DOCSLIB.ORG

Introduction to Digital Communications System

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introduction to Digital Communications System Wireless Information Transmission System Lab. Introduction to Digital Communications System Institute of Communications Engineering National Sun Yat-sen University Recommended Books Digital Communications / Fourth Edition (textbook) -- John G. Proakis, McGraw Hill Communication Systems / 4th Edition -- Simon Haykin, John Wiley & Sons, Inc. Digital Communications – Fundamentals and Applications / 2nd Edition -- Bernard Sklar, Prentice Hall Principles of Communications / Fifth Edition -- Rodger E. Ziemer and William H. Tranter, John Wiley & Sons, Inc. Modern Digital and Analog Communication Systems -- B.P. Lathi, Holt, Rinehart and Winston, Inc. 2 Example of Communications System Local Loop Switch T1/E1 Facilities Mobile Switching Transmission Center Equipment regenerator Base Central Office A/D Conversion (Digitization) Station Local Loop SONET Switch T1/E1 Facilities M SDH U Transmission T1/E1 Facilities Equipment regenerator X Central Office A/D Conversion (Digitization) Local Loop Switch T1/E1 Facilities Transmission regenerator Equipment Mobile Central Office A/D Conversion Switching (Digitization) Center Public Switched Telephone Network (PSTN) Base Station 3 Basic Digital Communication Nomenclature Textual Message: information comprised of a sequence of characters. Binary Digit (Bit): the fundamental information unit for all digital systems. Symbol (mi where i=1,2,…M): for transmission of the bit stream; groups of k bits are combined to form new symbol from a finite set of M such symbols; M=2k. Digital Waveform: voltage or current waveform representing a digital symbol. Data Rate: Symbol transmission is associated with a symbol duration T. Data rate R=k/T [bps]. Baud Rate: number of symbols transmitted per second [baud]. 4 Nomenclature Examples 5 Messages, Characters, and Symbols 6 Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits TX Source Channel Frequency Multiple Format Encryption Interleaving Multiplexing Modulation RF Encoding Encoding Spreading Access PA si (t) Digital Input C m i H Bit Digital A Synchronization N Stream Waveform N Digital E Output L mˆ i sˆi (t) RX Source Channel Frequency Multiple Format Decryption Deinterleaving Demultiplexing Demodulation RF Decoding Decoding Despreading Access IF Information Sink Source Bits Channel Bits Optional Essential To Other Destinations 7 Wireless Information Transmission System Lab. Format Institute of Communications Engineering National Sun Yat-sen University Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits TX Source Channel Frequency Multiple Format Encryption Interleaving Multiplexing Modulation RF Encoding Encoding Spreading Access PA si (t) Digital Input C m i H Bit Digital A Synchronization N Stream Waveform N Digital E Output L mˆ i sˆi (t) RX Source Channel Frequency Multiple Format Decryption Deinterleaving Demultiplexing Demodulation RF Decoding Decoding Despreading Access IF Information Sink Source Bits Channel Bits Optional Essential To Other Destinations 9 Formatting and Baseband Transmission 10 Sampling Theorem 11 Sampling Theorem Sampling Theorem: A bandlimited signal having no spectral components above fm hertz can be determined uniquely by values sampled at uniform intervals of Ts seconds, where 1 T ≤ S or sampling rate f S ≥ 2 f m 2 fm In sample-and-hold operation, a switch and storage mechanism form a sequence of samples of the continuous input waveform. The output of the sampling process is called pulse amplitude modulation (PAM). 12 Sampling Theorem 1 ∞ X S ( f ) = X ( f )∗ X δ ( f ) = ∑ X ( f − nfS ) TS n=−∞ 13 Spectra for Various Sampling Rates 14 Natural Sampling 15 Pulse Code Modulation (PCM) PCM is the name given to the class of baseband signals obtained from the quantized PAM signals by encoding each quantized sample into a digital word. The source information is sampled and quantized to one of L levels; then each quantized sample is digitally encoded into an ℓ-bit (ℓ=log2L) codeword. 16 Example of Constructing PCM Sequence 17 Uniform and Non-uniform Quantization 18 Statistical Distribution of Single-Talker Speech Amplitudes 50% of the time, speech voltage is less than ¼ RMS. Only 15% of the time, voltage exceeds RMS. Typical voice signal dynamic range is 40 dB. 19 Problems with Linear Quantization Fact: Unacceptable S/N for small signals. Solution: Increasing quantization levels – price is too high. Applying nonlinear quantization – achieved by first distorting the original signal with a logarithmic compression characteristic and then using a uniform quantizer. At the receiver, an inverse compression characteristic, called expansion, is applied so that the overall transmission is not distorted. The processing pair is referred to as companding. 20 Implementation of Non-linear Quantizer 21 Companding Characteristics In North America: μ-law compression: loge[1+ µ( x / xmax)] y = ymax ⋅sgn x loge (1+ µ) where ⎧+1 for x ≥ 0 sgn x = ⎨ ⎩−1 for x < 0 In Europe: A-law compression: ⎧ A( x / xmax ) x 1 ⎪ ymax ⋅sgn x 0 < ≤ ⎪ 1+ log A x A y = ⎨ e max 1+ log [ A( x / x )] 1 x ⎪ y e max ⋅sgn x < ≤ 1 ⎪ max ⎩ 1+ log e A A xmax 22 Compression Characteristics Standard values of μ is 255 and A is 87.6. 23 Wireless Information Transmission System Lab. Source Coding Institute of Communications Engineering National Sun Yat-sen University Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits TX Source Channel Frequency Multiple Format Encryption Interleaving Multiplexing Modulation RF Encoding Encoding Spreading Access PA si (t) Digital Input C m i H Bit Digital A Synchronization N Stream Waveform N Digital E Output L mˆ i sˆi (t) RX Source Channel Frequency Multiple Format Decryption Deinterleaving Demultiplexing Demodulation RF Decoding Decoding Despreading Access IF Information Sink Source Bits Channel Bits Optional Essential To Other Destinations 25 Source Coding Source coding deals with the task of forming efficient descriptions of information sources. For discrete sources, the ability to form reduced data rate descriptions is related to the information content and the statistical correlation among the source symbols. For analog sources, the ability to form reduced data rate descriptions, subject to a fixed fidelity criterion I related to the amplitude distribution and the temporal correlation of the source waveforms. 26 Huffman Coding The Huffman code is source code whose average word length approaches the fundamental limit set by the entropy of a discrete memoryless source. The Huffman code is optimum in the sense that no other uniquely decodable set of code-words has smaller average code-word length for a given discrete memoryless source. 27 Huffman Encoding Algorithm 1. The source symbols are listed in order of decreasing probability. The two source symbols of lowest probability are assigned a 0 and a 1. 2. These two source symbols are regarded as being combined into a new source symbol with probability equal to the sum of the two original probabilities. The probability of the new symbol is placed in the list in accordance with its value. 3. The procedure is repeated until we are left with a final list of source statistics of only two for which a 0 and a 1 are assigned. 4. The code for each (original) source symbol is found by working backward and tracing the sequence of 0s and 1s assigned to that symbol as well as its successors. 28 Example of Huffman Coding Symbol Probability Code Word S0 0.4 00 S1 0.2 10 S2 0.2 11 S3 0.1 010 S4 0.1 011 Symbol Stage 1 Stage 2 Stage 3 Stage 4 S0 0.4 0.4 0.4 0.6 0 S1 0.2 0.2 0.4 0 0.4 1 S2 0.2 0.2 0 0.2 0 1 S3 0.1 0.2 1 S4 0.1 1 29 Properties of Huffman Code Huffman encoding process is not unique. Code words for different Huffman encoding process can have different lengths. However, the average code-word length is the same. When a combined symbol is moved as high as possible, the resulting Huffman code has a significantly smaller variance than when it is moved as low as possible. Huffman code is a prefix code. A prefix code is defined as a code in which no code-word is the prefix of any other code-word. 30 Bit Compression Technologies for Voice Differential PCM (DPCM) Adaptive DPCM Delta Modulation (DM) Adaptive DM (ADM) . Speech Encoding 31 Differential PCM (DPCM) 32 Delta Modulation (DM) Delta modulation is a one-bit DPCM. Advantage: bit compression. Disadvantage: slope overload. 33 Speech Coding Objective Reduce the number of bits needed to be transmitted, therefore lowering the bandwidth required. 34 Speech Properties Voiced Sound Arises in generation of vowels and latter portion of some consonants. Displays long-term repetitive pattern corresponding to the duration of a pitch interval Pulse-like waveform. Unvoiced Sound Arises in pronunciation of certain consonants such as “s”, “f”, “p”, “j”, “x”, …, etc. Noise-like waveform. 35 Categories of Speech Encoding Waveform Encoding Treats voice as analog signal and does not use properties of speech: Source Model Coding or Vocoding Treats properties of speech to preserve word information Hybrid or parametric methods Combines waveform and vocoding 36 Linear Predictive Coder (LPC) 37 Multi-Pulse Linear Predictive Coder (MP-LPC) 38 Regular Pulse Excited Long Term Prediction Coder (RPE-LPT) 39 Code-Excited Linear Predictive (CELP) 40 Speech Coder Complexity 41 Speech Processing for GSM Composition of the 13 kbps signal: 36 bits for filter parameters every 20 ms. 9 bits for LTP every 5 ms. 47 bits for RPE every 5 ms. Thus, in a 20 ms (2080-bit block, or 260 sample) interval, we need a total of 36+9*20/5+47*20/5=260 bits. Data Rate = 260/(20 ms) = 13 kbps. 42 Speech Processing for IS-54 Composition of the 7.95 kbps signal: 43 bits for filter parameters every 20 ms. 7 bits for LTP every 5 ms.
Load more

Recommended publications
  • Criteria for Choosing Line Codes in Data Communication
    ISTANBUL UNIVERSITY – YEAR : 2003 (843-857) JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING VOLUME : 3 NUMBER : 2 CRITERIA FOR CHOOSING LINE CODES IN DATA COMMUNICATION Demir Öner Istanbul University, Engineering Faculty, Electrical and Electronics Engineering Department Avcılar, 34850, İstanbul, Turkey E-mail: [email protected] ABSTRACT In this paper, line codes used in data communication are investigated. The need for the line codes is emphasized, classification of line codes is presented, coding techniques of widely used line codes are explained with their advantages and disadvantages and criteria for chosing a line code are given. Keywords: Line codes, correlative coding, criteria for chosing line codes.. coding is either performed just before the 1. INTRODUCTION modulation or it is combined with the modulation process. The place of line coding in High-voltage-high-power pulse current The transmission systems is shown in Figure 1. purpose of applying line coding to digital signals before transmission is to reduce the undesirable The line coder at the transmitter and the effects of transmission medium such as noise, corresponding decoder at the receiver must attenuation, distortion and interference and to operate at the transmitted symbol rate. For this ensure reliable transmission by putting the signal reason, epecially for high-speed systems, a into a form that is suitable for the properties of reasonably simple design is usually essential. the transmission medium. For example, a sampled and quantized signal is not in a suitable form for transmission. Such a signal can be put 2. ISSUES TO BE CONSIDERED IN into a more suitable form by coding the LINE CODING quantized samples.
    [Show full text]
  • Multilevel Sequences and Line Codes
    COPYRIGHT AND CITATION CONSIDERATIONS FOR THIS THESIS/ DISSERTATION o Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. o NonCommercial — You may not use the material for commercial purposes. o ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. How to cite this thesis Surname, Initial(s). (2012) Title of the thesis or dissertation. PhD. (Chemistry)/ M.Sc. (Physics)/ M.A. (Philosophy)/M.Com. (Finance) etc. [Unpublished]: University of Johannesburg. Retrieved from: https://ujdigispace.uj.ac.za (Accessed: Date). MULTILEVEL SEQUENCES AND LINE CODES by LOUIS BOTHA Thesis submitted as partial fulfilment of the requirements for the degree MASTER OF ENGINEERING in ELECTRICAL AND ELECTRONIC ENGINEERING in the FACULTY OF ENGINEERING at the RAND AFRIKAANS UNIVERSITY SUPERVISOR: PROF HC FERREIRA MAY 1991 SUMMARY As the demand for high-speed data communications over conventional channels such as coaxial cables and twisted pairs grows, it becomes neccesary to optimize every aspect of the communication system at reasonable cost to meet this demand effectively. The choice of a line code is one of the most important aspects in the design of a communications system, as the line code determines the complexity, and thus also the cost, of several circuits in the system. It has become known in recent years that a multilevel line code is preferable to a binary code in cases where high-speed communications are desired.
    [Show full text]
  • Optical Modulation for High Bit Rate Transport Technologies by Ildefonso M
    Technology Note Optical Modulation for High Bit Rate Transport Technologies By Ildefonso M. Polo I October, 2009 Scope There are plenty of highly technical and extremely mathematical articles published about optical modulation formats, showing complex formulas, spectral diagrams and almost unreadable eye diagrams, which can be considered normal for every emerging technology. The main purpose of this article is to demystify optical modulation in a way that the rest of us can visualize and understand them. Nevertheless, some of these modulations are so complex that they can’t be properly represented in a simple time domain graph, so polar (constellation) or spherical coordinates are often used to represent the different states of the signal. Within this document some of these polar diagrams have been enhanced with the state diagram (blue) to indicate the possible transitions and logic. Introduction Back in the early ‘90s, copper lines moved from digital baseband line coding (e.g. 2B1Q, 4B3T, AMI, and HDB3, among others) to complex modulation schemes to increase speed, reach, and reliability. We were all skeptical that a technology like DSL would have been able to transmit 256 simultaneous QAM16 signals and achieve 8 Mbit/s. Today copper is already reaching the 155 Mbit/s mark. This is certainly a full circle. We moved from analog to digital transmission to increase data rates and reliability, and then we resorted to analog signals (through modulation) to carry digital information farther, faster and more reliably. Back then, 155 Mbit/s were only thought of for fiber optics transmission. It is also interesting to note that only a few years ago we seemed to be under the impression that ‘fiber optics offered an almost infinite amount of bandwidth’ or more than we would ever need.
    [Show full text]
  • Chapter 1 Introduction
    Chapter 1 Intro duction The advancement in multimedia applications and the development of the In- ternet have created a demand for high-sp eed digital communications. Sophisti- cated audio and video co ding metho ds have reduced the bit rate requirements for audio and video transmission. This in turn motivated the development of communication systems to achieve these requirements. Both technologies enabled high-quality audio and video transmission and intro duced a number of new applications for businesses and residential consumers. Key applications other than voice communications include Internet ac- cess, streaming audio, and broadcast video. Table 1.1 and 1.2 list several residential and business applications and their data rate requirements. Down- stream घfrom the service provider to the consumerङ and upstream घfrom the consumer to the service providerङ requirements are listed in separate columns b ecause some applications have asymmetric requirements. For example, video broadcasting is an asymmetric application requiring a fast downstream link but no upstream link. Table 1.1 shows that the residential consumer application requirements can be satis ed with a data rate of 3 Mb/s with the exception 1 Application downstream upstream data rate घkb/sङ data rate घkb/sङ Voice telephony 16{64 16{64 Internet access 14 { 3,000 14 { 384 Electronic Mail 9 { 128 9{ 64 High de nition TV 12,000 {24,000 0 Broadcast video 1,500 { 6,000 0 Music on demand 384 { 3,000 9 Videophone 128 { 1,500 128 { 1,500 Distance Learning 384 { 3,000 128 { 3,000 Database Access 14 { 384 9 Software download 384 { 3,000 9 Shop at home 128 { 1,500 9{ 64 Video games 64 { 1,500 64 { 1,500 Table 1.1: Some residential consumer applications and their upstream and downstream data rate requirements [1].
    [Show full text]
  • Line Coding” Mobile Communications Handbook Ed
    LoCicero, J.L. & Patel, B.P. “Line Coding” Mobile Communications Handbook Ed. Suthan S. Suthersan Boca Raton: CRC Press LLC, 1999 c 1999byCRCPressLLC LineCoding 6.1 Introduction 6.2 CommonLineCodingFormats UnipolarNRZ(BinaryOn-OffKeying) • UnipolarRZ • Polar NRZ • PolarRZ[Bipolar,AlternateMarkInversion(AMI),or Pseudoternary] • ManchesterCoding(SplitPhaseorDigital Biphase) 6.3 AlternateLineCodes DelayModulation(MillerCode) • SplitPhase(Mark) • Biphase (Mark) • CodeMarkInversion(CMI) • NRZ(I) • BinaryN ZeroSubstitution(BNZS) • High-DensityBipolarN(HDBN) • TernaryCoding 6.4 MultilevelSignalling,PartialResponseSignalling,and DuobinaryCoding MultilevelSignalling • PartialResponseSignallingandDuobi- naryCoding JosephL.LoCicero 6.5 BandwidthComparison IllinoisInstituteofTechnology 6.6 ConcludingRemarks BhaskerP.Patel DefiningTerms IllinoisInstituteofTechnology References 6.1 Introduction Theterminologylinecodingoriginatedintelephonywiththeneedtotransmitdigitalinformation acrossacoppertelephoneline;morespecifically,binarydataoveradigitalrepeateredline.The conceptoflinecoding,however,readilyappliestoanytransmissionlineorchannel.Inadigitalcom- municationsystem,thereexistsaknownsetofsymbolstobetransmitted.Thesecanbedesignatedas {mi},i=1;2;:::;N,withaprobabilityofoccurrence{pi},i=1;2;:::;N,wherethesequentially transmittedsymbolsaregenerallyassumedtobestatisticallyindependent.Theconversionorcoding oftheseabstractsymbolsintoreal,temporalwaveformstobetransmittedinbasebandistheprocess oflinecoding.Sincethemostcommontypeoflinecodingisforbinarydata,suchawaveformcanbe
    [Show full text]
  • 2B1Q, 142–143 4B3T Modified Monitored State
    Derickson.book Page 911 Thursday, November 8, 2007 11:11 AM Index 2B1Q, 142–143 optical sampling demonstrations, 427 4B3T modified monitored state (MMS43), optical waveform measurement techniques, 423 142–143 optical waveform sampling, 423–426 4B5B block substitution, 70–74 See also All-optical sampling implementations, 4B5B encoder efficiency, 89 experimental; Fiber FWM-based sampling 8B10B system, performance analysis of; Optical block substitution, 74–77 sampling principles; Sampling gate control words, 154, 162 implementations; Third-order nonlinearity- encoder efficiency, 89 based sampling; Timebase designs encoding rules, 862–872 All-optical sampling implementations, 10GBase control codes, 157 experimental 10GBase stress testing, 619–628 analog-to-digital conversion of acquired 10GBase-KR, 642, 651–654 samples, 480–482 10GBase-LR, 619 χ2-based sampling in bulk KTP, 482–484 10GBase-LRM, 634 χ2-based sampling using quasi-phase matching 64B66B encoder in PPLN, 484–486 code blocks, 160 χ3-based Kerr switch with parametric gain in control characters, 157 HNLF, 487–488 deserializer architecture, 158 χ3-based sampling system using XPM-induced frame structure, 161 frequency shift in HNLF, 486–487 scrambler, 162–163 coherent detection sampling (linear sampling), serializer architecture, 158 489–491 fiber FWM-based sampling in HNLF, 488–489 A gain-transparent ultrafast nonlinear interferometer, 489–490 Accelerated BER measurements, 192 optimization for 40 Gbit/s signals, 491–492 Active bias T, 122–123, 902–910 sampling pulse sources, 475–480
    [Show full text]
  • Network Troubleshooting
    Network Troubleshooting by Othmar Kyas K Index An Agilent Technologies Publication Agilent Technologies Index K 10 Mbit/s Ethernet Networks 173 Asynchronous Transfer Mode (ATM) 297, 301 100Base-T Full-Duplex Connections 177 Asynchronous transmission 277 100Base-T Switch Links 179 ATM Adaptation Layer (AAL) 346 100Base-T Uplinks 179 ATM addressing 367 10Base-T 174 ATM and DXI interfaces 323 2B1Q (two binary, one quaternary) 97 ATM cell 328 2B1Q coding 441 ATM cell streams at 25.6 Mbit/s 323 2B1Q lines 442 ATM cell streams over FDDI infrastructures (TAXI) 322 4B3T lines 442 ATM cell streams over V.35, EIA/TIA 449/530, HSSI, 322 4B5B encoding 123 ATM cell types 335 55555555 197 ATM data rates 307 802.2 LLC XID Test Packet 191 ATM forum signaling: UNI 3.0 372 8B6T encoding 123 ATM forum signaling: UNI 4.0 373 ATM forum UNI signaling: UNI 3.0, 3.1, 4.0 369 A ATM in heterogeneous LAN environments 299 A/C Error (Isolating) 247 ATM in homogeneous private networks 298 AAAAAAAA 197 ATM in PDH networks 307 AAL Type 0 347 ATM in public wide-area networks 301 AAL Type 1 347 ATM in SDH and SONET networks 314 AAL Type 2 349 ATM interface cards 417 AAL Type 3/4 353 ATM interworking 375 AAL Type 5 353 ATM layer 328 AAL2 error messages 351 ATM layer model 303 Abort error (isolating) 247 ATM layer OAM functions 341 Abstract Test Suite (ATS) 118, 119 ATM over 100 Ohm copper cable 320, 321 Acceptance testing 37 ATM over 150 Ohm Shielded Twisted Pair (STP) 321 Accounting management 46 ATM over 6.312 Mbit/s and 97.728 Mbit/s 311 Active Line State (ALS) 267
    [Show full text]
  • Advanced Communications Project
    Advanced Communications Project Technology Reference Document ELO DEV PM & EN H T C C R E A N E T S E Prepared for E R R The United States Coast Guard Research & Development Center U 1082 Shennecossett Rd. N D I R T A Groton, CT 06340-6096 E U D G S T T A S T E S C O A By VisiCom Laboratories Inc. 1198 Gulf Breeze Parkway Gulf Breeze, FL 32561 September 1993 EXECUTIVE SUMMARY This document is an updated version of the 1985 Technology Reference Document prepared for the U.S. Coast Guard Research and Development Center. It has fully incorporated the contents of the 1985 document. No attempt was made to perform any editorial changes on the 1985 material, with the sole exception of correcting any information which is no longer accurate or applicable due to the evolution of technology. The major changes to the document have been in the area of reorganization / style, the addition of new telecommunications technology information, and the inclusion of information regarding the U.S. navy Satellite Communications System. To provide an all encompassing technology document was beyond the scope of this particular effort. Consequently, the new technology introduced with this updated document has focused on selected topics which were considered by the authors to be of prime importance to U.S. Coast Guard personnel. The following technologies were selected: • Electromagnetic Frequency • Transmission Hardware Spectrum Technology • Over the Horizon Radio • Analog Modulation Communications • Digital Modulation • Radio Frequency Modulation • Information Coding/Processing • Communications Channel Multiplex/ Access • Communications Networks • Integrated Services Digital Network • Cellular Mobile Transmission • Satellite Communications • Computer Architecture Concepts • Security • Communications and Network • Fleet Satellite Communications Services • U.S.
    [Show full text]
  • Ternary Line Codes and Their Efficiency
    Ternary Line Codes and their Efficiency Bachelor Thesis by Thomas Schellekens June 2007. An early example of a line code: Morse code. From the British Admiralty's Handbook of Signalling, 1913. Abstract We collect and describe eleven ternary line codes from the literature, describe the criteria of line codes in general, and try to make a comparison of the selected line codes. We investigated the effect of runlength and digital sum variation constraints on the efficiency of a line code. Using previous research, we were able to obtain an exact result of the effect of runlength constraints on the efficiency. We made an approximation using an automated program of the effect of digital sum variation constraints on the efficiency. For the selected codes, the effect of runlength constraints on the efficiency is small. The digital sum variation constraints have a larger impact, resulting in a theoretical maximum efficiency of 63% for a digital sum variation of 1, saturating to > 95% theoretical maximum efficiency for digital sum variation values of 5 and higher. In general, the more constrained a code is, the less efficient it is. Good trade­offs have to made between efficiency and runlength and dsv constraints. At the Chair for Design and Analysis of Communication Systems (DACS) at the University of Twente, the Netherlands. Supervised by Dr. Ir. Pieter-Tjerk de Boer Contents 1. Introduction to the assignment 3 1.1 Original and adjusted goal of this bachelorassignment 3 1.2 General structure of the text 4 2. Introduction to line coding 4 2.1 Definitions 4 2.2 Introduction 5 2.3 Two Approaches to line coding 6 3.
    [Show full text]