Download or read book Multi scale Error correcting Codes and Their Decoding Using Belief Propagation written by Yong Seok Yoo and published by . This book was released on 2014 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is motivated from error-correcting codes in the brain. To counteract the effect of representation noise, a large number of neurons participate in encoding even low-dimensional variables. In many brain areas, the mean firing rates of neurons as a function of represented variable, called the tuning curve, have unimodal shape centered at different values, defining a unary code. This dissertation focuses on a new type of neural code where neurons have periodic tuning curves, with a diversity of periods. Neurons that exhibit this tuning are grid cells of the entorhinal cortex, which represent self-location in two-dimensional space. First, we investigate mutual information between such multi-scale codes and the coded variable as a function of tuning curve width. For decoding, we consider maximum likelihood (ML) and plausible neural network (NN) based models. For unary neural codes, Fisher information increases with narrower tuning, regardless of the decoding method. By contrast, for the multi-scale neural code, the optimal tuning curve width depends on the decoding method. While narrow tuning is optimal for ML decoding, a finite width, matched to statistics of the noise, is optimal with a NN decoder. This finding may explain why actual neural tuning curves have relatively wide tuning. Next, motivated by the observation that multi-scale codes involve non-trivial decoding, we examine a decoding algorithm based on belief propagation (BP) because BP promises certain gains in decoding efficiency. The decoding problem is first formulated as a subset selection problem on a graph and then approximately solved by BP. Even though the graph has many cycles, BP converges to a fixed point after few iterations. The mean square error of BP approaches to that of ML at high signal-to-noise ratios. Finally, using the multi-scale code, we propose a joint source-channel coding scheme that allows separate senders to transmit complementary information over additive Gaussian noise channels without cooperation. The receiver decodes one sender's codeword using the other as side information and achieves a lower distortion using the same number of transmissions. The proposed scheme offers a new framework to design distributed joint source-channel codes for continuous variables.

Download or read book Turbo Decoding of High Performance Error Correcting Codes Via Belief Propagation written by and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We studied AWGN coding theorems for ensembles of coding systems which are built from fixed convolutional codes interconnected with random interleavers. We call these systems turbo-like codes and they include as special cases both the classical turbo codes and the serial concatenation of interleaved convolutional codes. We offered a general conjecture about the behavior of the ensemble (maximum-likehood decoder) word error probability as the word length approaches infinity. We proved this conjecture for a simple class of rate l/q serially concatenated codes where the outer code is a q-fold repetition code and the inner code is rate 1 convolutional code with transfer function 1/(1+D). We call these codes "RA" (repeat and accumulate) codes. This was the first rigorous proof of a coding theorem for turbo-like codes.

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 Iterative Decoding Beyond Belief Propagation of Low Density Parity Check Codes written by Shiva Kumar Planjery and published by . This book was released on 2013 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent renaissance of one particular class of error-correcting codes called low-density parity-check (LDPC) codes has revolutionized the area of communications leading to the so-called field of modern coding theory. At the heart of this theory lies the fact that LDPC codes can be efficiently decoded by an iterative inference algorithm known as belief propagation (BP) which operates on a graphical model of a code. With BP decoding, LDPC codes are able to achieve an exceptionally good error-rate performance as they can asymptotically approach Shannon's capacity. However, LDPC codes under BP decoding suffer from the error floor phenomenon, an abrupt degradation in the error-rate performance of the code in the high signal-to-noise ratio region, which prevents the decoder from achieving very low error-rates. It arises mainly due to the sub-optimality of BP decoding on finite-length loopy graphs. Moreover, the effects of finite precision that stem from hardware realizations of BP decoding can further worsen the error floor phenomenon. Over the past few years, the error floor problem has emerged as one of the most important problems in coding theory with applications now requiring very low error rates and faster processing speeds. Further, addressing the error floor problem while taking finite precision into account in the decoder design has remained a challenge. In this dissertation, we introduce a new paradigm for finite precision iterative decoding of LDPC codes over the binary symmetric channel (BSC). These novel decoders, referred to as finite alphabet iterative decoders (FAIDs), are capable of surpassing the BP in the error floor region at a much lower complexity and memory usage than BP without any compromise in decoding latency. The messages propagated by FAIDs are not quantized probabilities or log-likelihoods, and the variable node update functions do not mimic the BP decoder. Rather, the update functions are simple maps designed to ensure a higher guaranteed error correction capability which improves the error floor performance. We provide a methodology for the design of FAIDs on column-weight-three codes. Using this methodology, we design 3-bit precision FAIDs that can surpass the BP (floating-point) in the error floor region on several column-weight-three codes of practical interest. While the proposed FAIDs are able to outperform the BP decoder with low precision, the analysis of FAIDs still proves to be a difficult issue. Furthermore, their achievable guaranteed error correction capability is still far from what is achievable by the optimal maximum-likelihood (ML) decoding. In order to address these two issues, we propose another novel class of decoders called decimation-enhanced FAIDs for LDPC codes. For this class of decoders, the technique of decimation is incorporated into the variable node update function of FAIDs. Decimation, which involves fixing certain bits of the code to a particular value during decoding, can significantly reduce the number of iterations required to correct a fixed number of errors while maintaining the good performance of a FAID, thereby making such decoders more amenable to analysis. We illustrate this for 3-bit precision FAIDs on column-weight-three codes and provide insights into the analysis of such decoders. We also show how decimation can be used adaptively to further enhance the guaranteed error correction capability of FAIDs that are already good on a given code. The new adaptive decimation scheme proposed has marginally added complexity but can significantly increase the slope of the error floor in the error-rate performance of a particular FAID. On certain high-rate column-weight-three codes of practical interest, we show that adaptive decimation-enhanced FAIDs can achieve a guaranteed error-correction capability that is close to the theoretical limit achieved by ML decoding.

Download or read book List Decoding of Error Correcting Codes written by Venkatesan Guruswami and published by Springer. This book was released on 2004-11-29 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of “error-correcting codes”. This theory has traditionally gone hand in hand with the algorithmic theory of “decoding” that tackles the problem of recovering from the errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof“list-decoding” can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or “encode”) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2.

Download or read book Error Correcting Codes Finite Geometries and Cryptography written by Aiden A. Bruen and published by American Mathematical Soc.. This book was released on 2010-09-03 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary volume contains papers from both a conference and special session on Error-Control Codes, Information Theory and Applied Cryptography. The conference was held at the Fields Institute in Toronto, On, Canada from December 5-6, 2007, and the special session was held at the Canadian Mathematical Society's winter meeting in London, ON, Canada from December 8-10, 2007. The volume features cutting-edge theoretical results on the Reed-Muller and Reed-Solomon codes, classical linear codes, codes from nets and block designs, LDPC codes, perfect quantum and orthogonal codes, iterative decoding, magnetic storage and digital memory devices, and MIMO channels. There are new contributions on privacy reconciliation, resilient functions, cryptographic hash functions, and new work on quantum coins. Related original work in finite geometries concerns two-weight codes coming from partial spreads, (0, 1) matrices with forbidden configurations, Andre embeddings, and representations of projective spaces in affine planes. Great care has been taken to ensure that high expository standards are met by the papers in this volume. Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interst and of benefit both to the experienced and to newcomers alike.

Download or read book An Introduction to Error Correcting Codes with Applications written by Scott A. Vanstone and published by Springer Science & Business Media. This book was released on 1989-05-31 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 Finite Fields and Factoring xn-l over GF(q) 181 5. 9 Another Method for Factoring xn-l over GF(q)t 187 5. 10 Exercises 193 Chapter 6 BCH Codes and Bounds for Cyclic Codes 6. 1 Introduction 201 6. 2 BCH Codes and the BCH Bound 205 6. 3 Bounds for Cyclic Codest 210 6. 4 Decoding BCH Codes 215 6. 5 Linearized Polynomials and Finding Roots of Polynomialst 224 6. 6 Exercises 231 Chapter 7 Error Correction Techniques and Digital Audio Recording 7. 1 Introduction 237 7. 2 Reed-Solomon Codes 237 7. 3 Channel Erasures 240 7. 4 BCH Decoding with Erasures 244 7. 5 Interleaving 250 7. 6 Error Correction and Digital Audio Recording 256 7.

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 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 A Course in Error correcting Codes written by Jørn Justesen and published by European Mathematical Society. This book was released on 2004 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as a text for a course aimed at advanced undergraduates. Chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts.

Download or read book Machine Learning for Future Wireless Communications written by Fa-Long Luo and published by John Wiley & Sons. This book was released on 2020-02-10 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review to the theory, application and research of machine learning for future wireless communications In one single volume, Machine Learning for Future Wireless Communications provides a comprehensive and highly accessible treatment to the theory, applications and current research developments to the technology aspects related to machine learning for wireless communications and networks. The technology development of machine learning for wireless communications has grown explosively and is one of the biggest trends in related academic, research and industry communities. Deep neural networks-based machine learning technology is a promising tool to attack the big challenge in wireless communications and networks imposed by the increasing demands in terms of capacity, coverage, latency, efficiency flexibility, compatibility, quality of experience and silicon convergence. The author – a noted expert on the topic – covers a wide range of topics including system architecture and optimization, physical-layer and cross-layer processing, air interface and protocol design, beamforming and antenna configuration, network coding and slicing, cell acquisition and handover, scheduling and rate adaption, radio access control, smart proactive caching and adaptive resource allocations. Uniquely organized into three categories: Spectrum Intelligence, Transmission Intelligence and Network Intelligence, this important resource: Offers a comprehensive review of the theory, applications and current developments of machine learning for wireless communications and networks Covers a range of topics from architecture and optimization to adaptive resource allocations Reviews state-of-the-art machine learning based solutions for network coverage Includes an overview of the applications of machine learning algorithms in future wireless networks Explores flexible backhaul and front-haul, cross-layer optimization and coding, full-duplex radio, digital front-end (DFE) and radio-frequency (RF) processing Written for professional engineers, researchers, scientists, manufacturers, network operators, software developers and graduate students, Machine Learning for Future Wireless Communications presents in 21 chapters a comprehensive review of the topic authored by an expert in the field.

Download or read book Learning Algorithms for Error Correction written by Loren Lugosch and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Channel coding enables reliable communication over unreliable, noisy channels: by encoding messages with redundancy, it is possible to decode the messages in such a way that errors introduced by the channel are corrected. Modern channel codes achieve very low error rates at long block lengths, but long blocks are often not acceptable for low-latency applications.While there exist short block codes with excellent error-correction performance when decoded optimally, designing practical, low-complexity decoding algorithms that can achieve close-to-optimal results for short codes is still an open problem. In this thesis, we explore an approach to decoding short block codes in which the decoder is recast as a machine learning algorithm.After providing the background concepts on error-correcting codes and machine learning, we review the literature on learning algorithms for error correction, with a special emphasis on the recently introduced ``neural belief propagation'' algorithm. We then describe a set of modifications to neural belief propagation which improve its performance and reduce its implementation complexity. We also propose a new syndrome-based output layer for neural error-correcting decoders which takes the code structure into account during training to yield decoders with lower frame error rate.Finally, we suggest some future work." --

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 Quantum Error Correction Decoders written by Eduard Bordas Marchante and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Error correction is used to correct any errors that may arise when sending any message, as errors are prone to appear due to noise. For classical codes, there are many decoders used, for example, belief propagation. Unfortunately, these classical decoders are less efficient for quantum codes. A proposed remedy to improve the decoders efficiency is to use a neural network for decoding. In this thesis, we will implement belief propagation on the toric code and check its efficiency. We will see that for few errors, belief propagation works, but it fails for other cases. We also introduce the modifications needed for neural belief propagation, a modification of the original algorithm that integrates a neural network on the algorithm structure.

Download or read book Advanced Hardware Design for Error Correcting Codes written by Cyrille Chavet and published by Springer. This book was released on 2014-10-30 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides thorough coverage of error correcting techniques. It includes essential basic concepts and the latest advances on key topics in design, implementation, and optimization of hardware/software systems for error correction. The book’s chapters are written by internationally recognized experts in this field. Topics include evolution of error correction techniques, industrial user needs, architectures, and design approaches for the most advanced error correcting codes (Polar Codes, Non-Binary LDPC, Product Codes, etc). This book provides access to recent results, and is suitable for graduate students and researchers of mathematics, computer science, and engineering. • Examines how to optimize the architecture of hardware design for error correcting codes; • Presents error correction codes from theory to optimized architecture for the current and the next generation standards; • Provides coverage of industrial user needs advanced error correcting techniques. Advanced Hardware Design for Error Correcting Codes includes a foreword by Claude Berrou.

Download or read book Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes written by Bart Preneel and published by IOS Press. This book was released on 2009 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Research Workshop on Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes has been organized in Veliko Tarnovo, Bulgaria, on October 6-9, 2008. This title includes the papers based on the lectures of the invited speakers, and on the talks of the participants in the workshop.

Download or read book Error Correcting Coding and Security for Data Networks written by Grigorii Kabatiansky and published by Wiley. This book was released on 2005-03-11 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error correcting coding is often analyzed in terms of its application to the separate levels within the data network in isolation from each other. In this fresh approach, the authors consider the data network as a superchannel (a multi-layered entity) which allows error correcting coding to be evaluated as it is applied to a number of network layers as a whole. By exposing the problems of applying error correcting coding in data networks, and by discussing coding theory and its applications, this original technique shows how to correct errors in the network through joint coding at different network layers. Discusses the problem of reconciling coding applied to different layers using a superchannel approach Includes thorough coverage of all the key codes: linear block codes, Hamming, BCH and Reed-Solomon codes, LDPC codes decoding, as well as convolutional, turbo and iterative coding Considers new areas of application of error correcting codes such as transport coding, code-based cryptosystems and coding for image compression Demonstrates how to use error correcting coding to control such important data characteristics as mean message delay Provides theoretical explanations backed up by numerous real-world examples and practical recommendations Features a companion website containing additional research results including new constructions of LDPC codes, joint error-control coding and synchronization, Reed-Muller codes and their list decoding By progressing from theory through to practical problem solving, this resource contains invaluable advice for researchers, postgraduate students, engineers and computer scientists interested in data communications and applications of coding theory.