Decoding Linear Codes Via Optimization and Graph-based Techniques - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Decoding Linear Codes Via Optimization and Graph-based Techniques write by Mohammad H. Taghavi. This book was released on 2008. Decoding Linear Codes Via Optimization and Graph-based Techniques available in PDF, EPUB and Kindle. Low-density parity-check (LDPC) codes have made it possible to communicate at information rates very close to the Shannon capacity by combining sparsity with quasi-randomness, which enables the use of low-complexity iterative message-passing (IMP) decoders. So far, most systematic studies of IMP decoders have focused on evaluating the average performance of random ensembles of LDPC codes with infinite length. However, the statistical nature of IMP algorithms does not seem very suitable for rigorous analysis the decoding of individual finite-length codes. The need for finite-length studies are most critical in applications such as data storage, where the required decoding error rate is too low to be verifiable by simulation. As an alternative to IMP algorithms, linear programming (LP) decoding is based on relaxing the optimal decoding into a linear optimization. The geometric nature of this approach makes it more amenable to deterministic finite-length analysis than IMP decoding. On the other hand, LP decoding is computationally more complex than IMP decoding, due to both the large number of constraints in the relaxed problem, and the inefficiency of using general-purpose LP solvers. In this dissertation, we study several aspects of LP decoding, starting by some steps toward reducing its complexity. We introduce an adaptive implementation of LP decoding, where the relaxed problem is replaced by a sequence of subproblems of much smaller size, resulting in a complexity reduction by orders of magnitude. This is followed by a sparse implementation of an interior-point LP solver which exploits the structure of the decoding problem. We further propose a cutting-plane approach to improve the error-correcting capability of LP decoding. Along the way, several properties are proved for LP decoding and its proposed variations. We continue by investigating the application of an optimization-based approach to decoding linear codes in the presence of intersymbol interference (ISI). By relaxing the optimal detection problem into a linear program, we derive a new graphical representation for the ISI channel, which can be used for combined equalization and decoding by LP or IMP decoders. Finally, in a separate piece of work, we study the effect of nonlinearities on the multiuser capacity of optical fibers.
On Linear Programming Based Decoding of Graph-based Codes
On Linear Programming Based Decoding of Graph-based Codes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Linear Programming Based Decoding of Graph-based Codes write by Idan Goldenberg. This book was released on 2013. On Linear Programming Based Decoding of Graph-based Codes available in PDF, EPUB and Kindle.
Fundamentals of Codes, Graphs, and Iterative Decoding
Fundamentals of Codes, Graphs, and Iterative Decoding - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fundamentals of Codes, Graphs, and Iterative Decoding write by Stephen B. Wicker. This book was released on 2006-04-18. Fundamentals of Codes, Graphs, and Iterative Decoding available in PDF, EPUB and Kindle. Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.
Design Techniques for Graph-based Error-correcting Codes and Their Applications
Design Techniques for Graph-based Error-correcting Codes and Their Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Design Techniques for Graph-based Error-correcting Codes and Their Applications write by Ching Fu Lan. This book was released on 2006. Design Techniques for Graph-based Error-correcting Codes and Their Applications available in PDF, EPUB and Kindle. In Shannon's seminal paper, "A Mathematical Theory of Communication", he defined "Channel Capacity" which predicted the ultimate performance that transmission systems can achieve and suggested that capacity is achievable by error-correcting (channel) coding. The main idea of error-correcting codes is to add redundancy to the information to be transmitted so that the receiver can explore the correlation between transmitted information and redundancy and correct or detect errors caused by channels afterward. The discovery of turbo codes and rediscovery of Low Density Parity Check codes (LDPC) have revived the research in channel coding with novel ideas and techniques on code concatenation, iterative decoding, graph-based construction and design based on density evolution. This dissertation focuses on the design aspect of graph-based channel codes such as LDPC and Irregular Repeat Accumulate (IRA) codes via density evolution, and use the technique (density evolution) to design IRA codes for scalable image/video communication and LDPC codes for distributed source coding, which can be considered as a channel coding problem. The first part of the dissertation includes design and analysis of rate-compatible IRA codes for scalable image transmission systems. This part presents the analysis with density evolution the effect of puncturing applied to IRA codes and the asymptotic analysis of the performance of the systems. In the second part of the dissertation, we consider designing source-optimized IRA codes. The idea is to take advantage of the capability of Unequal Error Protection (UEP) of IRA codes against errors because of their irregularities. In video and image transmission systems, the performance is measured by Peak Signal to Noise Ratio (PSNR). We propose an approach to design IRA codes optimized for such a criterion. In the third part of the dissertation, we investigate Slepian-Wolf coding problem using LDPC codes. The problems to be addressed include coding problem involving multiple sources and non-binary sources, and coding using multi-level codes and nonbinary codes.
Performance Analysis of Linear Codes Under Maximum-likelihood Decoding
Performance Analysis of Linear Codes Under Maximum-likelihood Decoding - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Performance Analysis of Linear Codes Under Maximum-likelihood Decoding write by Igal Sason. This book was released on 2006. Performance Analysis of Linear Codes Under Maximum-likelihood Decoding available in PDF, EPUB and Kindle. Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial focuses on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their performance without resorting to computer simulations. Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial is a comprehensive introduction to this important topic for students, practitioners and researchers working in communications and information theory.
