Book contents
- Frontmatter
- Contents
- Preface
- Abbreviations
- 1 Introduction
- 2 Basics
- 3 Erasure Channel Models and Bounds
- 4 Low-Density Parity-Check Codes
- 5 Weight Distribution and Minimum Distance of LDPC Codes
- 6 Iterative and Maximum-Likelihood Decoding of LDPC Codes
- 7 Iterative LDPC Decoder Analysis
- 8 Maximum-Likelihood LDPC Decoder Analysis
- 9 Low-Density Parity-Check Codes: Generalizations
- 10 Polar Codes
- 11 Fountain Codes
- Appendix A Applications of Erasure Codes
- Appendix B Random Matrices over Finite Fields
- Index
- References
7 - Iterative LDPC Decoder Analysis
Published online by Cambridge University Press: aN Invalid Date NaN
Book contents
- Frontmatter
- Contents
- Preface
- Abbreviations
- 1 Introduction
- 2 Basics
- 3 Erasure Channel Models and Bounds
- 4 Low-Density Parity-Check Codes
- 5 Weight Distribution and Minimum Distance of LDPC Codes
- 6 Iterative and Maximum-Likelihood Decoding of LDPC Codes
- 7 Iterative LDPC Decoder Analysis
- 8 Maximum-Likelihood LDPC Decoder Analysis
- 9 Low-Density Parity-Check Codes: Generalizations
- 10 Polar Codes
- 11 Fountain Codes
- Appendix A Applications of Erasure Codes
- Appendix B Random Matrices over Finite Fields
- Index
- References
Summary
Performance analysis for iterative decoders: In Chapter 7, we discuss the behavior of LDPC codes under iterative erasure decoding. When the blocklength goes to infinity, for many LDPC codes, the symbol error probability exhibits a so-called threshold phenomenon that is, there exists a certain channel erasure probability below which error-free communication is possible, while this is not guaranteed above it. We discuss how to compute this threshold for ensembles of LDPC codes on memoryless erasure channels. In the finite-length setting, one may observe a flattening of the symbol error rate curve owing to stopping sets – specific structures in the code’s bipartite graph. Knowing their number and size allows predicting this so-called error floor. Based on our findings, we discuss how to design good LDPC for memoryless erasure channels with extension to channels with memory.
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- Coding for Erasure Channels , pp. 161 - 201Publisher: Cambridge University PressPrint publication year: 2026
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