信道编码：经典和现代方法

　　The title ofthis book， Channel Codes： Classical and Modern，was selected to reflect the fact that this book does indeed cover both classical and modern channel codes，It includes BCH codes， Reed-Solomon codes， convolutional codes， finite-geometry codes， turbo codes， low-density parity-check （LDPC） codes， and product codes.However， the title has a second interpretation. While the majority of this book is on LDPC codes， these can rightly be considered to be both classical （having been first discovered in 1961） and modern （having been rediscovered circa 1996）. This is exemplified by David Forney's statement at his August 1999 IMA talk on codes on graphs，lt feels like the early days. As another example of the classical/modern duality， finite-geometry codes were studied in the 1960s and thus are classical codes. However， they were rediscovered by Shu Lin et a/. circa 2000 as a class of LDPC codes with very appealing features and are thus modern codes as well. The classical and modern incarnations of flnite-geometry codes are distinguished by their decoders： one-step hard-decision decoding （classical） versus iterative soft-decision decoding （modern）.

　　威廉·瑞安（William E. Ryan）教授是通信理论和信道编码领域专家，是国际电气与电子工程师协会的杰出会士（IEEE Fellow）。他本科毕业于美国的凯斯西储大学，博士毕业于弗吉尼亚大学，后在新墨西哥州立大学和亚利桑那大学任教近20年，他目前是泽塔联合公司（Zeta Associates， Inc.）的高级合伙人。他的研究兴趣主要在编码和信号处理及其在数据存储和无线数据通信中的应用，发表过100多篇学术论文，并曾担任IEEE Transactions on Communications的副主编。林舒（Shu Lin）教授是世界知名的编码理论专家，曾担任IEEE信息论学会主席。他本科毕业于台湾大学，博士毕业于美国的莱斯大学，后在夏威夷大学檀香山分校、得克萨斯农工大学、加州大学戴维斯分校等大学任教50余年。他是国际电气与电子工程师协会的终生杰出会士（IEEE Life Fellow），获得过洪堡研究奖（1996）、 IEEE第三千年奖章（2000）、NASA杰出公共成就奖章（2014）、马奎斯世界名人录终身成就奖（2019）和IEEE研究生教育奖（2020）。他在编码理论领域撰写过多部著作，“香农信息科学经典”系列里已出版了《差错控制编码 第2版》《信道编码：经典和现代方法》和《低密度奇偶校验码：设计、构造与统一框架》。

Preface
1 Coding and Capacity
1．1 Digital Data Communication and Storage
1．2 Channel-Coding Overview
1．3 Channel-Code Archetype： The (7，4) Hamming Code
1．4 Design Criteria and Performance Measures
1．5 Channel-Capacity Formulas for Common Channel Models
1．5．1 Capacity for Binary-Input Memoryless Channels
1．5．2 Coding Limits for M-ary-Input Memoryless Channels
1．5．3 Coding Limits for Channels with Memory
Problems
References
2 Finite Fields， Vector Spaces， Finite Geometries， and Graphs
2．1 Sets and Binary Operations
2．2 Groups
2．2．1 Basic Concepts of Groups
2．2．2 Finite Groups
2．2．3 Subgroups and Cosets
2．3 Fields
2．3．1 Definitions and Basic Concepts
2．3．2 Finite Fields
2．4 Vector Spaces
2．4．1 Basic Definitions and Properties
2．4．2 Linear Independence and Dimension
2．4．3 Finite Vector Spaces over Finite Fields
2．4．4 Inner Products and Dual Spaces
2．5 Polynomials over Finite Fields
2．6 Construction and Properties of Galois Fields
2．6．1 Construction of Galois Fields
2．6．2 Some Fundamental Properties of Finite Fields
2．6．3 Additive and Cyclic Subgroups
2．7 Finite Geometries
2．7．1 Euclidean Geometries
2．7．2 Projective Geometries
2．8 Graphs
2．8．1 Basic Concepts
2．8．2 Paths and Cycles
2．8．3 Bipartite Graphs
Problems
References
Appendix A
3 Linear Block Codes
3．1 Introduction to Linear Block Codes
3．1．1 Generator and Parity-Check Matrices
3．1．2 Error Detection with Linear Block Codes
3．1．3 Weight Distribution and Minimum Hamming Distance of a Linear Block Code
3．1．4 Decoding of Linear Block Codes
3．2 Cyclic Codes
3．3 BCH Codes
3．3．1 Code Construction
3．3．2 Decoding
3．4 Nonbinary Linear Block Codes and Reed-Solomon Codes
3．5 Product， Interleaved， and Concatenated Codes
3．5．1 Product Codes
3．5．2 Interleaved Codes
3．5．3 Concatenated Codes
3．6 Quasi-Cyclic Codes
3．7 Repetition and Single-Parity-Check Codes
Problems
References
4 Convolutional Codes
4．1 The Convolutional Code Archetype
4．2 Algebraic Description of Convolutional Codes
4．3 Encoder Realizations and Classifications
4．3．1 Choice of Encoder Class
4．3．2 Catastrophic Encoders
4．3．3 Minimal Encoders
4．3．4 Design of Convolutional Codes
4．4 Alternative Convolutional Code Representations
4．4．1 Convolutional Codes as Semi-Infinite Linear Codes
4．4．2 Graphical Representations for Convolutional Code Encoders
……
5 Low-Density Parity-Check Codes
6 Computer-Based Design of LDPC Codes
7 Turbo Codes
8 Ensemble Enumerators for Turbo and LDPC Codes
9 Ensemble Decoding Thresholds for LDPC and Turbo Codes
10 Finite-Geometry LDPC Codes
11 Constructions of LDPC Codes Based on Finite Fields
12 LDPC Codes Based on Combinatorial Designs， Graphs， and Superposition
13 LDPC Codes for Binary Erasure Channels
14 Nonbinary LDPC Codes
15 LDPC Code Applications and Advanced Topics