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 Dialogues polonais fran ais et allemands written by and published by . This book was released on 1816 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Communication System Security written by Lidong Chen and published by CRC Press. This book was released on 2012-05-29 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helping current and future system designers take a more productive approach in the field, Communication System Security shows how to apply security principles to state-of-the-art communication systems. The authors use previous design failures and security flaws to explain common pitfalls in security design.Divided into four parts, the book begins w

Download or read book LDGM Codes for Wireless and Quantum Systems written by Hanqing Lou and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, helped by the increase in computing power, capacity approaching codes, such as turbo codes and low-density parity check (LDPC) codes, have been proposed. The common characteristics of these codes are their long length and their random-like codeword structure. However, the decoding complexity of turbo codes and the encoding complexity of LDPC codes are substantial. In order to alleviate this problem, we propose the use of low-density generator matrix (LDGM) codes, which are a special class of LDPC codes with low encoding and decoding complexity. In this work, we explore different avenues to successfully apply LDGM codes in different communications environments such as quantum systems, realistic wireless channels with memory, and MIMO channels. In order to do so, it is necessary to generate LDGM codes for different rates. Thus, the first contribution of our work is showing that LDGM codes are very flexible and can be easily modified to achieve different rates. Then, we investigate the following topics: (1) In quantum environments, stabilizer codes are a special yet large class of quantum error-correcting codes, which introduce a connection between classical block codes and quantum codes. (2) We have proposed a modified algorithm for decoding of LDGM codes over hidden Markov channels. The proposed scheme clearly outperforms the system in which the channel statistics are not exploited at the decoder side. (3) In order to approach the capacity limit in MIMO systems, powerful channel codes have to be utilized. We compare schemes based on (i) the concatenation of space-time codes and powerful channel codes and (ii) systems based on just using channel coding (no space-time code) in the context of bit-interleaved coded modulation with an iterative process between the demapper and the code. (4) We compare different transmission schemes for multiple antenna transmission systems based on multilevel codes (MLC) in terms of the maximum rate that they can achieve. We introduce a new architecture that can provide nearly optimum performance without iterative demapping and has lower complexity than the full multilevel coding scheme. (5) We focus on the design of layered transmission schemes that can approach outage capacity in quasi-static fading channels in the high spectral efficiency regime without demapper iterations. (Abstract shortened by UMI.).

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 Post Quantum Cryptography written by Philippe Gaborit and published by Springer. This book was released on 2013-06-04 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013, held in Limoges, France, in June 2013. The 17 revised full papers presented were carefully reviewed and selected from 24 submissions. The papers cover all technical aspects of cryptographic research related to the future world with large quantum computers such as code-based cryptography, lattice-based cryptography, multivariate cryptography, cryptanalysis or implementations.

Download or read book Applications of LDPC Codes to RF Optical Hybrid Systems and the Line Product Code written by Jonathan Vu Nguyen and published by . This book was released on 2022 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of an introduction, four main sections, and conclusion. The introduction gives a quick overview of communication channels and the basics of message passing algorithms. The first section focuses on the challenges of communicating over a fading channel using optical transmitters and receivers. Recognizing the limitations of a purely optical transmission system during environmental fades, the section proposes a hybrid RF-Optical system. The hybrid system consists of a high-throughput optical link closed by a Low Density Parity Check (LDPC) code alongside a separate RF link. The section proposes two different architectures for a hybrid system with varying degrees of mixing between the two links. For each architecture, their performance was evaluated during on a simulated fading channel and Additive White Gaussian Noise (AWGN) channel. The second section of this thesis capitalizes on the recent advancements in deep learning and applies it to the most popular LDPC decoding process known as message passing. The section first deconstructs the steps of message passing into nodes that can be interpreted as a type of Neural Network. Then, utilizing gradient descent methods including Adaptive Movement Estimation (ADAM), multiplicative weights for message passing are found and optimized. The key contribution of the section is the connection between these multiplicative weights and properties intrinsic to the LDPC code structure. By exploiting this relationship, a weight-sharing paradigm based on node degree is proposed, resulting in a Neural-Normalized MinSum (N-NMS) decoder which dramatically reduces the complexity of both training and implementation compared to typical neural network based decoders. The third section discusses a unique case study involving the Consultative Committee for Space Data Systems (CCSDS) 141.11-O-1 Line Product Code (LPC). Being such a short block-length code, two Maximum Likelihood (ML) decoders were evaluated against message passing decoders including MinSum (MS), Belief Propagation (BP), and Neural-Normalized MinSum (N-NMS). Analysis was carried out considering both the decoding performance and resulting hardware complexity of the decoders. Continuing on this, the fourth and final section aims to give additional insight as to why the N-NMS decoder performed so well on the LPC. This section proposes that the unique graph structure of the LPC allowed for key optimizations such as breaking length-4 cycles that the N-NMS training process capitalized on during its training.

Download or read book Big Data Technology and Applications written by Wenguang Chen and published by Springer. This book was released on 2016-02-02 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First National Conference on Big Data Technology and Applications, BDTA 2015, held in Harbin, China, in December 2015. The 26 revised papers presented were carefully reviewed and selected from numerous submissions. The papers address issues such as the storage technology of Big Data; analysis of Big Data and data mining; visualization of Big Data; the parallel computing framework under Big Data; the architecture and basic theory of Big Data; collection and preprocessing of Big Data; innovative applications in some areas, such as internet of things and cloud computing.

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 Weight Distributions and Constructions of Low density Parity check Codes written by Chung-Li Wang and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-density parity-check (LDPC) codes are currently the most promising coding technique to achieve the Shannon capacities for a wide range of channels. These codes were first discovered by Gallager in 1962 and then rediscovered in late 1990's. Ever since their rediscovery, a great deal of research effort has been expended in design, construction, encoding, decoding, performance analysis, generalizations, and applications of LDPC codes. This research is set up to investigate two major aspects of LDPC codes: weight distributions and code constructions. The research focus of the first part is to analyze the asymptotic weight distributions of various ensembles. Analysis shows that for generalized LDPC (G-LDPC) and doubly generalized LDPC (DG-LDPC) code ensembles with some conditions, the average minimum distance grows linearly with the code length. This implies that both ensembles contain good codes. The effect of changing the component codes of the ensemble on the minimum distance is clarified. The computation of asymptotic weight and stopping set enumerators is improved. Furthermore, the average weight distribution of a multi-edge type code ensemble is investigated to obtain its upper and lower bounds. Based on them, the growth rate of the number of codewords is defined. For the growth rate of codewords with small linear, logarithmic, and constant weights, the approximations are given with two critical coefficients. It is shown that for infinite code length, the properties of the weight distribution are determined by its asymptotic growth rate. The second part of the research emphasizes specific designs and constructions of LDPC codes that not only perform well but can also be efficiently encoded. One such construction is the serial concatenation of an LDPC outer code and an accumulator with an interleaver. Such construction gives a code called an LDPCA code. The study shows that well designed LDPCA codes perform just as well as the regular LDPC codes. It also shows that the asymptotic minimum distance of regular LDPCA codes grows linearly with the code length.

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.

Download or read book LDPC Coding for Magnetic Storage Low Floor Decoding Algorithms System Design and Performance Analysis written by Yang Han and published by . This book was released on 2008 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-density parity check (LDPC) codes have experienced tremendous popularity due to their capacity-achieving performance. In this dissertation, several different aspects of LDPC coding and its applications to magnetic storage are investigated. One of the most significant issues that impedes the use of LDPC codes in many systems is the error-rate floor phenomenon associated with their iterative decoders. By delineating the fundamental principles, we extend to partial response channels algorithms for predicting the error rate performance in the floor region for the binary-input AWGN channel. We develop three classes of decoding algorithms for mitigating the error floor by directly tackling the cause of the problem: trapping sets. In our experiments, these algorithms provide multiple orders of improvement over conventional decoders at the cost of various implementation complexity increases. Product codes are widely used in magnetic recording systems where errors are both isolated and bursty. A dual-mode decoding technique for Reed-Solomon-code-based product codes is proposed, where the second decoding mode involves maximum-likelihood erasure decoding of the binary images of the Reed-Solomon codewords. By exploring a tape storage application, we demonstrate that this dual-mode decoding system dramatically improves the performance of product codes. Moreover, the complexity added by the second decoding mode is manageable. We also show the performance of this technique on a product code which has an LDPC code in thecolumns. Run-length-limited (RLL) codes are ubiquitous in today's disk drives. Using RLL codes has enabled drive designers to pack data very efficiently onto the platter surface by ensuring stable symbol-timing recovery. We consider a concatenation system design with an LDPC code and an RLL code as components to simultaneously achieve desirable features such as: soft information availability to the LDPC decoder, the preservation of the LDPC code's structure, and the capability of correcting long erasure bursts. We analyze the performance of LDPC-coded magnetic recording channel in the presence of media noise. We employ advanced signal processing for the pattern-dependent-noise-predictive channel detectors, and demonstrate that a gain of over 1 dB or a linear density gain of about 8% relative to a comparable Reed-Solomon is attainable by using an LDPC code.

Download or read book Optimizing and Decoding LDPC Codes with Graph based Techniques written by Amir H. Djahanshahi and published by . This book was released on 2010 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-density parity-check (LDPC) codes have been known for their outstanding error-correction capabilities. With low-complexity decoding algorithms and a near capacity performance, these codes are among the most promising forward error correction schemes. LDPC decoding algorithms are generally sub-optimal and their performance not only depends on the codes, but also on many other factors, such as the code representation. In particular, a given non-binary code can be associated with a number of different field or ring image codes. Additionally, each LDPC code can be described with many different Tanner graphs. Each of these different images and graphs can possibly lead to a different performance when used with iterative decoding algorithms. Consequently, in this dissertation we try to find better representations, i.e., graphs and images, for LDPC codes. We take the first step by analyzing LDPC codes over multiple-input single-output (MISO) channels. In an n_T by 1 MISO system with a modulation of alphabet size 2^M, each group of n_T transmitted symbols are combined and produce one received symbol at the receiver. As a result, we consider the LDPC-coded MISO system as an LDPC code over a 2^{M n_T}-ary alphabet. We introduce a modified Tanner graph to represent MISO-LDPC systems and merge the MISO symbol detection and binary LDPC decoding steps into a single message passing decoding algorithm. We present an efficient implementation for belief propagation decoding that significantly reduces the decoding complexity. With numerical simulations, we show that belief propagation decoding over modified graphs outperforms the conventional decoding algorithm for short length LDPC codes over unknown channels. Subsequently, we continue by studying images of non-binary LDPC codes. The high complexity of belief propagation decoding has been proven to be a detrimental factor for these codes. Thereby, we suggest employing lower complexity decoding algorithms over image codes instead. We introduce three classes of binary image codes for a given non-binary code, namely: basic, mixed, and extended binary image codes. We establish upper and lower bounds on the minimum distance of these binary image codes, and present two techniques to find binary image codes with better performance under belief propagation decoding algorithm. In particular, we present a greedy algorithm to find optimized binary image codes. We then proceed by investigation of the ring image codes. Specifically, we introduce matrix-ring-image codes for a given non-binary code. We derive a belief propagation decoding algorithm for these codes, and with numerical simulations, we demonstrate that the low-complexity belief propagation decoding of optimized image codes has a performance very close to the high complexity BP decoding of the original non-binary code. Finally, in a separate study, we investigate the performance of iterative decoders over binary erasure channels. In particular, we present a novel approach to evaluate the inherent unequal error protection properties of irregular LDPC codes over binary erasure channels. Exploiting the finite length scaling methodology, that has been used to study the average bit error rate of finite-length LDPC codes, we introduce a scaling approach to approximate the bit erasure rates in the waterfall region of variable nodes with different degrees. Comparing the bit erasure rates obtained from Monte Carlo simulation with the proposed scaling approximations, we demonstrate that the scaling approach provides a close approximation for a wide range of code lengths. In view of the complexity associated with the numerical evaluation of the scaling approximation, we also derive simpler upper and lower bounds and demonstrate through numerical simulations that these bounds are very close to the scaling approximation.

Download or read book Coded Computing written by Songze Li and published by . This book was released on 2020 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce the concept of “coded computing”, a novel computing paradigm that utilizes coding theory to effectively inject and leverage data/computation redundancy to mitigate several fundamental bottlenecks in large-scale distributed computing, namely communication bandwidth, straggler’s (i.e., slow or failing nodes) delay, privacy and security bottlenecks.

Download or read book Physical Layer Security and Quantum Key Distribution written by Ivan B. Djordjevic and published by Springer Nature. This book was released on 2019-09-14 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook integrates the most advanced topics of physical-layer security, cryptography, covert/stealth communications, quantum key distribution (QKD), and cyber security to tackle complex security issues. After introducing the reader to various concepts and practices, the author addresses how these can work together to target problems, rather than treating them as separate disciplines. This book offers students an in-depth exposition on: cryptography, information-theoretic approach to cryptography, physical-layer security, covert/stealth/low-probability of detection communications, quantum information theory, QKD, and cyber security; to mention few. The goal is to provide a unified description of the most advanced topics related to: (i) modern cryptography, (ii) physical-layer security, (iii) QKD, (iv) covert communications, and (v) cyber security. Each chapter is followed by a set of problems. Also, for readers to better understand the book, an appendix covers all needed background. Homework problems and lecture notes are available online. The book does not require any prior knowledge or prerequisite material.

Download or read book The First Outstanding 50 Years of Universit Politecnica delle Marche written by Sauro Longhi and published by Springer Nature. This book was released on 2020-01-03 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes significant multidisciplinary research findings at the Università Politecnica delle Marche and the expected future advances. It addresses some of the most dramatic challenges posed by today’s fast-growing, global society and the changes it has caused, while also discussing solutions to improve the wellbeing of human beings. The book covers the main research achievements made in the social sciences and humanities, and includes chapters that focus on understanding mechanisms that are relevant to all aspects of economic and social interactions among individuals. In line with Giorgio Fuà’s contribution, the interdisciplinary research being pursued at the Faculty of Economics of Università Politecnica delle Marche is aimed at interpreting the process of economic development in all of its facets, both at the national and local level, with a particular focus on profit and non-profit organizations. Various disciplines are covered, from economics to sociology, history, statistics, mathematics, law, accounting, finance and management.

Download or read book Computational Cryptography written by Joppe Bos and published by . This book was released on 2021-12-09 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.