jim) Xu Networking & Telecommunications Group College of Computing Georgia Institute of Technology (Joint
More informationThe Effect of Network Cabling on Bit Error Rate Performance. By Paul Kish NORDX/CDT
The Effect of Network Cabling on Bit Error Rate Performance By Paul Kish NORDX/CDT Table of Contents Introduction... 2 Probability of Causing Errors... 3 Noise Sources Contributing to Errors... 4 Bit Error
More informationWhite Paper Real Time Monitoring Explained
White Paper Real Time Monitoring Explained Video Clarity, Inc. 1566 La Pradera Dr Campbell, CA 95008 www.videoclarity.com 4083796952 Version 1.0 A Video Clarity White Paper page 1 of 7 Real Time Monitor
More informationIntroduction to Arithmetic Coding  Theory and Practice
Introduction to Arithmetic Coding  Theory and Practice Amir Said Imaging Systems Laboratory HP Laboratories Palo Alto HPL200476 April 21, 2004* entropy coding, compression, complexity This introduction
More information2011, The McGrawHill Companies, Inc. Chapter 3
Chapter 3 3.1 Decimal System The radix or base of a number system determines the total number of different symbols or digits used by that system. The decimal system has a base of 10 with the digits 0 through
More informationImage compression. Stefano Ferrari. Università degli Studi di Milano Elaborazione delle immagini (Image processing I)
Image compression Stefano Ferrari Università degli Studi di Milano stefano.ferrari@unimi.it Elaborazione delle immagini (Image processing I) academic year 2011 2012 Data and information The representation
More information15441: Computer Networks Homework 1
15441: Computer Networks Homework 1 Assigned: January 29, 2008 Due: February 7, 2008 1. Suppose a 100Mbps pointtopoint link is being set up between Earth and a new lunar colony. The distance from the
More informationFast Ethernet and Gigabit Ethernet. Computer Networks: Fast and Gigabit Ethernet
Fast Ethernet and Gigabit Ethernet 1 Fast Ethernet (100BASET) How to achieve 100 Mbps capacity? MII LLC MAC Convergence Sublayer Media Independent Interface Media Dependent Sublayer Data Link Layer Physical
More informationNetwork Requirements for DSL systems, (ADSL through G.Fast) (A summarized view)
Network Requirements for DSL systems, (ADSL through G.Fast) (A summarized view) Gilberto GG Guitarte, BB Connectivity Director TE Connectivity FTTH LATAM Chapter CHAIRMAN 2/24/2014 G.A.Guitarte 1 Executive
More informationWhitepaper November 2008. Iterative Detection Read Channel Technology in Hard Disk Drives
Whitepaper November 2008 Iterative Detection Read Channel Technology in Hard Disk Drives / Table of Contents Table of Contents Executive Summary... 1 Background...2 Achieving Enhanced Performance Through
More informationFirst Semester Examinations 2011/12 INTERNET PRINCIPLES
PAPER CODE NO. EXAMINER : Martin Gairing COMP211 DEPARTMENT : Computer Science Tel. No. 0151 795 4264 First Semester Examinations 2011/12 INTERNET PRINCIPLES TIME ALLOWED : Two Hours INSTRUCTIONS TO CANDIDATES
More informationFacultyofComputingandInformationTechnology DepartmentofRoboticsandDigitalTechnology TechnicalReport9311
FacultyofComputingandInformationTechnology DepartmentofRoboticsandDigitalTechnology TechnicalReport9311 TheTheoryofCCITTRecommendationH.261, p64kbit/s"andreviewofsuchacodec \VideoCodecforAudiovisualServicesat
More informationImage Compression Using Wavelet Methods
Image Compression Using Wavelet Methods Yasir S. AL  MOUSAWY*,1, Safaa S. MAHDI 1 *Corresponding author *,1 Medical Eng. Dept., AlNahrain University, Baghdad, Iraq Yasir_bio@yahoo.com, dr_safaaisoud@yahoo.com
More informationBroadband Networks. Prof. Dr. Abhay Karandikar. Electrical Engineering Department. Indian Institute of Technology, Bombay. Lecture  29.
Broadband Networks Prof. Dr. Abhay Karandikar Electrical Engineering Department Indian Institute of Technology, Bombay Lecture  29 Voice over IP So, today we will discuss about voice over IP and internet
More informationSilicon Seminar. Optolinks and Off Detector Electronics in ATLAS Pixel Detector
Silicon Seminar Optolinks and Off Detector Electronics in ATLAS Pixel Detector Overview Requirements The architecture of the optical links for the ATLAS pixel detector ROD BOC Optoboard Requirements of
More information