Construction, Decoding and Application of Low-density Parity-check Codes PDF Download
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Languages : en
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In this doctoral dissertation, a construction of binary and nonbinary low-density parity-check (LDPC) codes with quasi-cyclic (QC) structures is presented. First, a general construction of RC-constrained arrays of circulant permutation matrices is introduced, then a specific construction method based on additive subgroups of finite fields is presented. Array masking is also proposed to improve the waterfall-region performance of the QC-LDPC codes, where an algorithm to construct irregular masking matrices is introduced for low error floors. Simulations show that all the above-constructed codes perform well on AWGN channels. Also presented in this dissertation is an LDPC-based error control scheme in a multicast network where a well-known network coding is used. With this scheme, error performance of the system can be improved and equal error protection can be achieved. Finally, an iterative decoding with backtracking is presented. This decoding algorithm greatly lowers the error floors of many regular and irregular LDPC codes of different constructions, and in many cases can push the error floors down to a level limited by the codes' minimum distances. Performance analysis and error floor estimation for the proposed algorithm are also performed.
Author:
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Languages : en
Pages :
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Book Description
In this doctoral dissertation, a construction of binary and nonbinary low-density parity-check (LDPC) codes with quasi-cyclic (QC) structures is presented. First, a general construction of RC-constrained arrays of circulant permutation matrices is introduced, then a specific construction method based on additive subgroups of finite fields is presented. Array masking is also proposed to improve the waterfall-region performance of the QC-LDPC codes, where an algorithm to construct irregular masking matrices is introduced for low error floors. Simulations show that all the above-constructed codes perform well on AWGN channels. Also presented in this dissertation is an LDPC-based error control scheme in a multicast network where a well-known network coding is used. With this scheme, error performance of the system can be improved and equal error protection can be achieved. Finally, an iterative decoding with backtracking is presented. This decoding algorithm greatly lowers the error floors of many regular and irregular LDPC codes of different constructions, and in many cases can push the error floors down to a level limited by the codes' minimum distances. Performance analysis and error floor estimation for the proposed algorithm are also performed.
Author: Xudong Ma
Publisher:
ISBN: 9780494433096
Category :
Languages : en
Pages : 125
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Book Description
This thesis focuses on designing Low-Density Parity-Check (LDPC) codes for forward-error-correction. The target application is real-time multimedia communications over packet networks. We investigate two code design issues, which are important in the target application scenarios, designing LDPC codes with low decoding latency, and constructing capacity-approaching LDPC codes with very low error probabilities. On designing LDPC codes with low decoding latency, we present a framework for optimizing the code parameters so that the decoding can be fulfilled after only a small number of iterative decoding iterations. The brute force approach for such optimization is numerical intractable, because it involves a difficult discrete optimization programming. In this thesis, we show an asymptotic approximation to the number of decoding iterations. Based on this asymptotic approximation, we propose an approximate optimization framework for finding near-optimal code parameters, so that the number of decoding iterations is minimized. The approximate optimization approach is numerically tractable. Numerical results confirm that the proposed optimization approach has excellent numerical properties, and codes with excellent performance in terms of number of decoding iterations can be obtained. Our results show that the numbers of decoding iterations of the codes by the proposed design approach can be as small as one-fifth of the numbers of decoding iterations of some previously well-known codes. The numerical results also show that the proposed asymptotic approximation is generally tight for even non-extremely limiting cases. On constructing capacity-approaching LDPC codes with very low error probabilities, we propose a new LDPC code construction scheme based on 2-lifts. Based on stopping set distribution analysis, we propose design criteria for the resulting codes to have very low error floors. High error floors are the main problems of previously constructed capacity-approaching codes, which prevent them from achieving very low error probabilities. Numerical results confirm that codes with very low error floors can be obtained by the proposed code construction scheme and the design criteria. Compared with the codes by the previous standard construction schemes, which have error floors at the levels of 10−3 to 10−4, the codes by the proposed approach do not have observable error floors at the levels higher than 10−7. The error floors of the codes by the proposed approach are also significantly lower compared with the codes by the previous approaches to constructing codes with low error floors.
Author: Keqin Feng
Publisher: Birkhäuser
ISBN: 3034878656
Category : Computers
Languages : en
Pages : 403
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Book Description
It has long been recognized that there are fascinating connections between cod ing theory, cryptology, and combinatorics. Therefore it seemed desirable to us to organize a conference that brings together experts from these three areas for a fruitful exchange of ideas. We decided on a venue in the Huang Shan (Yellow Mountain) region, one of the most scenic areas of China, so as to provide the additional inducement of an attractive location. The conference was planned for June 2003 with the official title Workshop on Coding, Cryptography and Combi natorics (CCC 2003). Those who are familiar with events in East Asia in the first half of 2003 can guess what happened in the end, namely the conference had to be cancelled in the interest of the health of the participants. The SARS epidemic posed too serious a threat. At the time of the cancellation, the organization of the conference was at an advanced stage: all invited speakers had been selected and all abstracts of contributed talks had been screened by the program committee. Thus, it was de cided to call on all invited speakers and presenters of accepted contributed talks to submit their manuscripts for publication in the present volume. Altogether, 39 submissions were received and subjected to another round of refereeing. After care ful scrutiny, 28 papers were accepted for publication.
Author: Gabofetswe Alafang Malema
Publisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 160
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Book Description
The main contribution of this thesis is the development of LDPC code construction methods for some classes of structured LDPC codes and techniques for reducing decoding time. Two main methods for constructing structured codes are introduced. In the first method, column-weight two LDPC codes are derived from distance graphs. A wide range of girths, rates and lengths are obtained compared to existing methods. The performance and implementation complexity of obtained codes depends on the structure of their corresponding distance graphs. In the second method, a search algorithm based on bit-filing and progressive-edge growth algorithms is introduced for constructing quasi-cyclic LDPC codes. The algorithm can be used to form a distance or Tanner graph of a code. This method could also obtain codes over a wide range of parameters. The outcome of this study is a simple, programmable and high throughput decoder architecture based on matrix permutation and space restriction techniques.
Author: Vikram Arkalgud Chandrasetty
Publisher: Academic Press
ISBN: 0128112565
Category : Technology & Engineering
Languages : en
Pages : 192
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Book Description
This book takes a practical hands-on approach to developing low complexity algorithms and transforming them into working hardware. It follows a complete design approach – from algorithms to hardware architectures - and addresses some of the challenges associated with their design, providing insight into implementing innovative architectures based on low complexity algorithms.The reader will learn: Modern techniques to design, model and analyze low complexity LDPC algorithms as well as their hardware implementation How to reduce computational complexity and power consumption using computer aided design techniques All aspects of the design spectrum from algorithms to hardware implementation and performance trade-offs Provides extensive treatment of LDPC decoding algorithms and hardware implementations Gives a systematic guidance, giving a basic understanding of LDPC codes and decoding algorithms and providing practical skills in implementing efficient LDPC decoders in hardware Companion website containing C-Programs and MATLAB models for simulating the algorithms, and Verilog HDL codes for hardware modeling and synthesis
Author: Martin Tomlinson
Publisher: Springer
ISBN: 3319511033
Category : Technology & Engineering
Languages : en
Pages : 527
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Book Description
This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th ese codes. Part IV deals with decoders designed to realize optimum performance. Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking. This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field. This book is open access under a CC BY 4.0 license.
Author: Abhiram Prabhakar
Publisher:
ISBN:
Category :
Languages : en
Pages : 136
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Author: Lei Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 340
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Author: Cornelius Thomas Healy
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: William Ryan
Publisher: Cambridge University Press
ISBN: 1139483013
Category : Technology & Engineering
Languages : en
Pages : 709
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Book Description
Channel coding lies at the heart of digital communication and data storage, and this detailed introduction describes the core theory as well as decoding algorithms, implementation details, and performance analyses. In this book, Professors Ryan and Lin provide clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes. They also present detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, and product codes, providing a one-stop resource for both classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design. 250 varied and stimulating end-of-chapter problems are also included to test and enhance learning, making this an essential resource for students and practitioners alike.
