- Title
- Multi-edge type density evolution: analysis, code optimization and applications to raptor code design
- Creator
- Jayasooriya, Jayasooriya Arachchige Sachini Nisansala
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2017
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- The field of error correcting codes has been revolutionized by the introduction of graph-based codes, such as low-density parity-check (LDPC) codes and turbo codes. These codes exhibit dramatic performance improvement with significantly lower decoding complexity over previously developed coding schemes such as Hamming codes and BCH codes, which are overwhelmingly algebraic. Since then, understanding the performance of these codes, and using this understanding to design capacity-approaching codes, is one of the utmost subjects of interest among coding specialists. This thesis adds to this field, developing analytical tools and supporting theory for designing capacity-approaching codes using the concept of multi-edge parametrization. The benefit of multi-edge parametrization is greater flexibility in code structure, which enables the specification of graphs not possible in the standard LDPC framework. The first two parts of this thesis are dedicated to developing analytical tools for graph-based codes. In the first part, we consider the design of LDPC and multi-edge type LDPC (MET-LDPC) codes, and propose an algorithm to jointly optimize the node degree distribution and the code structure of a code ensemble for given values of the maximum number of edge-types and maximum node degrees. This joint optimization is particularly important for MET-LDPC codes, because it systematically finds good MET-LDPC code structures as opposed to trial and error or intuition in conventional approaches. In the second part, we consider density evolution (DE) for LDPC and MET-LDPC codes over the binary input additive white Gaussian noise (BI-AWGN) channel. We analyze several single-parameter Gaussian approximations for DE and show that the assumption of symmetric Gaussian distribution for the DE messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Based on these observations, we introduce a new DE approximation algorithm for LDPC and MET-LDPC codes, which is a combination of full density evolution (full-DE) and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after DE messages closely follow a symmetric Gaussian distribution. The proposed method improves the accuracy of the code threshold estimation. In addition, it significantly reduces the computational time of evaluating the code threshold compared with full-DE, thereby making it more suitable for code design. In the final part of this thesis, we employ the analytical tools designed in the first part to the problem of code design for rateless coding, in particular for Raptor codes. The main focus of this part is to analyze and design Raptor codes over a BI-AWGN channel using a multi-edge framework. We first propose a new representation of Raptor codes as MET-LDPC codes and then apply analytical tools developed in the first part of this thesis to design them. The benefit of multi-edge representation of Raptor codes is that it enables us to perform a comprehensive analysis of the asymptotic performance of Raptor codes using MET density evolution. We consider two decoding schemes based on the belief propagation (BP) decoding, namely tandem decoding and joint decoding in the multi-edge framework, and analyze the convergence behavior of the BP decoder. Finally, we extend the analysis to design higher-order modulated Raptor codes using the multi-edge framework.
- Subject
- LDPC codes; MET-LDPC codes; density evolution; code optimzation; raptor codes; belief-propagation; Gaussian approximation; modulation
- Identifier
- http://hdl.handle.net/1959.13/1343092
- Identifier
- uon:29091
- Rights
- Copyright 2017 Jayasooriya Arachchige Sachini Nisansala Jayasooriya
- Language
- eng
- Full Text
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