Download or read book Low density Parity check Codes with Erasures and Puncturing written by Jeongseok Ha Ha and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we extend applications of Low-Density Parity-Check (LDPC) codes to a combination of constituent sub-channels, which is a mixture of Gaussian channels with erasures. This model, for example, represents a common channel in magnetic recordings where thermal asperities in the system are detected and represented at the decoder as erasures. Although this channel is practically useful, we cannot find any previous work that evaluates performance of LDPC codes over this channel. We are also interested in practical issues such as designing robust LDPC codes for the mixture channel and predicting performance variations due to erasure patterns (random and burst), and finite block lengths. On time varying channels, a common error control strategy is to adapt the coding rate according to available channel state information (CSI). An effective way to realize this coding strategy is to use a single code and puncture it in a rate-compatible fashion, a so-called rate-compatible punctured code (RCPC). We are interested in the existence of good puncturing patterns for rate-changes that minimize performance loss. We show the existence of good puncturing patterns with analysis and verify the results with simulations. Universality of a channel code across a broad range of coding rates is a theoretically interesting topic. We are interested in the possibility of using the puncturing technique proposed in this thesis for designing universal LDPC codes. We also consider how to design high rate LDPC codes by puncturing low rate LDPC codes. The new design method can take advantage of longer effect block lengths, sparser parity-check matrices, and larger minimum distances of low rate LDPC codes.
Download or read book Design of Rate compatible Structured Low density Parity check Codes written by Jaehong Kim and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of our research is to design practical low-density parity-check (LDPC) codes which provide a wide range of code rates in a rate-compatible fashion. To this end, we first propose a rate-compatible puncturing algorithm for LDPC codes at short block lengths (up to several thousand symbols). The proposed algorithm is based on the claim that a punctured LDPC code with a smaller level of recoverability has better performance. The proposed algorithm is verified by comparing performance of intentionally punctured LDPC codes (using the proposed algorithm) with randomly punctured LDPC codes. The intentionally punctured LDPC codes show better bit error rate (BER) performances at practically short block lengths. Even though the proposed puncturing algorithm shows excellent performance, several problems are still remained for our research objective. First, how to design an LDPC code of which structure is well suited for the puncturing algorithm. Second, how to provide a wide range of rates since there is a puncturing limitation with the proposed puncturing algorithm. To attack these problems, we propose a new class of LDPC codes, called efficiently-encodable rate-compatible (E2RC) codes, in which the proposed puncturing algorithm concept is imbedded. The E2RC codes have several strong points. First, the codes can be efficiently encoded. We present low-complexity encoder implementation with shift-register circuits. In addition, we show that a simple erasure decoder can also be used for the linear-time encoding of these codes. Thus, we can share a message-passing decoder for both encoding and decoding in transceiver systems that require an encoder/decoder pair. Second, we show that the non-systematic parts of the parity-check matrix are cycle-free, which ensures good code characteristics. Finally, the E2RC codes having a systematic rate-compatible puncturing structure show better puncturing performance than any other LDPC codes in all ranges of code rates.
Download or read book Topics in Low Density Parity Check Codes for the Binary Erasure Channel written by Ohad Barak and published by . This book was released on 2002 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Puncturing Mapping and Design of Low density Parity check Codes written by Gerd Richter and published by . This book was released on 2009 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Essentials of Error Control Coding written by Jorge Castiñeira Moreira and published by John Wiley & Sons. This book was released on 2006-08-04 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid advances in electronic and optical technology have enabled the implementation of powerful error-control codes, which are now used in almost the entire range of information systems with close to optimal performance. These codes and decoding methods are required for the detection and correction of the errors and erasures which inevitably occur in digital information during transmission, storage and processing because of noise, interference and other imperfections. Error-control coding is a complex, novel and unfamiliar area, not yet widely understood and appreciated. This book sets out to provide a clear description of the essentials of the subject, with comprehensive and up-to-date coverage of the most useful codes and their decoding algorithms. A practical engineering and information technology emphasis, as well as relevant background material and fundamental theoretical aspects, provides an in-depth guide to the essentials of Error-Control Coding. Provides extensive and detailed coverage of Block, Cyclic, BCH, Reed-Solomon, Convolutional, Turbo, and Low Density Parity Check (LDPC) codes, together with relevant aspects of Information Theory EXIT chart performance analysis for iteratively decoded error-control techniques Heavily illustrated with tables, diagrams, graphs, worked examples, and exercises Invaluable companion website features slides of figures, algorithm software, updates and solutions to problems Offering a complete overview of Error Control Coding, this book is an indispensable resource for students, engineers and researchers in the areas of telecommunications engineering, communication networks, electronic engineering, computer science, information systems and technology, digital signal processing and applied mathematics.
Download or read book OFDM Baseband Receiver Design for Wireless Communications written by Tzi-Dar Chiueh and published by John Wiley & Sons. This book was released on 2008-04-15 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal frequency-division multiplexing (OFDM) access schemes are becoming more prevalent among cellular and wireless broadband systems, accelerating the need for smaller, more energy efficient receiver solutions. Up to now the majority of OFDM texts have dealt with signal processing aspects. To address the current gap in OFDM integrated circuit (IC) instruction, Chiueh and Tsai have produced this timely text on baseband design. OFDM Baseband Receiver Design for Wireless Communications covers the gamut of OFDM technology, from theories and algorithms to architectures and circuits. Chiueh and Tsai give a concise yet comprehensive look at digital communications fundamentals before explaining modulation and signal processing algorithms in OFDM receivers. Moreover, the authors give detailed treatment of hardware issues -- from design methodology to physical IC implementation. Closes the gap between OFDM theory and implementation Enables the reader to transfer communication receiver concepts into hardware design wireless receivers with acceptable implementation loss achieve low-power designs Contains numerous figures to illustrate techniques Features concrete design examples of MC-CDMA systems and cognitive radio applications Presents theoretical discussions that focus on concepts rather than mathematical derivation Provides a much-needed single source of material from numerous papers Based on course materials for a class in digital communication IC design, this book is ideal for advanced undergraduate or post-graduate students from either VLSI design or signal processing backgrounds. New and experienced engineers in industry working on algorithms or hardware for wireless communications devices will also find this book to be a key reference.
Download or read book Algebraic Low density Parity check Codes written by Qiuju Diao and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The ever-growing needs for cheaper, faster, and more reliable communication systems have forced many researchers to seek means to attain the ultimate limits on reliable communications. Low densityparity-check (LDPC) codes are currently the most promising coding technique to achieve the Shannon capacities for a wide range of channels. Many LDPC codes have been chosen as the standard codes for various next generations of communication systems and they are appearing in recent data storage products. More applications are expected to come.Major methods for constructing LDPC codes can be divided into two general categories, graphtheoretic-based methods (using computer search) and algebraic methods. Each type of constructions has its advantages and disadvantages in terms overall error performance, encoding and decoding implementations. In general, algebraically constructed LDPC codes have lower error-floor and their decoding using iterative message-passing algorithms converges at a much faster rate than the LDPC codes constructed using a graph theoretic-based method. Furthermore, it is much easier to constructalgebraic LDPC codes with large minimum distances.This research project is set up to investigate several important aspects of algebraic LDPC codes for the purpose of achieving overall good error performance required for future high-speed communication systems and high-density data storage systems. The subjects to be investigated include: (1) new constructions of algebraic LDPC codes based on finite geometries; (2) analysis of structural properties of algebraic LDPC codes, especially the trapping set structure that determines how lowthe error probability of a given LDPC code can achieve; (3) construction of algebraic LDPC codes and design coding techniques for correcting combinations of random errors and erasures that occursimultaneously in many physical communication and storage channels; and (4) analysis and construction of algebraic LDPC codes in transform domain.Research effort has resulted in important findings in all four proposed research subjects which may have a significant impact on future generations of communication and storage systems andadvance the state-of-the-art of channel coding theory.
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 843 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.
Download or read book Coding Theory and Applications written by Ángela I. Barbero and published by Springer. This book was released on 2017-08-22 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017. The 24 full papers presented were carefully reviewed and selected for inclusion in this volume. The papers cover relevant research areas in modern coding theory, including codes and combinatorial structures, algebraic geometric codes, group codes, convolutional codes, network coding, other applications to communications, and applications of coding theory in cryptography.
Download or read book Low Density Parity Check Codes Based on Finite Geometries written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-09-15 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.Kou, Yu and Lin, Shu and Fossorier, MarcGoddard Space Flight CenterEUCLIDEAN GEOMETRY; ALGORITHMS; DECODING; PARITY; ALGEBRA; INFORMATION THEORY; PROJECTIVE GEOMETRY; TWO DIMENSIONAL MODELS; COMPUTERIZED SIMULATION; ERRORS; BLOCK DIAGRAMS...
Download or read book Properties of LDGM LDPC Codes with Applications to Secrecy Coding written by Manik Raina and published by . This book was released on 2010 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ensemble of low-density generator-matrix/low-density parity-check (LDGM-LDPC) codes has been proposed in literature. In this thesis, an irregular LDGM-LDPC code is studied as a sub-code of an LDPC code with some randomly emph{punctured} output-bits. It is shown that the LDGM-LDPC codes achieve rates arbitrarily close to the channel-capacity of the binary-input symmetric-output memoryless (BISOM) channel with a finite lower-bound on the emph{complexity}. The measure of complexity is the average-degree (per information-bit) of the check-nodes for the factor-graph of the code. A lower-bound on the average degree of the check-nodes of the irregular LDGM-LDPC codes is obtained. The bound does not depend on the decoder used at the receiver. The stability condition for decoding the irregular LDGM-LDPC codes over the binary-erasure channel (BEC) under iterative-decoding with message-passing is described. The LDGM-LDPC codes are capacity achieving with bounded complexity and possess natural binning/nesting structure. These codes are applied to secrecy coding. The problem of secrecy coding for the type-II binary symmetric memoryless wiretap channel is studied. In this model, the main channel is binary-input and noiseless and the eavesdropper channel is binary-symmetric memoryless. A coding strategy based on emph{secure nested codes} is proposed. A capacity achieving length-$n$ code for the eavesdropper channel bins the space ${0,1}^n$ into co-sets which are used for secret messaging. The resulting co-set scheme achieves secrecy capacity of the type-II binary symmetric memoryless channel. As an example, the ensemble of capacity-achieving regular low-density generator-matrix/low-density parity-check (LDGM-LDPC) codes is studied as a basis for binning. The previous result is generalized to the case of a noisy main-channel. The problem of secrecy-coding for a specific type-I wiretap channel is studied. In the type-I wiretap channel under consideration, the main channel is a binary-input symmetric-output memoryless (BISOM) channel and the eavesdropper channel is a binary-symmetric channel (BSC). A secure-nested-code that achieves perfect-secrecy for the above type-I channel is proposed. The secure-nested-code is based on a nested regular LDGM-LDPC code construction.
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 A Study on Burst Erasure Correction Methods Using Low density Parity check Codes written by Gou Hosoya and published by . This book was released on 2008 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book IETE Technical Review written by and published by . This book was released on 2004 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Coding Theory written by Tom Richardson and published by Cambridge University Press. This book was released on 2008-03-17 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Having trouble deciding which coding scheme to employ, how to design a new scheme, or how to improve an existing system? This summary of the state-of-the-art in iterative coding makes this decision more straightforward. With emphasis on the underlying theory, techniques to analyse and design practical iterative coding systems are presented. Using Gallager's original ensemble of LDPC codes, the basic concepts are extended for several general codes, including the practically important class of turbo codes. The simplicity of the binary erasure channel is exploited to develop analytical techniques and intuition, which are then applied to general channel models. A chapter on factor graphs helps to unify the important topics of information theory, coding and communication theory. Covering the most recent advances, this text is ideal for graduate students in electrical engineering and computer science, and practitioners. Additional resources, including instructor's solutions and figures, available online: www.cambridge.org/9780521852296.
