目錄
PREFACE
1 INTRODUCTION
§1.1 Why You Should Read This Book
§1.2 Communications Problem
§1.3 Coding: Trial and Error
§1.4 Codes and Ensembles
§1.5 MAP and ML Decoding and APP Processing
§1.6 Channel Coding Theorem
§1.7 Linear Codes and Complexity
§1.8 Rate, Probability, Complexity, and Length
§1.9 Tour of Iterative Decoding
§1.10 Notation, Conventions, and Useful Facts
Notes
Problems
References
2 FACTOR GRAPHS . page
§2.1 Distributive Law
§2.2 Graphical Representation ofFactorizations
§2.3 Recursive Determination of Marginals
§2.4 Marginalization via Message Passing
§2.5 Decoding via Message Passing
§2.6 Limitations of Cycle-Free Codes
§2.7 Message Passing on Codes with Cycles
Notes
Problems
References
3 BINARY ERASURE CHANNEL
§3.1 ChannelModel
§3.2 Transmission via Linear Codes
§3.3 Tanner Graphs
§3.4 Low-DensityParity-Check Codes
§3.5 Message-PassingDecoder
§3.6 Two Basic Simplifications
§3.7 Computation Graph and Tree Ensemble
§3.8 Tree Channel and Convergence to Tree Channel
§3.9 Density Evolution
§3.10 Monotonicity
§3.11 Xhreshold
§3.12 Fixed Point Characterization of Threshold
§3.13 Stability
§3.14 EXIT Charts
§3.15 Capacity-Achieving Degree Distributions
§3.16 Gallager's Lower Bound on Density
§3.17 Optimally Sparse Degree Distribution Pairs
§3.18 Degree Distributions with Given Maximum Degree
§3.19 Peeling Decoder and Order of Limits
§3.20 EXIT Function and MAP Performance
§3.21 Maxwell Decoder
§3.22 Exact Finite-Length Analysis
§3.23 Finite-Length Scaling
§3.24 Weight Distribution and Error Floor
Notes
Problems
References
4 BINARY MEMORYLESS SYMMETRIC CHANNELS
§4.1 Basic Definitions and Examples
§4.2 Message-PassingDecoder
§4.3 Two Basic Simplifications
§4.4 Tree Channel and Convergence to Tree Channel
§4.5 Density Evolution
§4.6 Monotonicity
§4.7 Threshold
§4.8 Fixed Point Characterization of Threshold
§4.9 Stability
§4.1 o EXIT Charts
§4.11 Gallager's Lower Bound on Density
§4.12 GEXIT Function and MAP Performance
§4.13 Finite-Length Scaling
§4.14 Error Floor under MAP Decoding
Notes
Problems
References
5 GENERAL CHANNELS
§5.1 Fading Channel
§5.2 Z Channel
§5.3 Channels with Memory
§5.4 Coding for High Spectral Efficiency
§5.5 Multiple-Access Channel
Notes
Problems
References
6 TURBO CODES
§6.1 Convolutional Codes
§6.2 Structure and Encoding
§6.3 Decoding
§6.4 Basic Simplifications
§6.5 Density Evolution
§6.6 Stability Condition
§6.7 EXIT Charts
§6.8 GEXlT Function and MAP Performance
§6.9 Weight Distribution and Error Floor
§6.1 o Variations on the Theme
Notes
Problems
References
7 GENERAL ENSEMBLES
§7.1 Multi-Edge-Type LDPC Code Ensembles
§7.2 Multi-Edge-Type LDPC Codes: Analysis
§7.3 Structured Codes
§7.4 Non-BinaryCodes
§7.5 Low-Density Generator Codes and Rateless Codes
Notes
Problems
References
8 EXPANDER CODES AND FLIPPING ALGORITHM
§8.1 Building Codes from Expanders
§8.2 Flipping Algorithm
§8.3 Bound on Expansion of a Graph
§8.4 Expansion of a Random Graph
Notes
Problems
References
A ENCODING Low-DENSITY PARITY-CHECK CODES
§A.1 Encoding Generic LDPC Codes
§A.2 Greedy Upper Triangulation
§A.3 Linear Encoding Complexity
§A.4 Analysis of Asymptotic Gap
Notes
Problems
References
EFFICIENT IMPLEMENTATION OF DENSITY EVOLUTION
§B.1 Quantization
§B.2 Variable-Node Update via Fourier Transform
§B.3 Check-Node Update via Table Method
§B.4 Check-Node Update via Fourier Method
Notes
Problems
References
C CONCENTRATION INEQUALITIES
§C.1 First and Second Moment Method
§C.2 Bernstein's Inequality
§C.3 Martingales
§C.4 Wormald's Differential Equation Approach
§C.5 Convergence to Poisson Distribution
Notes
Problems
References
D FORMAL POWER SUMS
§D.1 Definition
§D.2 Basic Properties
§D.3 Summation of Subsequences
§D.4 Coefficient Growth of Powers of Polynomials
§D.5 Unimodality
Notes
Problems
References
E CONVEXITY, DEGRADATION, AND STABILITY
AUTHORS
INDEX
[