Digital Communications 1: Fundamentals and Techniques

It is a complete training in digital communications in the same book with all the aspects involved in such training: courses, tutorials with many typical problems targeted with detailed solutions, practical work concretely illustrating various aspects of technical implementation implemented. It breaks down into three parts. The Theory of information itself, which concerns both the sources of information and the channels of its transmission, taking into account the errors they introduce in the transmission of information and the means of protect by the use of appropriate coding methods. Then for the technical aspects of transmission, first the baseband transmission is presented with the important concept and fundamental technique of equalization. The performance evaluation in terms of probability of errors is systematically developed and detailed as well as the online codes used. Finally, the third part presents the Transmissions with digital modulation of carriers used in radio transmissions but also on electric cables. A second important aspect in learning a learner's knowledge and skills is this book. It concerns the "Directed Work" aspect of a training. This is an ordered set of 33 typical problems with detailed solutions covering the different parts of the course with practical work. Finally, the last aspect concerns the practical aspects in the proper sense of the term, an essential complement to training going as far as know-how. We propose here a set of 5 practical works.

Table of Contents:
Foreword xi Part 1. Theory of Information 1 Introduction to Part 1 3 Chapter 1. Introduction to Telecommunications 5 1.1. Role of a communication system 5 1.1.1. Types of services offered by communication systems 6 1.1.2. Examples of telecommunications services 7 1.2. Principle of communication 7 1.3. Trend towards digital communications 10 Chapter 2. Measurement of Information of a Discrete Source and Channel Capacity 13 2.1. Introduction and definitions 13 2.2. Examples of discrete sources 14 2.2.1. Simple source (memoryless) 14 2.2.2. Discrete source with memory 14 2.2.3. Ergodic source: stationary source with finite memory 15 2.2.4. First order Markovian source (first order Markov chain) 15 2.3. Uncertainty, amount of information and entropy (Shannon’s 1948 theorem) 16 2.3.1. Entropy of a source 18 2.3.2. Fundamental lemma 18 2.3.3. Properties of entropy 19 2.3.4. Examples of entropy 19 2.4. Information rate and redundancy of a source 20 2.5. Discrete channels and entropies 20 2.5.1. Conditional entropies 22 2.5.2. Relations between the various entropies 24 2.6. Mutual information 25 2.7. Capacity, redundancy and efficiency of a discrete channel 27 2.7.1. Shannon’s theorem: capacity of a communication system 27 2.8. Entropies with k random variables 29 Chapter 3. Source Coding for Non-disturbance Channels 31 3.1. Introduction 31 3.2. Interest of binary codes 31 3.3. Single decoding codes 32 3.3.1. Regular code 33 3.3.2. Single-decoded code (decipherable or decodable code) 33 3.3.3. Instantaneous code (irreducible code) 34 3.3.4. Prefix 34 3.3.5. Design of an instantaneous binary code 35 3.3.6. Kraft McMillan inequality 36 3.4. Average codeword length 36 3.4.1. Coding efficiency in terms of transmission speed 36 3.4.2. Minimum average codeword length lmin 37 3.5. Capacity, efficiency and redundancy of a code 38 3.6. Absolute optimal codes 38 3.7. K-order extension of a source 39 3.7.1. Entropy of the 2nd order extension of a source [S] 39 3.7.2. Simple example of the interest of coding a source extension 40 3.8. Shannon’s first theorem 41 3.9. Design of optimal binary codes 42 3.9.1. Shannon–Fano coding 42 3.9.2. Huffman code 43 Chapter 4. Channel Coding for Disturbed Transmission Channels 47 4.1. Introduction 47 4.2. Shannon’s second theorem (1948) 48 4.3. Error correction strategies 48 4.4. Classification of error detection codes or error correction codes 49 4.5. Definitions related to code performance 50 4.5.1. Efficiency 50 4.5.2. Weight of linear code or Hamming’s weight 50 4.5.3. Hamming distance 51 4.6. Form of the decision 51 4.6.1. Maximum a posteriori likelihood decoding 52 4.7. Linear group codes 53 4.7.1. Decoding ball concept: Hamming’s theorem 54 4.7.2. Generating matrix [G] and test matrix [H] 55 4.7.3. Error detection and correction 58 4.7.4. Applications: Hamming codes (r = 1) 59 4.7.5. Coding and decoding circuits 62 4.7.6. Extension of Hamming codes 63 4.7.7. Relationships between columns of the matrix [H’] 64 4.8. Cyclic codes 65 4.8.1. Introduction 65 4.8.2. Expression of a circular permutation 67 4.8.3. Generating polynomial g(x), generating matrix [G] and theorem of cyclic codes 68 4.8.4. Dual code generated by h(x) and parity control matrix [H] 71 4.8.5. Construction of the codewords (coding) 72 4.9. Linear feedback shift register (LFSR) and its applications 83 4.9.1. Properties 84 4.9.2. Linear feedback shift register encoder and decoder (LFSR) 85 4.9.3. Coding by multiplication: non-systematic code 92 4.9.4. Detection of standard errors with cyclic codes 95 4.9.5. Pseudo-random sequence generators: M-sequences, Gold, Kasami and Trivium 97 Part 2. Baseband Digital Transmissions and with Carrier Modulation 117 Introduction to Part 2 119 Chapter 5. Binary to M-ary Coding and M-ary to Signal Coding: On-line Codes 123 5.1. Presentation and typology 123 5.2. Criteria for choosing an on-line code 125 5.3. Power spectral densities (PSD) of on-line codes 126 5.4. Description and spectral characterization of the main linear on-line codes with successive independent symbols 127 5.4.1. Binary NRZ code (non-return to zero): two-level code, two types of code 128 5.4.2. NRZ M-ary code 131 5.4.3. Binary RZ code (return to zero) 132 5.4.4. Polar RZ on-line code 134 5.4.5. Binary biphase on-line code (Manchester code) 136 5.4.6. Binary biphase mark or differential code (Manchester mark code) 138 5.5. Description and spectral characterization of the main on-line non-linear and non-alphabetic codes with successive dependent symbols 139 5.5.1. Miller’s code 140 5.5.2. Bipolar RZ code or AMI code (alternate marked inversion) 141 5.5.3. CMI code (code mark inversion) 144 5.5.4. HDB-n code (high density bipolar on-line code of order n) 145 5.6. Description and spectral characterization of partial response linear codes 147 5.6.1. Generation and interest of precoding 148 5.6.2. Structure of the coder and precoder 150 5.6.3. Power spectral density of partial response linear on-line codes 153 5.6.4. Most common partial response linear on-line codes 155 Chapter 6. Transmission of an M-ary Digital Signal on a Low-pass Channel 167 6.1. Introduction 167 6.2. Digital systems and standardization for high data rate transmissions 168 6.3. Modeling the transmission of an M-ary digital signal through the communication chain 170 6.3.1. Equivalent energy bandwidth Δfe of a low-pass filter 174 6.4. Characterization of the intersymbol interference: eye pattern 175 6.4.1. Eye pattern 176 6.5. Probability of error Pe 179 6.5.1. Probability of error: case of binary symbols ak = ±1 180 6.5.2. Probability of error: case of binary RZ code 185 6.5.3. Probability of error: general case of M-ary symbols 187 6.5.4. Probability of error: case of bipolar code 193 6.6. Conditions of absence of intersymbol interference: Nyquist criteria 196 6.6.1. Nyquist temporal criterion 196 6.6.2. Nyquist frequency criterion 196 6.6.3. Interpretation of the Nyquist frequency criterion 197 6.7. Optimal distribution of filtering between transmission and reception 206 6.7.1. Expression of the minimum probability of error for a low-pass channel satisfying the Nyquist criterion 211 6.8. Transmission with a partial response linear coder 212 6.8.1. Transmission using the duobinary code 213 6.8.2. Transmission using 2nd order interleaved bipolar code 215 6.8.3. Reception of partial response linear codes 217 6.8.4. Probability of error Pe 220 Chapter 7. Digital Transmissions with Carrier Modulation 223 7.1. Introduction and schematic diagram of a digital radio transmission 223 7.2. Multiple access techniques and most common standards 225 7.3. Structure of a radio link, a satellite link and a mobile radio channel 230 7.3.1. Structure of a terrestrial link (one jump) 230 7.3.2. Structure of a satellite telecommunication link 230 7.3.3. Mobile radio channel 231 7.4. Effects of multiple paths and non-linearities of power amplifiers 232 7.4.1. Effects of multiple paths: simple case of a direct path and only one delayed path 232 7.4.2. Effects of non-linearities of power amplifiers 235 7.5. Linear digital carrier modulations 237 7.5.1. Principle 237 7.5.2. General characteristics of the modulated signal s(t) 238 7.6. Quadrature digital linear modulations: general structure of the modulator, spatial diagram, constellation diagram and choice of a constellation 241 7.6.1. General structure of the modulator 242 7.6.2. Spatial diagram (or vectorial) and constellation diagram 243 7.6.3. Choosing a constellation diagram 245 7.7. Digital radio transmission and equivalent baseband digital transmission: complex envelope 246 7.7.1. Equivalent baseband digital transmission: complex envelope 247 7.8. Equivalent baseband transmission, interest and justification: analytical signal and complex envelope 251 7.8.1. Interest: important simplification in numerical simulation 251 7.8.2. Analytical signal and complex envelope of a modulated signal 251 7.9. Relationship between band-pass filter H and equivalent low-pass filter He 253 7.9.1. Probability of errors 258 7.10. M-ary Phase Shift Keying Modulation (M-PSK) 258 7.10.1. Binary Phase Shift Keying (BPSK) modulation and demodulation 259 7.10.2. Quaternary Phase Shift Keying (QPSK) modulation and demodulation 262 7.10.3. Differential M-PSK receiver 267 7.10.4. Offset Quaternary Phase Shift Keying (OQPSK) 271 7.11. M-ary Quadrature Amplitude Modulation (M-QAM) 274 7.12. Detailed presentation of 16-QAM modulation and demodulation 275 7.12.1. Spectral occupancy of the 16-QAM modulated signal 277 7.13. Amplitude and Phase Shift Keying Modulation (APSK) 280 7.13.1. CIR (4, 4, 4, 4) modulation: 4 amplitudes, 4 phases (ITU-V29, 1980) 280 7.14. Detailed presentation of the 8-PSK modulation and demoludation 281 7.14.1. Differential coding and decoding of the 8-PSK modulation 284 7.14.2. Realization of the differential encoder and decoder: by Simulink simulation (MATLAB) and hardware implementation based on a ROM or EPROM memory 285 7.15. Performances of modulations in spectral occupancy and efficiency 291 References 293 Index 295

About the Author :
Safwan El Assad is Associate Professor (HDR) at Polytech Nantes, France. From 1988 to 2005, his research activities concerned radar imagery and digital communications. With a background in radar imagery and digital communications, today his research largely focuses on chaos-based cryptography. Dominique Barba is a retired Professor from Polytech Nantes. His research has focused for over 45 years on the processing of still and moving images (improvement, compression), their analysis, human and artificial vision, as well as digital communications (compression).