Instanton-based Techniques for Analysis and Reduction of Error Floor of LDPC 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 Instanton-based Techniques for Analysis and Reduction of Error Floor of LDPC Codes write by . This book was released on 2008. Instanton-based Techniques for Analysis and Reduction of Error Floor of LDPC Codes available in PDF, EPUB and Kindle. We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly to a variety of channels, discrete or continuous, and variety of sub-optimal decoders. Specifically, we consider: iterative belief propagation (BP) decoders, Gallager type decoders, and linear programming (LP) decoders performing over the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC). The instanton analysis suggests that the underlying topological structures of the most probable instanton of the same code but different channels and decoders are related to each other. Armed with this understanding of the graphical structure of the instanton and its relation to the decoding failures, we suggest a method to construct codes whose Tanner graphs are free of these structures, and thus have less significant error floors.
Channel Coding: Theory, Algorithms, and Applications
Channel Coding: Theory, Algorithms, and 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 Channel Coding: Theory, Algorithms, and Applications write by . This book was released on 2014-07-29. Channel Coding: Theory, Algorithms, and Applications available in PDF, EPUB and Kindle. This book gives a review of the principles, methods and techniques of important and emerging research topics and technologies in Channel Coding, including theory, algorithms, and applications. Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applications Ascertain how a topic relates to other areas and learn of the research issues yet to be resolved Quick tutorial reviews of important and emerging topics of research in Channel Coding Presents core principles in Channel Coding theory and shows their applications Reference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge
Analysis of Error Floor of LDPC Codes Under LP Decoding Over the BSC.
Analysis of Error Floor of LDPC Codes Under LP Decoding Over the BSC. - 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 Analysis of Error Floor of LDPC Codes Under LP Decoding Over the BSC. write by . This book was released on 2009. Analysis of Error Floor of LDPC Codes Under LP Decoding Over the BSC. available in PDF, EPUB and Kindle. We consider linear programming (LP) decoding of a fixed low-density parity-check (LDPC) code over the binary symmetric channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not a codeword. We propose an efficient algorithm termed the instanton search algorithm (ISA) which, given a random input, generates a set of flips called the BSC-instanton and prove that: (a) the LP decoder fails for any set of flips with support vector including an instanton; (b) for any input, the algorithm outputs an instanton in the number of steps upper-bounded by twice the number of flips in the input. We obtain the number of unique instantons of different sizes by running the ISA sufficient number of times. We then use the instanton statistics to predict the performance of the LP decoding over the BSC in the error floor region. We also propose an efficient semi-analytical method to predict the performance of LP decoding over a large range of transition probabilities of the BSC.
LDPC Codes
LDPC 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 LDPC Codes write by Xiaojie Zhang. This book was released on 2012. LDPC Codes available in PDF, EPUB and Kindle. Low-density parity-check (LDPC) codes have been the focus of much research over the past decade thanks to their near Shannon limit performance and to their efficient message-passing (MP) decoding algorithms. However, the error floor phenomenon observed in MP decoding, which manifests itself as an abrupt change in the slope of the error-rate curve, has hindered the adoption of LDPC codes and MP decoders in some applications requiring very low error rates. As an alternative to MP decoding, linear programming (LP) decoding is an approximation to maximum-likelihood decoding by relaxing the optimal decoding problem into a linear optimization problem. It has been noticed that, when the symbols error probability in channel output is low, LP decoding has superior error correction performance. However, due to the inefficiency of general-purpose LP solvers which are not optimized for solving LP problems, LP decoding is computationally more complex than MP decoding, especially for codes of large block size. In this dissertation, we first design an efficient exhaustive search algorithm to find all small error-prone substructures, some of which are commonly blamed for certain decoding failures of MP decoding. Then, we investigate the cause of error floors in LDPC codes from the perspective of the MP decoder implementation, with special attention to limitations that decrease the numerical accuracy of messages passed during decoding, and propose a quantization method for fixed-point implementation of MP decoding which significantly improves the error-floor performance by overcoming the limitations of standard quantization rules. For LP decoding, we improve the error-correcting capability of LP decoding by using an effective algorithm to generate additional redundant parity-check constraints which eliminate certain undesired solutions to LP decoding problem. We further propose an efficient message-passing algorithm to solve the LP decoding problem. This algorithm is based on the alternating direction method of multipliers (ADMM), a classic technique in convex optimization theory, and our key contribution is a novel, efficient projection algorithm that can improve the decoding speed of the ADMM-based LP decoder. The last part of this dissertation is a separate piece of work on optimizing video transmission over distributed cognitive radio network.
Error Floors of LDPC Codes and Related Topics
Error Floors of LDPC Codes and Related Topics - 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 Error Floors of LDPC Codes and Related Topics write by Brian K. Butler. This book was released on 2013. Error Floors of LDPC Codes and Related Topics available in PDF, EPUB and Kindle. Since their rediscovery in the late 1990s, low-density parity-check (LDPC) codes have rapidly become one the most important classes of error correcting codes. LDPC codes have a graphical description and are generally decoded iteratively. The graph of an iteratively decoded code's error rate performance versus the channel quality is typically divided into two regions. The error floor region appears at higher channel quality and is characterized by a more gradual decrease in error rate as channel quality improves. For iterative decoders the error floor is apparently determined by small structures within the code that are specific to the selected graphical description of the code and subtle details of the decoding algorithm. This thesis addresses several issues of LDPC error floors in the additive white Gaussian noise channel. First, we find the source of several well publicized error floors to be numerical issues within the message-passing decoder. We propose numerical improvements to several decoding formulations which substantially lower error floors. Next, we examine and refine error-floor prediction models. A time-variant linear state-space model is presented and analyzed. Graph theory is applied to analyze the small error-prone structures within the code. While we find our techniques encounter considerable problems in determining the error floors for iterative decoders with unrestricted dynamic range, their predictions are quite accurate when significant range restrictions are present. The final issue of LDPC error floors which we address relates to the minimum distance of quasi-cyclic (QC) LDPC codes. We derive improved minimum distance upper bounds for codes which are punctured and codes which contain a significant number of zeros in their protomatrices. These bound are then applied to a family of protograph-based LDPC codes standardized for use in deep-space communications. In the case of the rate-1/2 code, our upper bounds demonstrate that the previously promulgated ensemble lower bounds do not apply to QC constructions at block lengths beyond 4400 bits. The last part of this dissertation is a fairly separate piece of work on bounding the spectral radius of a large class of nonnegative matrices. We apply these bounds to digraphs and derive several associated equality conditions.
