麻省理工加拉格尔数字通信原理香农信息科学经典

本书是靠前信息领域泰斗、5G通信中的LDPC码技术提出者罗伯特·加拉格尔院士的经典之作，是加拉格尔教授在美国麻省理工学院50余年教学研究的结品，至今仍是麻省理工学院的研究生投课教材。加拉格尔院士的教投方法展示了其大师级的济晰条理和深刻洞察力，使读者能直观理解模型对解决实际问题的重要性。书中不仅讲述了信源编码、信道传输和信号检测的原理，更是讲清了这些通信原理背后的统一的数学结构。本书是深入理解数字通信原理的推荐阅读书籍，既可作为通信类专业高年级本科生和研究生教材，又可供工程技术人员参考。

Preface
Acknowledgements
1 Introduction to digital communication
1.1 Standardized interfaces and layering
1.2 Communication sources
1.2.1 Source coding
1.3 Communication channels
1.3.1 Channel encoding (modulation)
1.3.2 Error correction
1.4 Digital interface
1.4.1 Network aspects of the digital interface
1.5 Supplementary reading
2 Coding for discrete sources
2.1 Introduction
2.2 Fixed-length codes for discrete sources
2.3 Variable-length codes for discrete sources
2.3.1 Unique decodability
2.3.2 Prefix-free codes for discrete sources
2.3.3 The Kraft inequality for prefix-free codes
2.4 Probability models for discrete sources
2.4.1 Discrete memoryless sources
2.5 Minimum L for prefix-free codes
2.5.1 Lagrange multiplier solution for the minimum L
2.5.2 Entropy bounds on L
2.5.3 Hufman's algorithm for optimal source codes
2.6 Entropy and fixed-to-variable-length codes
2.6.1 Fixed-to-variable-length codes
2.7 The AEP and the source coding theorems
2.7.1 The weak law of large numbers
2.7.2 The asymptotic equipartition property
2.7.3 Source coding theorems
2.7.4 The entropy bound for general classes of codes
2.8 Markov sources
2.8.1 Coding for Markov sources
2.8.2 Conditional entropy
2.9 Lempel-Ziv universal data compression
2.9.1 The LZ77 algorithm
2.9.2 Why LZ77 works
2.9.3 Discussion
2.10 Summary of discrete source coding
2.11 Exercises
3 Quantization
3.1 Introduction to quantization
3.2 Scalar quantization
3.2.1 Choice of intervals for given representation points
3.2.2 Choice of representation points for given intervals
3.2.3 The Lloyd-Max algorithm
3.3 Vector quantization
3.4 Entropy-coded quantization
3.5 High-rate entropy-coded quantization
3.6 Differential entropy
3.7 Performance of uniform high-rate scalar quantizers
3.8 High-rate two-dimensional quantizers
3.9 Summary of quantization
3.10 Appendixes
3.10.1 Nonuniform scalar quantizers
3.10.2 Nonuniform 2D quantizers
3.11 Exercises
4 Source and channel waveforms
4.1 Introduction
4.1.1 Analog sources
4.1.2 Communication channels
4.2 Fourier series
4.2.1 Finite-energy waveforms
4.3 L2 functions and Lebesgue integration over [-T/2, T/2]
4.3.1 Lebesgue measure for a union of intervals
4.3.2 Measure for more general sets
4.3.3 Measurable functions and integration over [-T/2, T/2)
4.3.4 Measurability of functions defined by other functions
4.3.5 L1 and L2 functions over [-T/2, T/2]
4.4 Fourier series for L2 waveforms
4.4.1 The T-spaced truncated sinusoid expansion
4.5 Fourier transforms and L2 waveforms
4.5.1 Measure and integration over R
4.5.2 Fourier transforms of L2 functions
4.6 The DTFT and the sampling theorem
4.6.1 The discrete-time Fourier transform
4.6.2 The sampling theorem
4.6.3 Source coding using sampled waveforms
4.6.4 The sampling theorem for [△-W, △+W]
4.7 Aliasing and the sinc-weighted sinusoid expansion
4.7.1 The T-spaced sinc-weighted sinusoid expansion
4.7.2 Degrees of freedom
4.7.3 Aliasing-a time-domain approach
4.7.4 Aliasing-a frequency-domain approach
4.8 Summary
4.9 Appendix: Supplementary material and proofs
4.9.1 Countable sets
4.9.2 Finite unions of intervals over [-T/2, T/2]
4.9.3 Countable unions and outer measure over [-T/2, T/2]
4.9.4 Arbitrary measurable sets over [-T/2, 7/2]
4.10 Exercises
5 Vector spaces and signal space
5.1 Axioms and basic properties of vector spaces
5.1.1 Finite-dimensional vector spaces
5.2 Inner product spaces
5.2.1 The inner product spaces Rn and Cn
5.2.2 One-dimensional projections
5.2.3 The inner product space of L2 functions
5.2.4

罗伯特·加拉格尔（Robert G. Gallager）教授是美国国家科学院与国家工程院的两院院士。他曾担任靠前信息论学会的主席，他于1983年获得信息论的很高奖——香农奖（相当于信息论领域的诺贝尔奖），1990年获得靠前电气电子工程师学会很高荣誉奖章（相当于电子工程领域的诺贝尔奖），2003年获得马可尼奖（相当于通信领域的诺贝尔奖），2020年获得日本靠前奖（相当于整个应用科学领域的诺贝尔奖）。加拉格教授于1960年在美国麻省理工学院获得博士学位后留校任教至今，他1960年博士论文中提出的“低密度奇偶校验码”（LDPC）是目前所有5G设备都必用的信道编码。