Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

As the demand for data reliability increases, coding for error control becomes increasingly important in data transmission systems and has become an integral part of almost all data communication system designs. In recent years, various trellis-based soft-decoding algorithms for linear block codes have been devised. New ideas developed in the study of trellis structure of block codes can be used for improving decoding and analyzing the trellis complexity of convolutional codes. These recent developments provide practicing communication engineers with more choices when designing error control systems.
Trellises and Trellis-based Decoding Algorithms for Linear Block Codes combines trellises and trellis-based decoding algorithms for linear codes together in a simple and unified form. The approach is to explain the material in an easily understood manner with minimal mathematical rigor.
Trellises and Trellis-based Decoding Algorithms for Linear Block Codes is intended for practicing communication engineers who want to have a fast grasp and understanding of the subject. Only material considered essential and useful for practical applications is included. This book can also be used as a text for advanced courses on the subject.

Contenu

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.