1. Introduction.- 1.1 Trellis Representation of Codes.- 1.2 Organization of the Book.- 2. Linear Block Codes.- 2.1 Generation of Linear Block Codes.- 2.2 Coset Partition of a Linear Block Code.- 2.3 The minimum Distance and Weight Distribution of A Linear Block Code.- 2.4 Decoding.- 2.5 Reed-Muller Codes.- 3. Trellis Representation of Linear Block Codes.- 3.1 Trellis Representation of Codes.- 3.2 Bit-Level Trellises for Binary Linear Block Codes.- 3.3 Trellis Oriented Generator Matrix.- 3.4 State Space Formulation.- 3.5 State Transition and Output.- 3.6 Time-Varying structure.- 3.7 Structural Properties.- 4. State Labeling, Trellis Construction Procedures and Trellis Symmetry.- 4.1 State Labeling by the State Defining Information Set.- 4.2 State Labeling by Parity-check Matrix.- 4.3 Structural Symmetry.- 5. Trellis Complexity.- 5.1 State Complexity.- 5.2 Minimal Trellises.- 5.3 Branch Complexity.- 5.4 Trellis Structure of Cyclic Codes.- 5.5 Trellises for Nonbinary Linear Block Codes.- 6. Trellis Sectionalization.- 6.1 Sectionalization of a Code Trellis.- 6.2 Branch Complexity and State Connectivity.- 6.3 A Procedure for Constructing a Minimal L-Section Trellis.- 6.4 Parallel Structure.- 7. Parallel Decomposition and Low-weight Subtrellises.- 7.1 Parallel Decomposition of a Trellis Diagram.- 7.2 Low-Weight Subtrellis Diagrams.- 7.3 Structure Analysis and Construction of Low-Weight Subtrellises.- 8. Methods for Constructing Codes and Trellis.- 8.1 Squaring Construction of Codes.- 8.2 Trellises for Codes by Squaring Construction.- 8.3 Shannon and Cartesian Products.- 8.4 Multilevel Concatenated Codes and Their Trellis Construction.- 9. Trellises for Convolutional Codes and their Related Linear Block Codes.- 9.1 Description of Convolutional Codes.- 9.2 Trellis Structure forConvolutional Codes.- 9.3 Punctured Convolutional Codes.- 9.4 Termination of Convolutional Codes.- 9.5 RM Codes Viewed as Terminated Convolutional Codes.- 10. The Viterbi and Differential Trellis Decoding Algorithms.- 10.1 The Viterbi Decoding Algorithm.- 10.2 Optimum Sectionalization of a Code Trellis: Lafourcade-Vardy Algorithm.- 10.3 Some Design Issues for IC Implementation of Viterbi Decoders for Linear Block Codes.- 10.4 Differential Trellis Decoding.- 11. A Recursive Maximum Likelihood Decoding.- 11.1 Basic Concepts.- 11.2 The General Algorithm.- 11.3 Direct Methods for Constructing Composite Branch Metric Tables.- 11.4 The CombCBT Procedure.- 11.5 CombCBT-V(x, y; z) Procedure.- 11.6 RMLD-(I,V) and RMLD-(G,V) Algorithms.- 11.7 CombCBT-U(x, y; z) Procedure.- 11.8 RMLD-(G,U) Algorithm.- 11.9 Comparisons.- 12. An Iterative Decoding Algorithm for Linear Block Codes Based on a Low-weight Trellis Search.- 12.1 General Concepts.- 12.2 Optimality Conditions.- 12.3 Generation of Candidate Codewords and Test Error Patterns.- 12.4 An Iterative Decoding Algorithm.- 12.5 Computational Complexity.- 12.6 Error Performance.- 12.7 Shortcomings.- 13. The Map and Related Decoding Algorithms.- 13.1 The MAP Decoding Algorithm.- 13.2 The SOVA Decoding Algorithm.- 13.3 Bit Error Probability of MLD.- A-A Trellis Construction Procedure.- A.1 A Brief Review of the Trellis Oriented Generator Matrix for a Binary Linear Block Code.- A.2 State Labeling by the State Defining Information Set and Composite Branch Label.- A.3 Trellis Construction.- A.4 An Efficient Trellis Construction Procedure.- References.
