Review: Our Approach 2. CSC310 Information Theory


 Rosaline Wright
 2 years ago
 Views:
Transcription
1 CSC30 Informaton Theory Sam Rowes Lecture 3: Provng the KraftMcMllan Inequaltes September 8, 6 Revew: Our Approach The study of both compresson and transmsson requres that we abstract data and messages as sequences of symbols from a fnte alphabet (gnorng semantcs of content). Both problems nvolve two dstnct tasks: ) Modelng. We have to represent the stochastc behavour of the source and the channel usng probablstc models. ) Encodng/Decodng. Gven our source and channel models we want to algorthmcally desgn schemes for compresson and transmsson that have certan good propertes (correct/effcent/optmal). For now, we are assumng the models are known and are focusng on the codes. But later n the course we wll study adaptve/dctonary methods (e.g. LempelZff,gzp,PPM) whch combne modelng and codng together. Revew: Course Content Lossless Data Compresson Shannon s Noseless Codng Theorem Lower lmt on lossless compresson s the source entropy. Algorthms: Huffman Codng, Arthmetc Codng Transmsson over Nosy Channels Shannon s Nosy Codng Theorem Upper lmt on errorfree transmsson rate s channel capacty. Algorthms: Lnear Codes, Low Densty Party Check Codes (*)Lossy Compresson Shannon s RateDstorton Theorem Algorthms: mp3,jpeg,mpeg Revew: Mathematcal Setup 3 A stochastc source emts a sequence of symbols (from alphabet A) X = X,X,...,X N wth probablty p(x). Our encoder (code) C converts ths nto an (btstrng) encodng Z. We assume (for now) that the decoder can see Z exactly (noseless channel), that we are requred to reconstruct X exactly (lossless compresson) and that we are usng a symbol code, (.e. we encode each symbol X ndependently and concatenate ther encodngs). We requre the code to be unquely decodable (UD), and we saw that for any UD code there s always an nstantaneously decodable (ID) code wth the same codeword lengths. These lengths must satsfy the KraftMcMllan nequalty: l. We wll measure the qualty of our code by the average length (under p(x)) of the encodng Z, compared to the length of X.
2 Provng the Two Inequaltes 4 We can prove both Kraft s and McMllan s nequalty by provng that for any set of lengths, l,..., l I, for bnary codewords: A) If I = / l, we can construct an nstantaneous code wth codewords havng these lengths. B) If I = / l >, there s no unquely decodable code wth codewords havng these lengths. (A) s half of Kraft s nequalty. (B) s half of McMllan s nequalty. Usng the fact that nstantaneous codes are unquely decodable, (A) gves the other half of McMllan s nequalty, and (B) gves the other half of Kraft s nequalty. To do ths, we ll ntroduce a helpful way of thnkng about codes as...trees! Extendng the Tree to Maxmum Depth 6 We can extend the tree by fllng n the subtree underneath every actual codeword, down to the depth of the longest codeword. Each codeword then corresponds to ether a leaf or a subtree. Prevous tree extended, wth each codeword s leaf or subtree crcled: 0 Short codewords occupy more of the tree. For a bnary code, the fracton of leaves taken by a codeword of length l s / l Vsualzng PrefxFree Codes as Trees 5 We can vew codewords of an nstantaneous (prefxfree) code as leaves of a tree. The root represents the null strng; each level corresponds to addng another code symbol. Here s the tree for a code wth codewords 0,,, 0: Constructng Instantaneous Codes 7 Suppose that Kraft s Inequalty holds: I = l Order the lengths so l l I. Q: In the bnary tree wth depth l I, how can we allocate subtrees to codewords wth these lengths? A: We go from shortest to longest, =,...,I: ) Pck a node at depth l that sn t n a subtree prevously used, and let the code for codeword be the one at that node. ) Mark all nodes n the subtree headed by the node just pcked as beng used, and not avalable to be pcked later. Let s look at an example...
3 Buldng an Instantaneous Code (0) 8 Let the lengths of the codewords be {,,3,3}. Frst check: Intalze the tree (level 0). Buldng an Instantaneous Code () 0 Let the lengths of the codewords be {,,3,3}. Pck (arbtrarly) an unmarked node at level to use for codeword of length ; mark the subtree below t. Buldng an Instantaneous Code () 9 Let the lengths of the codewords be {,,3,3}. Pck (arbtrarly) an unmarked node at level to use for codeword of length ; mark the subtree below t. Buldng an Instantaneous Code (3) Let the lengths of the codewords be {,,3,3}. Pck two unmarked nodes at level 3 as codewords of length 3. 0
4 Buldng an Instantaneous Code Let the lengths of the codewords be {,,3,3}. Our fnal code can be read from the leaf nodes: {,,,0}. 0 UD Codes Must Obey the Inequalty 4 Let l l I be the codeword lengths. Defne K = I = l. For any postve nteger n, we can sum over all possble combnatons of values for,..., n n {,...,I} to get K n. K n =,..., n l l n We rewrte ths n terms of possble values for j = l + + l n : K n nl I N j,n = j= j N j,n s the # of sequences of n codewords wth total length j. If the code s unquely decodable, N j,n j, so K n nl I, whch for bg enough n s possble only f K. Ths proves that any UD code must satsfy l. Constructon Wll Always Be Possble 3 Q: Wll there always be a node avalable n step () above? If Kraft s nequalty holds, we wll always be able to do ths. To begn, there are l b nodes at depth l b. When we pck a node at depth l a, the number of nodes that become unavalable at depth l b (assumed not less than l a ) s l b l a. When we need to pck a node at depth l j, after havng pcked earler nodes at depths l (wth < j and l l j ), the number of nodes left to pck from wll be an nteger equal to l j j l j l = l j = j = l > 0 j Snce / l < I / l, by assumpton. = = Ths proves we can always construct an ID code f l. Tradeoffs Choosng Codeword Lengths 5 The KraftMcMllan nequaltes mply that to make some codewords shorter, we wll have to make others longer. Example: The obvous bnary encodng for eght symbols uses codewords that are all three bts long. Ths code s nstantaneous, and satsfes the Kraft nequalty, snce: = Suppose we want to encode the frst symbol usng only two bts. We ll have to make some other codewords longer eg, we can encode two of the other symbols n four bts, and the remanng fve symbols n three bts, snce = How should we choose among the possble codes?
5 Formalzng Whch Codes are the Best: Probabltes for Source Symbols 6 We d lke to choose a code that uses short codewords for common symbols and long ones for rare symbols. To formalze ths, we need to assgn each symbol n the source alphabet a probablty. Symbols a,...,a I wll have probabltes wrtten as p,...,p I. We assume that these probabltes don t change wth tme. We also assume that symbols n the source sequence, X, X,..., X N, are ndependent: P(X = a, X = a,..., X n = a N ) = P(X n = a n ) = p p p N n These assumptons are really too restrctve n practce, but we ll gnore that for now. Optmal Codes 8 We say a code s optmal for a gven source (wth gven symbol probabltes) f ts average length s at least as small as that of any other code. (There can be many optmal codes for the same source, all wth the same average length.) The KraftMcMllan nequaltes mply that f there s an optmal code, there s also an optmal nstantaneous code. More generally, for any unquely decodable code wth average length L, there s an nstantaneous code wth the same average length. Questons: Can we fgure out the codeword lengths of an optmal code startng from the symbol probabltes?.e. can we solve: mn p l subject to l {l } Can we fnd such an optmal code, and use t n practce? Answers: next class! Expected Codeword Length 7 Consder a code whose codewords for symbols a,...,a I have lengths l,...,l I. Let the probabltes of these symbols be p,...,p I. We defne the expected codeword length for ths code to be I L = L(C,X) = p l = Ths s the average length of the codeword encodng a sngle source symbol. But snce averagng s a lnear operaton, the average length of a coded message wth N source symbols s just NL. We am to choose a code for whch L s small. Bascally, we want to assgn short codeword lengths to the more probable symbols but we also need to satsfy the KM nequalty so we wll be forced to assgn longer lengths to the less probable symbols.
Digital Transmission
Dgtal Transmsson Most modern communcaton systems are dgtal, meanng that the transmtted normaton sgnal carres bts and symbols rather than an analog sgnal. The eect o C/N rato ncrease or decrease on dgtal
More informationChinese Remainder. Discrete Mathematics Andrei Bulatov
Chnese Remander Introducton Theorem Dscrete Mathematcs Andre Bulatov Dscrete Mathematcs Chnese Remander Theorem 342 Prevous Lecture Resdues and arthmetc operatons Caesar cpher Pseudorandom generators
More informationAdaptive Modulation for Multiple Antenna Channels
Adaptve Modulaton for Multple Antenna Channels June Chul Roh and Bhaskar D. Rao Department of Electrcal and Computer Engneerng Unversty of Calforna, San Dego La Jolla, CA 9937 Emal: jroh@ece.ucsd.edu,
More informationNATIONAL RADIO ASTRONOMY OBSERVATORY Green Bank, West Virginia SPECTRAL PROCESSOR MEMO NO. 25. MEMORANDUM February 13, 1985
NATONAL RADO ASTRONOMY OBSERVATORY Green Bank, West Vrgna SPECTRAL PROCESSOR MEMO NO. 25 MEMORANDUM February 13, 1985 To: Spectral Processor Group From: R. Fsher Subj: Some Experments wth an nteger FFT
More informationFall 2018 #11 Games and Nimbers. A. Game. 0.5 seconds, 64 megabytes
595 Fall 08 # Games and Nmbers A. Game 0.5 seconds, 64 megabytes There s a legend n the IT Cty college. A student that faled to answer all questons on the game theory exam s gven one more chance by hs
More informationInternational Journal of Scientific & Engineering Research, Volume 4, Issue 11, November2013 ISSN
Internatonal Journal of Scentfc & Engneerng Research, Volume 4, Issue, November203 ISSN 2229558 33 COMPARATIVE STUDY OF HUFFMAN CODING, SBAC AND CABAC USED IN VARIOUS VIDEO CODING STANDARS AND THEIR
More informationTest 2. ECON3161, Game Theory. Tuesday, November 6 th
Test 2 ECON36, Game Theory Tuesday, November 6 th Drectons: Answer each queston completely. If you cannot determne the answer, explanng how you would arrve at the answer may earn you some ponts.. (20 ponts)
More informationA Lower Bound for τ(n) of Any kperfect Numbers
Pure Mathematcal Scences, Vol. 4, 205, no. 3, 9903 HIKARI Ltd, www.mhar.com http://dx.do.org/0.2988/pms.205.4923 A Lower Bound for τn of Any Perfect Numbers Keneth Adran P. Dagal Department of Mathematcs
More informationPassive Filters. References: Barbow (pp ), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationEfficient Large Integers Arithmetic by Adopting Squaring and Complement Recoding Techniques
The th Worshop on Combnatoral Mathematcs and Computaton Theory Effcent Large Integers Arthmetc by Adoptng Squarng and Complement Recodng Technques ChaLong Wu*, DerChyuan Lou, and TeJen Chang *Department
More informationA General Framework for Codes Involving Redundancy Minimization
IEEE TRANSACTIONS ON INFORMATION THEORY A General Framework for Codes Involvng Redundancy Mnmzaton Mchael Baer, Member, IEEE Abstract A framework wth two scalar parameters s ntroduced for varous problems
More informationproblems palette of David Rock and Mary K. Porter 6. A local musician comes to your school to give a performance
palette of problems Davd Rock and Mary K. Porter 1. If n represents an nteger, whch of the followng expressons yelds the greatest value? n,, n, n, n n. A 60watt lghtbulb s used for 95 hours before t burns
More informationUNIT 11 TWOPERSON ZEROSUM GAMES WITH SADDLE POINT
UNIT TWOPERSON ZEROSUM GAMES WITH SADDLE POINT Structure. Introducton Obectves. Key Terms Used n Game Theory.3 The MaxmnMnmax Prncple.4 Summary.5 Solutons/Answers. INTRODUCTION In Game Theory, the word
More informationN( E) ( ) That is, if the outcomes in sample space S are equally likely, then ( )
Stat 400, secton 2.2 Axoms, Interpretatons and Propertes of Probablty notes by Tm Plachowsk In secton 2., we constructed sample spaces by askng, What could happen? Now, n secton 2.2, we begn askng and
More informationUtilitybased Routing
Utltybased Routng Je Wu Dept. of Computer and Informaton Scences Temple Unversty Roadmap Introducton Why Another Routng Scheme UtltyBased Routng Implementatons Extensons Some Fnal Thoughts 2 . Introducton
More informationSecure Transmission of Sensitive data using multiple channels
Secure Transmsson of Senstve data usng multple channels Ahmed A. Belal, Ph.D. Department of computer scence and automatc control Faculty of Engneerng Unversty of Alexandra Alexandra, Egypt. aabelal@hotmal.com
More informationUltimate X Bonus Streak Analysis
Ultmate X Bonus Streak Analyss Gary J. Koehler John B. Hgdon Emnent Scholar, Emertus Department of Informaton Systems and Operatons Management, 35 BUS, The Warrngton College of Busness, Unversty of Florda,
More informationAnalysis of Time Delays in Synchronous and. Asynchronous Control Loops. Bj rn Wittenmark, Ben Bastian, and Johan Nilsson
37th CDC, Tampa, December 1998 Analyss of Delays n Synchronous and Asynchronous Control Loops Bj rn Wttenmark, Ben Bastan, and Johan Nlsson emal: bjorn@control.lth.se, ben@control.lth.se, and johan@control.lth.se
More informationAN EFFICIENT SECURE UNIVERSAL BLOCK SOURCE CODING ALGORITHM FOR INTEGERS
AN EFFICIENT SECURE UNIVERSAL BLOCK SOURCE CODING ALGORITHM FOR INTEGERS * Mahd Nangr Department of Electrcal Engneerng, Khaje Nasr Unversty of Technology, Tehran, Iran *Author for Correspondence ABSTRACT
More informationLecture5: Lossless Compression Techniques
Fixed to fixed mapping: we encoded source symbols of fixed length into fixed length code sequences Fixed to variable mapping: we encoded source symbols of fixed length into variable length code sequences
More informationInformation Theory and Communication Optimal Codes
Information Theory and Communication Optimal Codes Ritwik Banerjee rbanerjee@cs.stonybrook.edu c Ritwik Banerjee Information Theory and Communication 1/1 Roadmap Examples and Types of Codes Kraft Inequality
More informationAlgorithms Airline Scheduling. Airline Scheduling. Design and Analysis of Algorithms Andrei Bulatov
Algorthms Arlne Schedulng Arlne Schedulng Desgn and Analyss of Algorthms Andre Bulatov Algorthms Arlne Schedulng 112 The Problem An arlne carrer wants to serve certan set of flghts Example: Boston (6
More informationLECTURE VI: LOSSLESS COMPRESSION ALGORITHMS DR. OUIEM BCHIR
1 LECTURE VI: LOSSLESS COMPRESSION ALGORITHMS DR. OUIEM BCHIR 2 STORAGE SPACE Uncompressed graphics, audio, and video data require substantial storage capacity. Storing uncompressed video is not possible
More informationDefine Y = # of mobiles from M total mobiles that have an adequate link. Measure of average portion of mobiles allocated a link of adequate quality.
Wreless Communcatons Technologes 6::559 (Advanced Topcs n Communcatons) Lecture 5 (Aprl th ) and Lecture 6 (May st ) Instructor: Professor Narayan Mandayam Summarzed by: Steve Leung (leungs@ece.rutgers.edu)
More informationHigh Speed ADC Sampling Transients
Hgh Speed ADC Samplng Transents Doug Stuetzle Hgh speed analog to dgtal converters (ADCs) are, at the analog sgnal nterface, track and hold devces. As such, they nclude samplng capactors and samplng swtches.
More informationOn the Usefulness of Fibonacci Compression Codes
The Computer Journal Advance Access publshed May 14, 2009 The Author 2009 Publshed by Oxford Unversty Press on behalf of The Brtsh Computer Socety All rghts reserved For Permssons, please emal: journalspermssons@oxfordjournalsorg
More informationRobust Image Transmission Performed by SPIHT and TurboCodes
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 5, No.2, November 2008, 353360 Robust Image Transmsson Performed by SPIHT and TurboCodes Abdelmounam Moulay Lakhdar, Rachda Mélan 2, Malka Kandouc 2 Abstract:
More informationRational Secret Sharing without Broadcast
Ratonal Secret Sharng wthout Broadcast Amjed Shareef, Department of Computer Scence and Engneerng, Indan Insttute of Technology Madras, Chenna, Inda. Emal: amjedshareef@gmal.com Abstract We use the concept
More informationA thesis presented to. the faculty of. the Russ College of Engineering and Technology of Ohio University. In partial fulfillment
Crcular Trells based Low Densty Party Check Codes A thess presented to the faculty of the Russ College of Engneerng and Technology of Oho Unversty In partal fulfllment of the requrements for the degree
More informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationCalculation of the received voltage due to the radiation from multiple cofrequency sources
Rec. ITUR SM.12710 1 RECOMMENDATION ITUR SM.12710 * EFFICIENT SPECTRUM UTILIZATION USING PROBABILISTIC METHODS Rec. ITUR SM.1271 (1997) The ITU Radocommuncaton Assembly, consderng a) that communcatons
More informationNOVEL ITERATIVE TECHNIQUES FOR RADAR TARGET DISCRIMINATION
NOVEL ITERATIVE TECHNIQUES FOR RADAR TARGET DISCRIMINATION Phaneendra R.Venkata, Nathan A. Goodman Department of Electrcal and Computer Engneerng, Unversty of Arzona, 30 E. Speedway Blvd, Tucson, Arzona
More informationJoint Power Control and Scheduling for TwoCell Energy Efficient Broadcasting with Network Coding
Communcatons and Network, 2013, 5, 312318 http://dx.do.org/10.4236/cn.2013.53b2058 Publshed Onlne September 2013 (http://www.scrp.org/journal/cn) Jont Power Control and Schedulng for TwoCell Energy Effcent
More informationNetwork Reconfiguration in Distribution Systems Using a Modified TS Algorithm
Network Reconfguraton n Dstrbuton Systems Usng a Modfed TS Algorthm ZHANG DONG,FU ZHENGCAI,ZHANG LIUCHUN,SONG ZHENGQIANG School of Electroncs, Informaton and Electrcal Engneerng Shangha Jaotong Unversty
More informationTECHNICAL NOTE TERMINATION FOR POINT TOPOINT SYSTEMS TN TERMINATON FOR POINTTOPOINT SYSTEMS. Zo = L C. ω  angular frequency = 2πf
TECHNICAL NOTE TERMINATION FOR POINT TOPOINT SYSTEMS INTRODUCTION Because dgtal sgnal rates n computng systems are ncreasng at an astonshng rate, sgnal ntegrty ssues have become far more mportant to
More informationNetwork Theory. EC / EE / IN. for
Network Theory for / / IN By www.thegateacademy.com Syllabus Syllabus for Networks Network Graphs: Matrces Assocated Wth Graphs: Incdence, Fundamental ut Set and Fundamental rcut Matrces. Soluton Methods:
More informationSpace Time Equalizationspace time codes System Model for STCM
Space Tme Eualzatonspace tme codes System Model for STCM The system under consderaton conssts of ST encoder, fadng channel model wth AWGN, two transmt antennas, one receve antenna, Vterb eualzer wth deal
More informationUnderstanding the Spike Algorithm
Understandng the Spke Algorthm Vctor Ejkhout and Robert van de Gejn May, ntroducton The parallel soluton of lnear systems has a long hstory, spannng both drect and teratve methods Whle drect methods exst
More informationEE 508 Lecture 6. Degrees of Freedom The Approximation Problem
EE 508 Lecture 6 Degrees of Freedom The Approxmaton Problem Revew from Last Tme Desgn Strategy Theorem: A crcut wth transfer functon T(s) can be obtaned from a crcut wth normalzed transfer functon T n
More informationA TWOPLAYER MODEL FOR THE SIMULTANEOUS LOCATION OF FRANCHISING SERVICES WITH PREFERENTIAL RIGHTS
A TWOPLAYER MODEL FOR THE SIMULTANEOUS LOCATION OF FRANCHISING SERVICES WITH PREFERENTIAL RIGHTS Pedro Godnho and oana Das Faculdade de Economa and GEMF Unversdade de Combra Av. Das da Slva 65 30045
More informationECE315 / ECE515 Lecture 5 Date:
Lecture 5 Date: 18.08.2016 Common Source Amplfer MOSFET Amplfer Dstorton Example 1 One Realstc CS Amplfer Crcut: C c1 : Couplng Capactor serves as perfect short crcut at all sgnal frequences whle blockng
More informationIntroduction to Source Coding
Comm. 52: Communication Theory Lecture 7 Introduction to Source Coding  Requirements of source codes  Huffman Code Length Fixed Length Variable Length Source Code Properties Uniquely Decodable allow
More informationIntroduction to Coalescent Models. Biostatistics 666 Lecture 4
Introducton to Coalescent Models Bostatstcs 666 Lecture 4 Last Lecture Lnkage Equlbrum Expected state for dstant markers Lnkage Dsequlbrum Assocaton between neghborng alleles Expected to decrease wth dstance
More informationRESOURCE CONTROL FOR HYBRID CODE AND TIME DIVISION SCHEDULING
RESOURCE CONTROL FOR HYBRID CODE AND TIME DIVISION SCHEDULING Vaslos A. Srs Insttute of Computer Scence (ICS), FORTH and Department of Computer Scence, Unversty of Crete P.O. Box 385, GR 7 Heraklon, Crete,
More informationDirect Sequence Spread Spectrum (DSSS)
Drect Sequence Spread Spectrum (DSSS) DSSS DSSS uses sequences for spectrum spreadng and phase modulaton Modulaton s bnary SK (BSK) or quaternary SK (QSK) Message BSK     QSK BSK Bt hase Dr. Cesar
More information1 GSW Multipath Channel Models
In the general case, the moble rado channel s pretty unpleasant: there are a lot of echoes dstortng the receved sgnal, and the mpulse response keeps changng. Fortunately, there are some smplfyng assumptons
More informationDecomposition Principles and Online Learning in CrossLayer Optimization for DelaySensitive Applications
Techncal Report Decomposton Prncples and Onlne Learnng n CrossLayer Optmzaton for DelaySenstve Applcatons Abstract In ths report, we propose a general crosslayer optmzaton framework n whch we explctly
More informationCommunication Theory II
Communication Theory II Lecture 13: Information Theory (cont d) Ahmed Elnakib, PhD Assistant Professor, Mansoura University, Egypt March 22 th, 2015 1 o Source Code Generation Lecture Outlines Source Coding
More informationPerformance Analysis of Multi User MIMO System with BlockDiagonalization Precoding Scheme
Performance Analyss of Mult User MIMO System wth BlockDagonalzaton Precodng Scheme Yoon Hyun m and Jn Young m, wanwoon Unversty, Department of Electroncs Convergence Engneerng, WolgyeDong, NowonGu,
More informationCapacity Estimation of NonSynchronous Covert Channels
Capacty Estmaton of onynchronous s Zhenghong Wang and uby B. Lee Department of Electrcal Engneerng Prnceton Unversty {zhenghon,rblee}@prnceton.edu Abstract Capacty estmaton s an mportant part of covert
More information4.3 Modeling the Diode Forward Characteristic
2/8/2012 3_3 Modelng the ode Forward Characterstcs 1/3 4.3 Modelng the ode Forward Characterstc Readng Assgnment: pp. 179188 How do we analyze crcuts wth juncton dodes? 2 ways: Exact Solutons ffcult!
More informationA NSGAII algorithm to solve a biobjective optimization of the redundancy allocation problem for seriesparallel systems
0 nd Internatonal Conference on Industral Technology and Management (ICITM 0) IPCSIT vol. 49 (0) (0) IACSIT Press, Sngapore DOI: 0.776/IPCSIT.0.V49.8 A NSGAII algorthm to solve a bobectve optmzaton of
More informationDistributed Resource Allocation and Scheduling in OFDMA Wireless Networks
Southern Illnos Unversty Carbondale OpenSIUC Conference Proceedngs Department of Electrcal and Computer Engneerng 112006 Dstrbuted Resource Allocaton and Schedulng n OFDMA Wreless Networks Xangpng Qn
More informationGraph Method for Solving Switched Capacitors Circuits
Recent Advances n rcuts, ystems, gnal and Telecommuncatons Graph Method for olvng wtched apactors rcuts BHUMIL BRTNÍ Department of lectroncs and Informatcs ollege of Polytechncs Jhlava Tolstého 6, 586
More informationShunt Active Filters (SAF)
ENTH05/004 Martt Tuomanen (9) Shunt Actve Flters (SAF) Operaton prncple of a Shunt Actve Flter. Nonlnear loads lke Varable Speed Drves, Unnterrupted Power Supples and all knd of rectfers draw a nonsnusodal
More informationGeneralized Incomplete TrojanType Designs with Unequal Cell Sizes
Internatonal Journal of Theoretcal & Appled Scences 6(1): 5054(2014) ISSN No. (Prnt): 09751718 ISSN No. (Onlne): 22493247 Generalzed Incomplete TrojanType Desgns wth Unequal Cell Szes Cn Varghese,
More informationSIMULATED PERFORMANCE A MATLAB IMPLEMENTATION OF LOWDENSITY PARITY CHECK CODES. By: Dan Dechene Kevin Peets. Supervised by: Dr.
SIMULATED PERFORMANCE OF LOWDENSITY PARITY CHECK CODES A MATLAB IMPLEMENTATION LAKEHEAD UNIVERSITY FACULTY OF ENGINEERING 2006 By: Dan Dechene Kevn Peets Supervsed by: Dr. Julan Cheng TABLE OF CONTENTS
More informationInteger Programming. P.H.S. Torr Lecture 5. Integer Programming
Integer Programmng P.H.S. Torr Lecture 5 Integer Programmng Outlne Mathematcal programmng paradgm Lnear Programmng Integer Programmng Integer Programmng Eample Unmodularty LP > IP Theorem Concluson Specal
More informationDynamic Optimization. Assignment 1. Sasanka Nagavalli January 29, 2013 Robotics Institute Carnegie Mellon University
Dynamc Optmzaton Assgnment 1 Sasanka Nagavall snagaval@andrew.cmu.edu 16745 January 29, 213 Robotcs Insttute Carnege Mellon Unversty Table of Contents 1. Problem and Approach... 1 2. Optmzaton wthout
More informationMultiband Jamming Strategies with Minimum Rate Constraints
Multband Jammng Strateges wth Mnmum Rate Constrants Karm Banawan, Sennur Ulukus, Peng Wang, and Bran Henz Department of Electrcal and Computer Engneerng, Unversty of Maryland, College Park, MD 7 US Army
More informationPower Minimization Under Constant Throughput Constraint in Wireless Networks with Beamforming
Power Mnmzaton Under Constant Throughput Constrant n Wreless etworks wth Beamformng Zhu Han and K.J. Ray Lu, Electrcal and Computer Engneer Department, Unversty of Maryland, College Park. Abstract In multaccess
More informationA Fuzzybased Routing Strategy for Multihop Cognitive Radio Networks
74 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 A Fuzzybased Routng Strategy for Multhop Cogntve Rado Networks Al El Masr, Naceur Malouch and Hcham
More informationIntroduction to Coalescent Models. Biostatistics 666
Introducton to Coalescent Models Bostatstcs 666 Prevously Allele frequences Hardy Wenberg Equlbrum Lnkage Equlbrum Expected state for dstant markers Lnkage Dsequlbrum Assocaton between neghborng alleles
More informationInternational Journal of Network Security & Its Application (IJNSA), Vol.2, No.1, January SYSTEL, SUPCOM, Tunisia.
Internatonal Journal of Network Securty & Its Applcaton (IJNSA), Vol.2, No., January 2 WEAKNESS ON CRYPTOGRAPHIC SCHEMES BASED ON REGULAR LDPC CODES Omessaad Hamd, Manel abdelhed 2, Ammar Bouallegue 2,
More informationPRACTICAL, COMPUTATION EFFICIENT HIGHORDER NEURAL NETWORK FOR ROTATION AND SHIFT INVARIANT PATTERN RECOGNITION. Evgeny Artyomov and Orly YadidPecht
68 Internatonal Journal "Informaton Theores & Applcatons" Vol.11 PRACTICAL, COMPUTATION EFFICIENT HIGHORDER NEURAL NETWORK FOR ROTATION AND SHIFT INVARIANT PATTERN RECOGNITION Evgeny Artyomov and Orly
More informationComparative Analysis of Reuse 1 and 3 in Cellular Network Based On SIR Distribution and Rate
Comparatve Analyss of Reuse and 3 n ular Network Based On IR Dstrbuton and Rate Chandra Thapa M.Tech. II, DEC V College of Engneerng & Technology R.V.. Nagar, Chttoor5727, A.P. Inda Emal: chandra2thapa@gmal.com
More informationEnergy Efficiency Analysis of a Multichannel Wireless Access Protocol
Energy Effcency Analyss of a Multchannel Wreless Access Protocol A. Chockalngam y, Wepng u, Mchele Zorz, and Laurence B. Mlsten Department of Electrcal and Computer Engneerng, Unversty of Calforna, San
More informationPlanning of Relay Station Locations in IEEE (WiMAX) Networks
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 010 proceedngs. Plannng of Relay Staton Locatons n IEEE 0.16 (WMAX) Networks
More informationOptimizing HARQ Feedback and Incremental Redundancy in Wireless Communications
Optmzng HARQ Feedback and Incremental Redundancy n Wreless Communcatons Ma Zhang, Andres Castllo, Borja Peleato Electrcal and Computer Engneerng Purdue Unversty West Lafayette IN 797 Emal: {maz,castl,bpeleato}@purdue.edu
More informationNoisy ChannelOutput Feedback Capacity of the Linear Deterministic Interference Channel
Nosy ChannelOutput Feedback Capacty of the Lnear Determnstc Interference Channel Vctor Quntero, Samr M. Perlaza, JeanMare Gorce arxv:.4649v6 [cs.it] Jan 6 Abstract In ths paper, the capacty regon of
More informationANNUAL OF NAVIGATION 11/2006
ANNUAL OF NAVIGATION 11/2006 TOMASZ PRACZYK Naval Unversty of Gdyna A FEEDFORWARD LINEAR NEURAL NETWORK WITH HEBBA SELFORGANIZATION IN RADAR IMAGE COMPRESSION ABSTRACT The artcle presents the applcaton
More informationDynamic Wavelength Routing in WDM Networks under Multiple Signal Quality Constraints
Dynamc Wavelength Routng n WDM Networks under Multple Sgnal Qualty Constrants Wey Zhang, Guolang Xue, Senor Member, IEEE, Jan Tang, Krshnayan Thulasraman, Fellow, IEEE Abstract Most research works n routng
More informationCapacitated setcovering model considering the distance objective and dependency of alternative facilities
IOP Conference Seres: Materals Scence and Engneerng PAPER OPEN ACCESS Capactated setcoverng model consderng the dstance obectve and dependency of alternatve facltes To cte ths artcle: I Wayan Suletra
More informationA NEW TRANSMISSION STRATEGY FOR SCALABLE MULTIMEDIA DATA ON OFDM SYSTEMS
15th European Sgnal Processng Conference (EUSIPCO 27), Poznan, Poland, September 37, 27, copyrght by EURASIP A NEW TRANSMISSION STRATEGY FOR SCALABLE MULTIMEDIA DATA ON OFDM SYSTEMS Heykel Houas, Cléo
More informationSTAR POWER BOM/BOQ SETTING IDEA 1  TWIST & SHOUT
Below are two deas for settng your blocks together. Of course, there are dozens more! Take your blocks out to play, and decde on a settng that makes you smle! STAR POWER BOM/BOQ SETTING IDEA 1  TWIST
More informationParameter Free Iterative Decoding Metrics for NonCoherent Orthogonal Modulation
1 Parameter Free Iteratve Decodng Metrcs for NonCoherent Orthogonal Modulaton Albert Gullén Fàbregas and Alex Grant Abstract We study decoder metrcs suted for teratve decodng of noncoherently detected
More informationAvailable online at ScienceDirect. IFACPapersOnLine (2016)
Avalable onlne at www.scencedrect.com ScenceDrect IFACPapersOnLne 49 (06) 09 0 Addng Informatonal Belefs to the Players Strategc Thnkng Model 06, IFAC (Internatonal Federaton of Automatc Control) Hostng
More informationMultihop Coordination in Gossipingbased Wireless Sensor Networks
Multhop Coordnaton n Gosspngbased Wreless Sensor Networks Zhlang Chen, Alexander Kuehne, and Anja Klen Communcatons Engneerng Lab, Technsche Unverstät Darmstadt, Germany Emal: {z.chen,a.kuehne,a.klen}@nt.tudarmstadt.de
More informationDCFREE TURBO CODING SCHEME FOR GPRS SYSTEM
DCFREE TURBO CODING SCHEME FOR GPRS SYSTEM Prof. Dr. M. Amr Mokhtar & Eng. A. RefaeyAhmed Electrcal Engneerng Department, Alexandra Unversty, Egypt. ABSTRACT A useful tool n the desgn of relable dgtal
More informationChapter 1. Online Choice of Online Algorithms. Yossi Azar Andrei Z. Broder Mark S. Manasse
Chapter Onlne Choce of Onlne Algorthms Yoss Azar Andre Z. Broder Mark S. Manasse Abstract Let fa ; A 2; ; Amg be a set of onlne algorthms for a problem P wth nput set I. We assume that P can be represented
More informationantenna antenna (4.139)
.6.6 The Lmts of Usable Input Levels for LNAs The sgnal voltage level delvered to the nput of an LNA from the antenna may vary n a very wde nterval, from very weak sgnals comparable to the nose level,
More informationInformationTheoretic Comparison of Channel Capacity for FDMA and DSCDMA in a Rayleigh Fading Environment
WSEAS TRANSATIONS on OMMUNIATIONS InformatonTheoretc omparson of hannel apacty for FDMA and DSDMA n a Raylegh Fadng Envronment PANAGIOTIS VARZAAS Department of Electroncs Technologcal Educatonal Insttute
More informationYutaka Matsuo and Akihiko Yokoyama. Department of Electrical Engineering, University oftokyo , Hongo, Bunkyoku, Tokyo, Japan
Optmzaton of Installaton of FACTS Devce n Power System Plannng by both Tabu Search and Nonlnear Programmng Methods Yutaka Matsuo and Akhko Yokoyama Department of Electrcal Engneerng, Unversty oftokyo 73,
More informationOptimal Placement of PMU and RTU by Hybrid Genetic Algorithm and Simulated Annealing for Multiarea Power System State Estimation
T. Kerdchuen and W. Ongsakul / GMSARN Internatonal Journal (09)  Optmal Placement of and by Hybrd Genetc Algorthm and Smulated Annealng for Multarea Power System State Estmaton Thawatch Kerdchuen and
More informationTraffic Modeling and Performance Evaluation in GSM/GPRS Networks
Proceedngs of the 3th WSEAS Internatonal Conference on COMMUNICATIONS Traffc Modelng and Performance Evaluaton n GSM/ Networks Cornel Balnt, Georgeta Budura, Marza Eugen Poltehnca Unversty of Tmsoara Bd..
More informationSideMatch Vector Quantizers Using Neural Network Based Variance Predictor for Image Coding
SdeMatch Vector Quantzers Usng Neural Network Based Varance Predctor for Image Codng Shuangteng Zhang Department of Computer Scence Eastern Kentucky Unversty Rchmond, KY 40475, U.S.A. shuangteng.zhang@eku.edu
More informationWalsh Function Based Synthesis Method of PWM Pattern for FullBridge Inverter
Walsh Functon Based Synthess Method of PWM Pattern for FullBrdge Inverter Sej Kondo and Krt Choesa Nagaoka Unversty of Technology 63, Kamtomokacho, Nagaoka 9, JAPAN Fax: +858795, Phone: +8587957
More informationFigure 1. DCDC Boost Converter
EE46, Power Electroncs, DCDC Boost Converter Verson Oct. 3, 11 Overvew Boost converters make t possble to effcently convert a DC voltage from a lower level to a hgher level. Theory of Operaton Relaton
More informationRevision of Lecture TwentyOne
Revson of Lecture TwentyOne FFT / IFFT most wdely found operatons n communcaton systems Important to know what are gong on nsde a FFT / IFFT algorthm Wth the ad of FFT / IFFT, ths lecture looks nto OFDM
More informationRejection of PSK Interference in DSSS/PSK System Using Adaptive Transversal Filter with Conditional Response Recalculation
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol., No., November 23, 39 Rejecton of PSK Interference n DSSS/PSK System Usng Adaptve Transversal Flter wth Condtonal Response Recalculaton Zorca Nkolć, Bojan
More informationThe Throughput of HybridARQ in Block Fading under Modulation Constraints
The Throughput of HybrdARQ n Block Fadng under Modulaton Constrants Tark Ghanm and Matthew C. Valent Lane Dept. of Comp. Sc. and Elect. Eng. West Vrgna Unversty Morgantown, WV 26506 6109 Emal: mvalent@wvu.edu
More information# 12 ECE 253a Digital Image Processing Pamela Cosman 11/4/11. Introductory material for image compression
# 2 ECE 253a Digital Image Processing Pamela Cosman /4/ Introductory material for image compression Motivation: Lowresolution color image: 52 52 pixels/color, 24 bits/pixel 3/4 MB 3 2 pixels, 24 bits/pixel
More informationLearning Ensembles of Convolutional Neural Networks
Learnng Ensembles of Convolutonal Neural Networks Lran Chen The Unversty of Chcago Faculty Mentor: Greg Shakhnarovch Toyota Technologcal Insttute at Chcago 1 Introducton Convolutonal Neural Networks (CNN)
More information4492 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 10, OCTOBER 2017
4492 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 10, OCTOBER 2017 OFDMBased Interference Algnment n SngleAntenna Cellular Wreless Networks Huacheng Zeng, Member, IEEE, YSh,Senor Member, IEEE, Y.
More informationEvaluate the Effective of Annular Aperture on the OTF for Fractal Optical Modulator
Global Advanced Research Journal of Management and Busness Studes (ISSN: 23155086) Vol. 4(3) pp. 082086, March, 2015 Avalable onlne http://garj.org/garjmbs/ndex.htm Copyrght 2015 Global Advanced Research
More informationOld text. From Through the Looking Glass by Lewis Carroll. Where is the setting of this place? Describe in your own words.
Old text Read ths extract carefully, then answer, n complete sentences, the questons that follow. For some mnutes Alce stood wthout speakng, lookng out n all drectons over the country and a most curous
More informationA study of turbo codes for multilevel modulations in Gaussian and mobile channels
A study of turbo codes for multlevel modulatons n Gaussan and moble channels Lamne Sylla and Paul Forter (sylla, forter)@gel.ulaval.ca Department of Electrcal and Computer Engneerng Laval Unversty, SteFoy,
More informationPiecewise Linear Approximation of Generators Cost Functions Using MaxAffine Functions
Pecewse Lnear Approxmaton of Generators Cost Functons Usng MaxAffne Functons Hamed Ahmad José R. Martí School of Electrcal and Computer Engneerng Unversty of Brtsh Columba Vancouver, BC, Canada Emal:
More informationThe Stability Region of the TwoUser Broadcast Channel
The Stablty Regon of the TwoUser Broadcast Channel Nkolaos appas *, Maros Kountours, * Department of Scence and Technology, Lnköpng Unversty, Campus Norrköpng, 60 74, Sweden Mathematcal and Algorthmc
More informationAN ALGORITHM TO COMBINE LINK ADAPTATION AND TRANSMIT POWER CONTROL IN HIPERLAN TYPE 2
AN ALGORITHM TO COMBINE LINK ADAPTATION AND TRANSMIT POWER CONTROL IN HIPERLAN TYPE 2 Markus Radmrsch Inst. f. Allgem. Nachrchtentechnk, Unv. Hannover, Appelstr. 9a, 3167 Hannover, Germany Tel.: +49511762
More information