本书融会了Gallager博士数十年的教学科研心得，介绍了信息论方面的基本概念及其对通信系统设计的作用，旨在帮助数字通信领域的师生和工程技术人员理解数字通信背后的基本原理。本书内容全面，包括了数字通信基本知识，离散信源的编码，量化，信源波形与信道波形，向量空间与信号空间，信道、调制与解调，随机过程与噪声，信号的检测与编解码，无线通信，等等。书中为数字通信原理搭建了一个简单的框架，以直观、简洁的方式介绍了复杂的现代通信系统。

本书甫一出版，即被业界奉为经典，目前已被麻省理工学院等世界级名校作为教材。配有习题答案，读者可登录图灵公司网站免费注册获取。

　　本书是世界通信权威、信息领域泰斗Robert G. Gallager博士新作，在数字通信原理的基础上精炼，重点阐述了理论、问题和工程设计之间的关系。内容涉及离散源编码、量化、信道波形、向量空间和信号空间、随机过程和噪声、编码、解码等数字通信基本问题，最后还简单介绍了无线数字通信。

本书是通信专业高年级本科生和研究生教材，也可供工程技术人员参考。

1　Introduction to digital communication　1

 1.1　Standardized interfaces and layering　3

 1.2　Communication sources　5

1.2.1　Source coding　6

 1.3　Communication channels　7

1.3.1　Channel encoding (modulation)　10

1.3.2　Error correction　11

1.4　Digital interface　12

1.4.1　Network aspects of the digital interface　12

 1.5　Supplementary reading　14

2　Coding for discrete sources　16

 2.1　Introduction　16

 2.2　Fixed-length codes for discrete sources　18

 2.3　Variable-length codes for discrete sources　19

2.3.1　Unique decodability　20

2.3.2　Prefix-free codes for discrete sources　21

2.3.3　The Kraft inequality for prefix-free codes　23

 2.4　Probability models for discrete sources　26

2.4.1　Discrete memoryless sources　26

 2.5　Minimum L for prefix-free codes　27

2.5.1　Lagrange multiplier solution for the minimum L　28

2.5.2　Entropy bounds on L　29

2.5.3　Huffman’s algorithm for optimal source codes　31

 2.6　Entropy and fixed-to-variable-length codes　35

2.6.1　Fixed-to-variable-length codes　37

 2.7　The AEP and the source coding theorems　38

2.7.1　The weak law of large numbers　39

2.7.2　The asymptotic equipartition property　40

2.7.3　Source coding theorems　43

2.7.4　The entropy bound for general classes of codes　44

 2.8　Markov sources　46

2.8.1　Coding for Markov sources　48

2.8.2　Conditional entropy　48

 2.9　Lempel-Ziv universal data compression　51

2.9.1　The LZ77 algorithm　51

2.9.2　Why LZ77 works　53

2.9.3　Discussion　54

 2.10　Summary of discrete source coding　55

 2.11　Exercises　56

3　Quantization　67

 3.1　Introduction to quantization　67

 3.2　Scalar quantization　68

3.2.1　Choice of intervals for given representation points　69

3.2.2　Choice of representation points for given intervals　69

3.2.3　The Lloyd-Max algorithm　70

 3.3　Vector quantization　72

 3.4　Entropy-coded quantization　73

 3.5　High-rate entropy-coded quantization　75

 3.6　Differential entropy　76

 3.7　Performance of uniform high-rate scalar quantizers　78

 3.8　High-rate two-dimensional quantizers　81

 3.9　Summary of quantization　84

 3.10　Appendixes　85

3.10.1　Nonuniform scalar quantizers　85

3.10.2　Nonuniform 2D quantizers　87

 3.11　Exercises　88

4　Source and channel waveforms　93

 4.1　Introduction　93

 4.1.1　Analog sources　93

 4.1.2　Communication channels　95

 4.2　Fourier series　96

4.2.1　Finite-energy waveforms　98

 4.3　L2 functions and Lebesgue integration over[-T/2,T/2]　101

4.3.1　Lebesgue measure for a union of intervals　102

4.3.2　Measure for more general sets　104

4.3.3　Measurable functions and integration over [-T/2,T/2]　106

4.3.4　Measurability of functions defined by other functions　108

4.3.5　L1 and L2 functions over [-T/2,T/2]　108

 4.4　Fourier series for L2 waveforms　109

4.4.1　The T-spaced truncated sinusoid expansion　111

 4.5　Fourier transforms and L2 waveforms　114

4.5.1　Measure and integration over R　116

4.5.2　Fourier transforms of L2 functions　118

 4.6　The DTFT and the sampling theorem　120

4.6.1　The discrete-time Fourier transform　121

4.6.2　The sampling theorem　122

4.6.3　Source coding using sampled waveforms　124

4.6.4　The sampling theorem for[Δ-W,Δ+W]　125

 4.7　Aliasing and the sinc-weighted sinusoid expansion　126

4.7.1　The T-spaced sinc-weighted sinusoid expansion　127

4.7.2　Degrees of freedom　128

4.7.3　Aliasing — a time-domain approach　129

4.7.4　Aliasing — a frequency-domain approach　130

 4.8　Summary　132

 4.9　Appendix: Supplementary material and proofs　133

4.9.1　Countable sets　133

4.9.2　Finite unions of intervals over [-T/2,T/2]　135

4.9.3　Countable unions and outer measure over [-T/2,T/2]　136

4.9.4　Arbitrary measurable sets over[-T/2,T/2]　139

 4.10　Exercises　143

5　Vector spaces and signal space　153

 5.1　Axioms and basic properties of vector spaces　154

5.1.1　Finite-dimensional vector spaces　156

 5.2　Inner product spaces　158

5.2.1　The inner product spaces Rn and Cn　158

5.2.2　One-dimensional projections　159

5.2.3　The inner product space of L2 functions　161

5.2.4　Subspaces of inner product spaces　162

 5.3　Orthonormal bases and the projection theorem　163

5.3.1　Finite-dimensional projections　164

5.3.2　Corollaries of the projection theorem　165

5.3.3　Gram–Schmidt orthonormalization　166

5.3.4　Orthonormal expansions in L2　167

 5.4　Summary　169

 5.5　Appendix: Supplementary material and proofs　170

5.5.1　The Plancherel theorem　170

5.5.2　The sampling and aliasing theorems　174

5.5.3　Prolate spheroidal waveforms　176

 5.6　Exercises　177

6　Channels, modulation, and demodulation　181

 6.1　Introduction　181

 6.2　Pulse amplitude modulation (PAM)　184

6.2.1　Signal constellations　184

6.2.2　Channel imperfections: a preliminary view　185

6.2.3　Choice of the modulation pulse　187

6.2.4　PAM demodulation　189

 6.3　The Nyquist criterion　190

6.3.1　Band-edge symmetry　191

6.3.2　Choosing {p(t-kT);k∈Z} an orthonormal set　193

6.3.3　Relation between PAM and analog source coding　194

 6.4　Modulation: baseband to passband and back　195

6.4.1　Double-sideband amplitude modulation　195

 6.5　Quadrature amplitude modulation (QAM)　196

6.5.1　QAM signal set　198

6.5.2　QAM baseband modulation and demodulation　199

6.5.3　QAM: baseband to passband and back　200

6.5.4　Implementation of QAM　201

 6.6　Signal space and degrees of freedom　203

6.6.1　Distance and orthogonality　204

 6.7　Carrier and phase recovery in QAM systems　206

6.7.1　Tracking phase in the presence of noise　207

6.7.2　Large phase errors　208

 6.8　Summary of modulation and demodulation　208

 6.9　Exercises　209

7　Random processes and noise　216

 7.1　Introduction　216

 7.2　Random processes　217

7.2.1　Examples of random processes　218

7.2.2　The mean and covariance of a random process　220

7.2.3　Additive noise channels　221

 7.3　Gaussian random variables, vectors, and processes　221

7.3.1　The covariance matrix of a jointly Gaussianrandom vector　224

7.3.2　The probability density of a jointly Gaussianrandom vector　224

7.3.3　Special case of a 2D zero-mean Gaussian random vector　227

7.3.4　Z=AW, where A is orthogonal　228

7.3.5　Probability density for Gaussian vectors in terms ofprincipal axes　228

7.3.6　Fourier transforms for joint densities　230

 7.4　Linear functionals and filters for random processes　231

7.4.1　Gaussian processes defined over orthonormalexpansions　232

7.4.2　Linear filtering of Gaussian processes　233

7.4.3　Covariance for linear functionals and filters　234

 7.5　Stationarity and related concepts　235

7.5.1　Wide-sense stationary (WSS) random processes　236

7.5.2　Effectively stationary and effectively WSSrandom processes　238

7.5.3　Linear functionals for effectively WSS random processes　239

7.5.4　Linear filters for effectively WSS random processes　239

 7.6　Stationarity in the frequency domain　242

 7.7　White Gaussian noise　244

7.7.1　The sinc expansion as an approximation to WGN　246

7.7.2　Poisson process noise　247

 7.8　Adding noise to modulated communication　248

7.8.1　Complex Gaussian random variables and vectors　250

 7.9　Signal-to-noise ratio　251

 7.10　Summary of random processes　254

 7.11　Appendix: Supplementary topics　255

7.11.1　Properties of covariance matrices　255

7.11.2　The Fourier series expansion of a truncated random process　257

7.11.3　Uncorrelated coefficients in a Fourier series　259

7.11.4　The Karhunen–Loeve expansion　262

 7.12　Exercises　263

8　Detection, coding, and decoding　268

 8.1　Introduction　268

 8.2　Binary detection　271

 8.3　Binary signals in white Gaussian noise　273

8.3.1　Detection for PAM antipodal signals　273

8.3.2　Detection for binary nonantipodal signals　275

8.3.3　Detection for binary real vectors in WGN　276

8.3.4　Detection for binary complex vectors in WGN　279

8.3.5　Detection of binary antipodal waveforms in WGN　281

 8.4　M-ary detection and sequence detection　285

8.4.1　M-ary detection　285

8.4.2　Successive transmissions of QAM signals in WGN　286

8.4.3　Detection with arbitrary modulation schemes　289

 8.5　Orthogonal signal sets and simple channel coding　292

8.5.1　Simplex signal sets　293

8.5.2　Biorthogonal signal sets　294

8.5.3　Error probability for orthogonal signal sets　294

 8.6　Block coding　298

8.6.1　Binary orthogonal codes and Hadamard matrices　298

8.6.2　Reed–Muller codes　300

 8.7　Noisy-channel coding theorem　302

8.7.1　Discrete memoryless channels　303

8.7.2　Capacity　304

8.7.3　Converse to the noisy-channel coding theorem　306

8.7.4　Noisy-channel coding theorem, forward part　307

8.7.5　The noisy-channel coding theorem for WGN　311

8.8　Convolutional codes　312

8.8.1　Decoding of convolutional codes　314

8.8.2　The Viterbi algorithm　315

 8.9　Summary of detection, coding, and decoding　317

 8.10　Appendix: Neyman–Pearson threshold tests　317

 8.11　Exercises　322

9　Wireless digital communication　330

 9.1　Introduction　330

 9.2　Physical modeling for wireless channels　334

9.2.1　Free-space, fixed transmitting and receiving antennas　334

9.2.2　Free-space, moving antenna　337

9.2.3　Moving antenna, reflecting wall　337

9.2.4　Reflection from a ground plane　340

9.2.5　Shadowing　340

9.2.6　Moving antenna, multiple reflectors　341

 9.3　Input/output models of wireless channels　341

9.3.1　The system function and impulse response for LTV systems　343

9.3.2　Doppler spread and coherence time　345

9.3.3　Delay spread and coherence frequency　348

 9.4　Baseband system functions and impulse responses　350

9.4.1　A discrete-time baseband model　353

 9.5　Statistical channel models　355

9.5.1　Passband and baseband noise　358

 9.6　Data detection　359

9.6.1　Binary detection in flat Rayleigh fading　360

9.6.2　Noncoherent detection with known channel magnitude　363

9.6.3　Noncoherent detection in flat Rician fading　365

 9.7　Channel measurement　367　

9.7.1　The use of probing signals to estimate the channel　368

9.7.2　Rake receivers　373

 9.8　Diversity　376

 9.9　CDMA: the IS95 standard　379

9.9.1　Voice compression　380

9.9.2　Channel coding and decoding　381

9.9.3　Viterbi decoding for fading channels　382

9.9.4　Modulation and demodulation　383

9.9.5　Multiaccess interference in IS95　386

 9.10　Summary of wireless communication　388

 9.11　Appendix: Error probability for noncoherent detection　390

 9.12　Exercises　391

References　398

Index　400