Principles of Communication Engineering

Introduction 1(11) Historical Sketch 1(7) Communication Theory 2(3) Randomness 5(1) Probabilistic Formulation of the Communication Problem 6(2) Plan of the Book 8(2) The Role of Communication Theory 10(2) Probability Theory 12(117) Randomness in the Real World 12(3) Random Experiments 13(1) Relative Frequencies 14(1) Mathematical Model of Probability Theory 15(22) Fundamental Definitions 16(2) Ancillary Definitions 18(1) Properties 19(1) Probability Systems 20(4) Relation of the Model to the Real World 24(5) Conditional Probability 29(2) Statistical Independence 31(6) Random Variables 37(47) Distribution Functions 38(6) Density Functions 44(13) Multidimensional Density Functions 57(1) Equality of Random Variables 58(1) Transformation of Variables 58(7) Conditional Probability Density 65(8) Mixed Probability Expressions 73(4) A Communication Example 77(7) Expected Value 84(10) The Fundamental Theorem of Expectation 85(3) Moments 88(6) Limit Theorems 94(35) The Weak Law of Large Numbers 96(1) Chernoff Bound 97(9) Central Limit Theorem 106(5) Reversible Transformation of Random Vectors 111(3) Problems 114(15) Random Waveforms 129(82) Random Processes 129(15) Interpretation of the Random-Process Model 131(1) Random Vectors Obtained from Random Processes 132(1) Specification of Random Processes 133(2) Stationary Random Processes 135(9) Filtered Impulse Noise 144(12) Statistical Characterization 145(3) Statistical Dependency 148(3) Joint Gaussian Density Function 151(5) The Multivariate Central Limit Theorem 156(15) Joint Characteristic Functions 157(3) Central Limit Argument 160(3) Gaussian Random Variables 163(1) Filtered Impulse Noise Process 164(1) Properties of Gaussian Random Variables 164(4) The Multivariate Gaussian Density Function 168(3) The Gaussian Process 171(8) Specification of Gaussian Processes 172(2) The Correlation Function 174(1) Stationary Gaussian Processes 175(2) Gaussian Processes through Linear Filters 177(2) Correlation Functions and Power Spectra 179(32) The Expectation of an Integral 179(2) Power Spectrum 181(5) Jointly Gaussian Processes 186(2) White Gaussian Noise 188(4) Matrix Notation 192(1) Definitions 192(4) Properties of Matrix Multiplication 196(1) Inverse Matrices 197(2) Problems 199(12) Optimum Receiver Principles 211(74) Basic Approach to Optimum Receiver Design 212(1) Vector Channels 212(11) Decision Regions 214(2) Additive Gaussian Noise 216(3) Multivector Channels 219(4) Waveform Channels 223(10) Waveform Synthesis 223(2) Geometric Interpretation of Signals 225(2) Recovery of the Signal Vectors 227(2) Irrelevant Data 229(3) Joint Density Function of the Relevant Noise 232(1) Invariance of the Vector Channel to Choice of Orthonormal Base 232(1) Receiver Implementation 233(12) Correlation Receiver 234(1) Matched Filter Receiver 234(10) Component Accuracy 244(1) Probability of Error 245(40) Equivalent Signal Sets 246(2) Rectangular Signal Sets 248(9) Orthogonal and Related Signal Sets 257(6) Completely Symmetric Signal Sets and A Priori Knowledge 263(1) Union Bound on the Probability of Error 264(2) Orthonormal Expansions and Vector Representations 266(7) Problems 273(12) Efficient Signaling for Message Sequences 285(78) Sequential Sources 285(3) Source Rate 286(1) Transmitter Power 287(1) Bit-by-Bit and Block-Orthogonal Signaling 288(5) Bit-by-Bit Signaling 289(1) Block-Orthogonal Signaling 290(2) Geometric Interpretation 292(1) Time, Bandwidth, and Dimensionality 293(4) Signal Dimensionality as a Function of T 294(2) Bandwidth Requirements with Block-Orthogonal Signaling 296(1) Efficient Signal Selection 297(23) Signaling with Sequences of Binary Waveforms 298(11) Signaling with Multilevel Sequences 309(11) Channel Capacity 320(21) Capacity Theorem 321(2) Proof of the Capacity Theorem 323(18) Discussion 341(1) Reliability Functions 341(22) Block-Orthogonal Signaling 342(4) Other Channels 346(2) Bandwidth-Constrained Orthonormal Functions 348(1) Constrained Linear Combinations 349(1) Constrained Orthonormal Functions 350(1) Discussion 351(1) Bandlimited Waveforms 352(2) Optimization of R0 354(1) The Volume of an N-Dimensional Sphere 355(2) Problems 357(6) Implementation of Coded Systems 363(122) Transmitter Implementation 365(21) The Encoding Problem 366(2) Recapitulation of the Derivation of R0 368(1) Parity-Check Codes 369(17) Receiver Quantization 386(19) Measure of Degradation 389(1) The Quantized-Channel Model 390(2) Calculation of R0' 392(4) Calculation of R0' with Increasingly Fine Quantization 396(3) Comparison of Quantization Schemes 399(6) Binary Convolutional Codes 405(20) The Binary Symmetric Channel 406(3) Convolutional Encoders 409(7) Error Probability 416(9) Sequential Decoding 425(14) Tree Searching 426(3) Basic Concepts 429(2) The Fano Algorithm 431(8) Summary of Results 439(46) Analytical Results 439(1) System Evaluation 440(4) Simulation Results 444(2) Dynamical Decoding Behavior 446(8) Two-Way Strategies 454(2) Experimental System Design 456(6) Extension and Analysis of the Fano Algorithm 462(2) Error Probability 464(9) Mean Computation 473(3) Problems 476(9) Important Channel Models 485(96) Effects of Filtering 485(7) Filtered-Signal Channels 485(3) Theorem on Reversibility 488(1) Additive Nonwhite Gaussian Noise 489(3) Bandpass Channels 492(16) DSB-SC Modulation 493(11) Single-Sideband Modulation 504(3) Comparison of DSB-SC and SSB 507(1) Random Amplitude and Phase 508(19) Random Amplitude 508(3) Random Phase 511(16) Fading Channels 527(23) Scattering Model 529(3) Single Transmission 532(1) Diversity Transmission 533(16) Optimum Diversity 549(1) Coding for Fading Channels 550(31) Unquantized Receiver 551(4) Binary Quantization 555(2) Null-Zone Quantization 557(3) Discussion 560(1) Whitening Filters 561(2) Convexity 563(4) Extension to Nonconvex Functions 567(3) Lemma 570(4) Problems 574(7) Waveform Communication 581(126) Linear Modulation 583(28) Single-Parameter Input 583(11) Sequences of Input Parameters 594(4) Waveform Inputs 598(13) Twisted Modulation 611(34) Geometrical Considerations 611(12) Pulse-Position Modulation 623(19) Frequency-Position Modulation 642(3) Frequency Modulation 645(21) Signal Bandwidth 646(3) Weak-Noise Suppression 649(12) Probability of Anomaly 661(5) Channel Capacity 666(8) Pulse-Code Modulation 674(33) Conventional PCM 675(1) PCM with Error Correction 676(2) The Sampling Theorem 678(5) Optimum Mean-Square Linear Filtering 683(3) Unrealizable Filters 686(1) Realizable Filters, White Input 687(2) Mean-Square Error 689(2) Nonwhite x(t) 691(1) Determination of the Probability that ns(t) Crosses Zero during a Short Interval 691(3) Weak-Noise Performance of FM Feedback Receivers 694(4) Problems 698(9) References and Selected Reading 707(6) Index 713