Download or read book Novel Code Construction and Decoding Techniques for LDPC Codes written by Richard Bresnan and published by . This book was released on 2004 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report a study of the record breaking error correcting codes known as low-density parity-check (LDPC) codes is presented. The science of finding efficient schemes by which information can be coded for reliable transmission through a noisy channel is called coding theory and this is the subject area of the thesis. Background research in coding theory and LDPC codes is described before the main work. Using a simulated decoder, detailed and very accurate decoding results were obtained, which fueled the remainder of this work. The standard sum-product decoder was implemented in software in the probability and log domains. Finite precision decoders were also implemented, which approximate the performance of a hardware implementation. Results of simulated decoding of graphical images are shown. A novel sleeping node LDPC decoder is presented. This decoder works by predicting the state of transmitted bits before the standard iterative decoding process has completed. The outcome of experiments shows that the decoder is sub-optimal, but more efficient than sum-product decoding. Results of numerous variations on the decoder are shown and hardware implementation issues are investigated. Several random code constructions are developed. The algorithms defined are intended to either search for or grow random LDPC codes with properties suitable for use in a sum-product decoder. Results of different techniques are compared with standard LDPC codes in the literature. Quasicyclic LDPC code constructions are also defined and investigated. Certain families of these codes have identical decoding complexity to randomly constructed LDPC codes and can be proven to work well under sum-product decoding. Hardware implementation benefits for encoding are discussed. Results of decoding simulations are compared with randomly constructed LDPC codes.

Download or read book Resource Efficient LDPC Decoders written by Vikram Arkalgud Chandrasetty and published by Academic Press. This book was released on 2017-12-05 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Error Correction Coding and Decoding written by Martin Tomlinson and published by Springer. This book was released on 2017-02-21 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book LDPC Code Designs Constructions and Unification written by Juane Li and published by Cambridge University Press. This book was released on 2017 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, leading authorities unify algebraic- and graph-based LDPC code designs and constructions into a single theoretical framework.

Download or read book Low Complexity Capacity approaching Codes for Data Transmission written by Christopher J. Nelson and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis analyzes the design of low complexity capacity approaching codes suitable for data transmission. The research documented in this thesis describes new and novel design methods for three well-known error control coding techniques, Turbo codes, LDPC block codes and LDPC convolutional codes, which are suitable for implementation in a number of modem digital communication systems. Firstly, we present Partial Unit Memory (PUM) based Turbo codes. A variant of Turbo codes which encompasses the advantages of both block and convolutional codes. The design methods of PUM Turbo codes are presented and Bit Error Rate (BER) simulations and Extrinsic Information Transfer (EXIT) chart analysis illustrates their performance. Partial Unit Memory codes are a class of low complexity, non-binary convolutional codes and have been shown to outperform equivalent convolutional codes. We present the EXIT charts of parallel concatenated PUM codes and PUM Woven Turbo Codes and analyse them to assess their performance compared with standard Turbo code designs. Resulting Extrinsic Information Transfer charts indicate that the proposed PUM-based codes have higher mutual information during iterative decoding than the equivalent Recursive, Systematic, Convolutional Turbo codes (RSC- TC) for the same Eb/No, i.e. the output of the decoders provides a better approximation of the decoded bits. The EXIT chart analysis is supported by BER plots, which confirms the behaviour predicted by the EXIT charts. We show that the concatenated PUM codes outperform the well-known turbo codes in the waterfall region, with comparable performance in the error floor region. In the second section we present Low Density Generator Matrix codes; a variant of LDPC codes that have low complexity encoding and decoding techniques. We present results of three construction methods and describe how LDGM codes can be modified to improve the error-floor region. We describe the design of random, structured and semi-random, semi- structured codes and how, by replacing the identity matrix with a staircase matrix, LDGM codes can show significant improvements in the error-floor region. Furthermore, we analyse the performance of serially concatenated LDGM codes and how they can benefit when we use the modified LDGM codes in either the outer code or the inner code. The results indicate that concatenated LDGM codes that incorporate LDGM staircase codes in the inner code will show improvements in error-floor performance while maintaining near capacity limit performances. While in the case of LDGM staircase codes being used as the outer codes no significant improvements in waterfall or error-floor regions are observed compared to a concatenated scheme that employs an LDGM identity outer code. Finally, we propose a new design of LDPC convolutional code, which we term as time invariant Low Density Parity Check Unit Memory (LDPC-UM) codes. The performance of LDPC block and Low Density Parity Check Unit Memory codes are compared, in each case, the Low Density Parity Check Unit Memory codes performance is at least as good as that of the LDPC block codes from which they are derived. LDPC-UM codes are the convolutional counterparts of LDPC block codes. Here, we describe techniques for the design of low complexity time invariant LDPC-UM codes by unwrapping the Tanner graph of algebraically constructed quasi-cyclic LDPC codes. The Tanner graph is then used to describe a pipelined message passing based iterative decoder for LDPC-UM codes and standard LDPC convolutional codes that outputs decoding results continuously.

Download or read book Codes and turbo codes written by Claude Berrou and published by Springer Science & Business Media. This book was released on 2011-01-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to one of the essential functions of modern telecommunications systems: channel coding or error correction coding. Its main topic is iteratively decoded algebraic codes, convolutional codes and concatenated codes.

Download or read book Ana Lysis of Failures of Decoders for LDPC Codes written by and published by . This book was released on 2008 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the publication of Shannon's seminal work in 1948, the search for capacity achieving codes hasled to many interesting discoveries in channel coding theory. Low-density parity-check (LDPC) codes originally proposed in 1963 were largely forgotten and rediscovered recently. The significance of LDPC codes lies in their capacity approaching performance even when decoded using low complexity sub-optimal decoding algorithms. Iterative decoders are one such class of decoders that work on a graphical representation of a code known as the Tanner graph. Their properties have been well understood in the asymptotic limit of the code length going to infinity. However, the behavior of various decoders for a given finite length code remains largely unknown. An understanding of the failures of the decoders is vital for the error floor analysis of a given code. Broadly speaking, error floor is the abrupt degradation in the frame error rate (FER) performance of a code in the high signal-to-noise ratio domain. Since the error floor phenomenon manifests in the regions not reachable by Monte-Carlo simulations, analytical methods are necessary for characterizing the decoding failures. In this work, we consider hard decision decoders for transmission over the binary symmetric channel (BSC). For column-weight-three codes, we provide tight upper and lower bounds on the guaranteed error correction capability of a code under the Gallager A algorithm by studying combinatorial objects known as trapping sets. For higher column weight codes, we establish bounds on the minimum number of variable nodes that achieve certain expansion as a function of the girth of the underlying Tanner graph, thereby obtaining lower bounds on the guaranteed error correction capability. We explore the relationship between a class of graphs known as cage graphs and trapping sets to establish upper bounds on the error correction capability. We also propose an algorithm to identify the most probable noise configurations, also known as instantons, that lead to error floorfor linear programming (LP) decoding over the BSC. With the insight gained from the above analysis techniques, we propose novel code construction techniques that result in codes with superior error floor performance.

Download or read book Advanced Error Control Techniques for Data Storage Systems written by Erozan M. Kurtas and published by CRC Press. This book was released on 2018-10-03 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the massive amount of data produced and stored each year, reliable storage and retrieval of information is more crucial than ever. Robust coding and decoding techniques are critical for correcting errors and maintaining data integrity. Comprising chapters thoughtfully selected from the highly popular Coding and Signal Processing for Magnetic Recording Systems, Advanced Error Control Techniques for Data Storage Systems is a finely focused reference to the state-of-the-art error control and modulation techniques used in storage devices. The book begins with an introduction to error control codes, explaining the theory and basic concepts underlying the codes. Building on these concepts, the discussion turns to modulation codes, paying special attention to run-length limited sequences, followed by maximum transition run (MTR) and spectrum shaping codes. It examines the relationship between constrained codes and error control and correction systems from both code-design and architectural perspectives as well as techniques based on convolution codes. With a focus on increasing data density, the book also explores multi-track systems, soft decision decoding, and iteratively decodable codes such as Low-Density Parity-Check (LDPC) Codes, Turbo codes, and Turbo Product Codes. Advanced Error Control Techniques for Data Storage Systems offers a comprehensive collection of theory and techniques that is ideal for specialists working in the field of data storage systems.

Download or read book Low density Parity check Codes written by Gabofetswe Alafang Malema and published by . This book was released on 2007 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fundamentals of Convolutional Coding written by Rolf Johannesson and published by John Wiley & Sons. This book was released on 2015-05-19 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Convolutional Coding, Second Edition, regarded as a bible of convolutional coding brings you a clear and comprehensive discussion of the basic principles of this field Two new chapters on low-density parity-check (LDPC) convolutional codes and iterative coding Viterbi, BCJR, BEAST, list, and sequential decoding of convolutional codes Distance properties of convolutional codes Includes a downloadable solutions manual

Download or read book Error Correction Coding and Decoding written by Mohammed Ahmed and published by . This book was released on 2020-10-08 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 these 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 work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

Download or read book Constructions Analyses and Decoding Algorithms of LDPC Codes and Error Control Codes for Flash Coding written by Qin Huang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental problem in communication or storage systems is that of reproducing a message at another location or another time with high reliability. Channel codes or error control codes are the key techniques to guarantee reliable information transmission and storage. In the past six decades, many researchers dedicated themselves to design highly efficient error control codes. Low-density parity-check (LDPC) codes form a class of capacity-achievable codes with powerful soft-decision decoding algorithms. These decoding algorithms have linear complexity. Thus, many LDPC codes have been chosen as the standard codes for various next generations of communication systems and their applications to digital data storage systems are now being seriously considered and investigated. LDPC codes and efficient algorithms for decoding them form the most attractive topic in coding theory in the past 15 years. Two desirable structures for efficient hardware implementation of encoding and decoding of LDPC codes are cyclic and quasi-cyclic structures. In this dissertation, a new class of cyclic and a new class of quasi-cyclic LDPC codes are constructed by circulant decomposition. The new construction of cyclic LDPC codes enlarges the repertoire of cyclic codes constructed from finite geometries in 2000. Also presented in this dissertation are two simple but efficient novel reliability-based iterative decoding algorithms of LDPC codes. Both algorithms are devised based on the simple concepts of the one-step-majority-logic decoding algorithm. They provide efficient trade-offs between performance and decoding complexity. These two algorithms can be implemented in a single decoder with dual mode. In this dissertation, we also investigate application of error control codes to flash memories to reduce block erasures. Flash memories are the most promising devices to replace hard disk drives. However, block erasures are the most challenge problem for the life time of flash memories. Such operations are not only time-consuming, but also cause physical degradation and reduce the longevity of flash memories. A new efficient approach based on error control codes is proposed to reduce the frequency of block erasures.

Download or read book Channel Coding Theory Algorithms and Applications written by and published by Academic Press. This book was released on 2014-07-29 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Turbo like Codes written by Aliazam Abbasfar and published by Springer Science & Business Media. This book was released on 2007-09-09 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces turbo error correcting concept in a simple language, including a general theory and the algorithms for decoding turbo-like code. It presents a unified framework for the design and analysis of turbo codes and LDPC codes and their decoding algorithms. A major focus is on high speed turbo decoding, which targets applications with data rates of several hundred million bits per second (Mbps).

Download or read book Improved Coding Techniques for Digital Recording Systems written by Aman Bhatia and published by . This book was released on 2015 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation addresses various problems related to data encoding and error-correction techniques to design more reliable and higher density digital data storage technologies. In the second chapter, the problem of rewriting for multilevel flash memories is considered and a novel construction method for WOM codes based on lattices is proposed. Using the continuous approximation, hyperbolic write-regions are shown to be sum-rate optimal for arbitrary number of writes. An algorithm that determines an optimal encoding scheme is proposed for the case of two cells. Using these ideas, WOM codes are proposed that achieve high sum-rates. In the third chapter, the problem of designing a block-precoder for a magnetic recording channel is considered with the objective of minimizing the error rate. The precoder design problem is equivalent to solving a quadratic assignment problem which is NP-complete in general. Precoders are constructed using a branch-and-bound technique with a reduced search space, as well as using a sub-optimal local search algorithm. Simulation results show that these block-precoders out-perform existing precoding techniques. The fourth chapter discusses a novel technique for using polar codes for partial response channels. Multiple polar codes of various rates are designed for memoryless channels estimated by removing the effects of intersymbol interference from the partial response channel. Data is encoded using these codes and the codewords are interleaved before transmission. Decoding is done sequentially using a multi-stage decoding technique. Simulation results demonstrate that the performance of these codes is comparable to LDPC codes. The fifth chapter studies the performance of stochastic decoding on LDPC code ensembles in the limit of infinite blocklength. Two methods to perform the density evolution for stochastic decoding are provided. Alternative descriptions of the variable node update in stochastic decoding are given and connections to other decoding algorithms are highlighted. The sixth chapter explores the performance of binary images of non-binary LDPC codes. For the binary erasure channel, it is shown that the collection of stopping sets for a non-binary LDPC code are a subset of the collection of stopping sets of its basic binary image. An efficient algorithm is proposed that eliminates these additional stopping sets by adding redundant parity checks to the basic binary images. Simulation results confirm that the few redundant checks are sufficient to match the performance of the original non-binary LDPC codes with lower complexity.

Download or read book Fundamentals of Classical and Modern Error Correcting Codes written by Shu Lin and published by Cambridge University Press. This book was released on 2021-12-09 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using easy-to-follow mathematics, this textbook provides comprehensive coverage of block codes and techniques for reliable communications and data storage. It covers major code designs and constructions from geometric, algebraic, and graph-theoretic points of view, decoding algorithms, error control additive white Gaussian noise (AWGN) and erasure, and dataless recovery. It simplifies a highly mathematical subject to a level that can be understood and applied with a minimum background in mathematics, provides step-by-step explanation of all covered topics, both fundamental and advanced, and includes plenty of practical illustrative examples to assist understanding. Numerous homework problems are included to strengthen student comprehension of new and abstract concepts, and a solutions manual is available online for instructors. Modern developments, including polar codes, are also covered. An essential textbook for senior undergraduates and graduates taking introductory coding courses, students taking advanced full-year graduate coding courses, and professionals working on coding for communications and data storage.

Download or read book LDPC Codes on Finite Fields written by Juane Li and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to their capacity-approaching performance which can be achieved with practically implementable iterative decoding algorithms devised based on belief-propagation, low-density parity-check (LDPC) codes have rapid dominance in the applications requiring error control coding. This dissertation is intended to address certain important aspects of the aforementioned issues about LDPC codes. Subjects to be investigated include: (1) flexible and systematic methods for constructing binary LDPC codes with quasi-cyclic structure based on finite fields; (2) construction of high-rate and low-rate quasi-cyclic (QC) LDPC codes to achieve very low error rates without error-floor and with high rate of decoding convergence; (3) construction of binary QC-LDPC codes whose Tanner graphs have girth 8 or larger and contain minimum number of short cycles; (4) developing effective algorithms for enumerating short cycles in the Tanner graph of LDPC codes; (5) devising reduced-complexity decoding schemes and algorithms for binary QC-LDPC codes; (6) effective matrix-theoretic methods for constructing nonbinary (NB) LDPC codes; and (7) reduced-complexity decoding schemes and algorithms for NB LDPC codes. The dissertation presents a simple, flexible and systematic method to construct both binary and nonbinary LDPC codes with quasi-cyclic (QC) structure based on two arbitrary subsets of a finite field. One technique for constructing QC-LDPC codes whose Tanner graphs have girth 8 or larger is also proposed. Simulation results show that these constructed codes perform well over both the additive white Gaussian noise and the binary erasure channels. Also presented in this dissertation is a reduced-complexity decoding scheme to decode binary QC-LDPC codes. The decoding scheme is devised based on the section-wise cyclic structure of the parity-check matrix of a QC-LDPC code. The proposed decoding scheme combined with iterative decoding algorithms of LDPC codes results in no or a relative small performance degradation. Two efficient algorithms for enumerating short cycles in the Tanners graph of LDPC codes are presented. One algorithm is devised based on iterative message-passing algorithm by introducing messages in term of monomials, which is an improvement of the work of Karimi and Banihashemi. The other one is based on the trellis of an LDPC code by finding the partial paths which can form cycles. By removing certain number of cycles, a new code whose Tanner graph has a smaller number of short cycles, a larger girth, or both can be constructed. An algorithm to count and find cycles of lengths four and six in a class of QC-LDPC codes is also proposed. In this dissertation, we also briefly investigate one of the algebraic-based constructions of LDPC code, namely superposition (SP) construction, and one of the graph-based constructions, namely protograph-based (PTG-based) construction. The SP-construction method is re-interpreted in a broader scope from both the algebraic and the graph-theoretic perspectives. From the graph-theoretic point of view, it is shown that the PTG-based construction of LDPC codes is a special case of the SP-construction. An algebraic method for constructing PTG-based QC-LDPC codes through decomposing a small matrix is proposed. Several methods for constructing QC-LDPC codes through the SP-construction are also presented.