Digital Modulation & Coding

Contents......Page 2
Ch1 Overview......Page 9
1.1.1 Sources, Channels & Limits to Communication......Page 11
1.1.2 Operations in Digital Transmission Pathway......Page 14
1.1.3 Modulation & Coding......Page 16
1.2 Historical Notes......Page 20
1.3 Outline of Book......Page 22
Bibliography......Page 23
Other Recommended Texts on Digital Transmission......Page 24
Ch2 Fundamental of Probability & Information Theory......Page 26
2.1 Probability......Page 27
2.1.1 Conditional Probability......Page 30
2.2 Random Variables: Discrete & Continuous......Page 32
2.2.1 Discrete Random Variables......Page 33
2.2.2 Continuous Random Variables......Page 35
2.2.3 Multidimensional Random Variables or Random Vectors......Page 41
2.2.4 Conditional Distributions & Densities......Page 43
2.2.5 Independence of Random Variables......Page 45
2.2.6 Transformations of Random Variables......Page 46
2.3 Expectations & Moments......Page 50
2.3.1 First & Second Moments......Page 51
2.3.2 Correlation & Covariance......Page 52
2.3.3 Characteristic Functions......Page 55
2.4.1 Bounds Based on First & Second Moments......Page 57
2.4.2 Chemoff Bounds......Page 58
2.4.3 Sequences, Sums & Laws of Large Numbers......Page 61
2.4.4 Central Limit Theorem......Page 63
2.5 Stochastic Processes......Page 65
2.5.1 Wide-Sense Stationality, Autocorrelation Function & Power Spectral Density......Page 68
2.5.2 Stochastic Processes in Linear Systems......Page 73
2.5.3 Time Averages versus Ensemble Averages......Page 75
2.5.4 Karhunen-Loeve Series Representation for Random Processes......Page 77
2.5.5 Markov Models......Page 81
2.6 Statistical Decision Theory......Page 84
2.6.1 Minimum Probability of Error Policies......Page 85
2.6.2 Irrelevant Data & Sufficient Statistics......Page 88
2.7 Concepts of Information Theory for Discrete Alphabets......Page 96
2.7.1 Entropy for Discrete Random Variables......Page 97
2.7.3 Mutual Information......Page 101
2.7.4 Discrete Channels & Channel Capacity......Page 103
2.7.5 Sequence Transmission......Page 106
2.7.6 Converse to Noisy Channel Coding Theorem......Page 108
2.8 Coding of Discrete Information Sources......Page 112
2.8.1 Block Source Codes......Page 113
2.8.2 Block- to Variable-Length Encoding......Page 115
2.8.3 Extensions to Discrete Markov Sources......Page 120
2.9 Information Theory for Continuous Random Variables & Processes......Page 121
2.9.1 Scalar Variable Case......Page 122
2.9.2 Vector Gaussian Channel Case......Page 125
2.9.3 Waveform Channel Case......Page 127
Bibliography......Page 131
Exercises......Page 133
Ch3 Modulation & Detection......Page 149
3.1 Transmission Model......Page 150
3.1.1 Digital Modulation......Page 151
3.1.2 Channel Filtering......Page 153
3.1.3 Channel Gain & Fading......Page 155
3.1.5 Model Limitations......Page 159
3.2 Signal Spaces......Page 160
3.2.1 Orthonormal Basis Sets......Page 161
3.2.2 M-ary Signal Constellations......Page 163
3.3 Single-Symbol Detection of Known Signals in AWGN......Page 169
3.3.1 Error Performance for General Binary Signals in AWGN......Page 179
3.3.2 Performance Bounds for M-ary Signaling......Page 183
3.3.3 Detection of M-ary Orthogonal, Biorthogonal & Simplex Modulation......Page 186
3.3.4 Detection of M-ary Phase Shift Keying (M-PSK)......Page 193
3.3.5 M-ary Amplitude Modulation & Quadrature Amplitude Modulation......Page 199
3.3.6 Multidimensional Lattice-Based Constellations for AWGN Channel......Page 204
3.3.7 Summary of Energy & Spectrum Efficiency of Modulation Techniques......Page 209
3.3.8 Extension to Single-Symbol Transmission on Nonideal Channels......Page 211
3.4 Noncoherent Demodulation of Carrier-Modulated Signals......Page 212
3.4.1 Structure of Optimal Noncoherent Demodulator......Page 213
3.4.2 Performance Analysis for Noncoherent Demodulation of Binary Orthogonal Signals......Page 219
3.4.3 Performance Analysis of Noncoherent Detection of M-ary Orthogonal Signals......Page 221
3.5 Phase Comparison or Differentially Coherent Demodulation of PSK......Page 224
3.5.1 Structure of Optimal Demodulator......Page 225
3.5.2 Performance Evaluation for M-DPSK......Page 228
3.6 Performance on Slow, Nonselective Rayleigh Fading Channel......Page 232
3.6.1 Binary Signaling with Rayleigh Fading......Page 233
3.6.2 M-ary Orthogonal Signaling with Noncoherent Detection......Page 238
3.6.3 M-ary PSK & DPSK......Page 239
3.7.1 Overview on Power Spectrum & Some Cautions......Page 241
3.7.2 Power Spectrum for General Memoryless Modulation......Page 243
3.7.3 Baseband Pulse-Amplitude Signaling......Page 246
3.7.4 Spectra for M-PSK and M-QAM Modulation......Page 249
3.7.5 Asympototic Bahavior of Power Spectrum; Rate of Dimensionality......Page 252
3.8 Spread-Sprectrum Modulation......Page 255
3.8.1 Direct Sequence Spread Spectrum......Page 256
3.8.2 Frequency-Hopping Spread Spectrum......Page 264
App3A1 Asymptotic Performance of M-ary Orthogonal Signals......Page 273
App3A2 Lattices......Page 276
App3A3 Derivation of Power Spectrum......Page 287
Bibliography......Page 292
Exercises......Page 294
Ch4 Channel Coding & its Potential......Page 308
4.1 Taxonomy of Codes......Page 309
4.2 Introduction to block coding and optimal decoding......Page 312
4.3 Two-Codeword error probability and Ro......Page 318
4.3.1 Ensemble Average Performance for Two-Codeword Codes......Page 323
4.3.2 Extension to Discrete-Input, Continuous-output Channels......Page 326
4.3.3 Generalizations......Page 329
4.4.1 Code Esembles and Simple Ensemble Bound on Performance......Page 330
4.4.2 Generalized Upper Bound for a Specific Code with Many Codewords......Page 333
4.4.3 Properties of Error Exponent and Coding Theorem......Page 336
4.4.4 Summary of Coding Potential for Block Codes on DMCs......Page 339
4.4.5 Remarks for Trells Codes......Page 343
4.5 Implications of Rb and C for signaling on AWGN Channels......Page 344
4.5.1 Ro and C Considerations for Binary Signaling, AWGN Channel, and Hard Decisions......Page 345
4.5.2 Binary Signaling, Unquantized Demodulation......Page 349
4.5.3 Binary Signaling with Soft-quantized Demodulation......Page 352
4.5.4 Summary for Binary Transmision, AWGN Channel......Page 354
4.5.5 Ro and C for Coding with M-ary Modulation, AWGN Channels......Page 355
4.6 Capacity and Ro for the Rayleign fading Channel......Page 364
4.6.1 Coding Poterntial for Binary Signaling on the Railegh Channel......Page 365
4.6.2 M-ary Noncoherent Transmision on the Rayleigh Channel......Page 371
4.6.3 Channel Capacity for Bandwidth-efficient Modulation on the Rayleigh Channel......Page 375
4.7.1 Photon Counting (or Direct Detection) Optical Communication......Page 378
4.7.2 Block Interference Channels......Page 384
App4A1: Decoding on Channels with memory......Page 387
Bibliography......Page 389
Exercises......Page 391