Download or read book Non binary Protograph based LDPC Codes written by Yizeng Sun and published by . This book was released on 2013 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-binary LDPC codes can outperform binary LDPC codes using sum-product algorithm with higher computation complexity. Non-binary LDPC codes based on protographs have the advantage of simple hardware architecture. In the first part of this thesis, we will use EXIT chart analysis to compute the thresholds of different protographs over GF(q). Based on threshold computation, some non-binary protograph-based LDPC codes are designed and their frame error rates are compared with binary LDPC codes. For maximum-likelihood decoder, weight enumerator can predict frame error rate of an LDPC code. In the second part of this thesis, we calculate weight enumerators of protograph-based non-binary LDPC code ensembles both for finite length case and asymptotic case. In addition, the trapping set and stopping set enumerators are presented.

Download or read book Theory and Practice of Non binary Graph based Codes written by Behzad Amiri and published by . This book was released on 2015 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are undergoing a revolution in data. The ever-growing amount of information in our world has created an unprecedented demand for ultra-reliable, affordable, and resource-efficient data storage systems. Error-correcting codes, as a critical component of any memory device, will play a crucial role in the future of data storage. One particular class of error-correcting codes, known as graph-based codes, has drawn significant attention in both academia and in industry. Graph-based codes offer superior performance compared to traditional algebraic codes. Recently, it has been shown that non-binary graph-based codes, which operate over finite fields rather than binary alphabets, outperform their binary counterparts and exhibit outstanding overall performance. For this reason, these codes are particularly suitable for emerging data storage systems. In this dissertation, we present a comprehensive combinatorial analysis of non-binary graph-based codes. We perform both finite-length and asymptotic analyses for these codes, providing a systematic framework to evaluate and optimize various families of non-binary graph-based codes. In the finite-length case, we provide a mathematical characterization of the error floor problem, including a general definition of absorbing sets over non-binary alphabets. We consider several structured low-density parity-check (LDPC) codes, including quasi-cyclic and spatially-coupled codes, as well as unstructured LDPC codes. We offer design guidelines for non-binary LDPC codes with outstanding performance in extremely low error-rate regimes; making them excellent candidates for data storage applications. In the asymptotic case, we provide a novel toolbox for the evaluation of families of non-binary graph-based codes. By utilizing insights from graph theory and combinatorics, we establish enumerators for a general family of graph-based codes which are constructed based on protographs. We provide asymptotic distributions of codewords and trapping sets for the family of protograph-based codes. Furthermore, we present an asymptotic enumeration of binary and non-binary elementary absorbing sets for regular code ensembles. The contributions of this dissertation can potentially impact a broad range of data storage and communication technologies that require excellent performance in high-reliability regimes.

Download or read book Algebraic Constructions of High Performance and Efficiently Encodable Non binary Quasi cyclic LDPC Codes written by Bo Zhou and published by . This book was released on 2008 with total page 292 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 A Class of Non binary LDPC Codes written by Deepak Gilra 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 study Low Density Parity Check (LDPC) and LDPC like codes over non-binary fields. We extend the concepts used for non-binary LDPC codes to generalize Product Accumulate (PA) codes to non-binary fields. We present simulation results that show that PA codes over GF(4) performs considerably better than binary PA codes at smaller block lengths and slightly better at large block lengths. We also propose a trellis based decoding algorithm to decode PA codes and show that its complexity is considerably lower than the message-passing algorithm. In the second part of the thesis we study the convergence properties of non-binary PA codes and non-binary LDPC codes. We use EXIT-charts to study the convergence properties of non-binary LDPC codes with different mean column weights and show why certain irregularities are better. Although the convergence threshold predicted by EXIT-charts on non-binary LDPC codes is quite optimistic we can still use EXIT-charts for comparison between non-binary LDPC codes with different mean column weights.

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 Artificial Intelligence and Evolutionary Algorithms in Engineering Systems written by L Padma Suresh and published by Springer. This book was released on 2014-11-25 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of high-quality peer-reviewed research papers presented in Proceedings of International Conference on Artificial Intelligence and Evolutionary Algorithms in Engineering Systems (ICAEES 2014) held at Noorul Islam Centre for Higher Education, Kumaracoil, India. These research papers provide the latest developments in the broad area of use of artificial intelligence and evolutionary algorithms in engineering systems. The book discusses wide variety of industrial, engineering and scientific applications of the emerging techniques. It presents invited papers from the inventors/originators of new applications and advanced technologies.

Download or read book Nested Low density Lattice Codes Based on Non binary LDPC Codes written by Ankit Ghiya and published by . This book was released on 2010 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: A family of low-density lattice codes (LDLC) is studied based on Construction-A for lattices. The family of Construction-A codes is already known to contain a large capacity-achieving subset. Parallels are drawn between coset non-binary low-density parity-check (LDPC) codes and nested low-density Construction-A lattices codes. Most of the related research in LDPC domain assumes optimal power allocation to encoded codeword. The source coding problem of mapping message to power optimal codeword for any LDPC code is in general, NP-hard. In this thesis, we present a novel method for encoding and decoding lattice based on non-binary LDPC codes using message-passing algorithms.

Download or read book Non Binary Error Control Coding for Wireless Communication and Data Storage written by Rolando Antonio Carrasco and published by John Wiley & Sons. This book was released on 2008-11-20 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to non-binary error-correction coding techniques Non-Binary Error Control Coding for Wireless Communication and Data Storage explores non-binary coding schemes that have been developed to provide an alternative to the Reed – Solomon codes, which are expected to become unsuitable for use in future data storage and communication devices as the demand for higher data rates increases. This book will look at the other significant non-binary coding schemes, including non-binary block and ring trellis-coded modulation (TCM) codes that perform well in fading conditions without any expansion in bandwidth use, and algebraic-geometric codes which are an extension of Reed-Solomon codes but with better parameters. Key Features: Comprehensive and self-contained reference to non-binary error control coding starting from binary codes and progressing up to the latest non-binary codes Explains the design and construction of good non-binary codes with descriptions of efficient non-binary decoding algorithms with applications for wireless communication and high-density data storage Discusses the application to specific cellular and wireless channels, and also magnetic storage channels that model the reading of data from the magnetic disc of a hard drive. Includes detailed worked examples for each coding scheme to supplement the concepts described in this book Focuses on the encoding, decoding and performance of both block and convolutional non-binary codes, and covers the Kötter-Vardy algorithm and Non-binary LDPC codes This book will be an excellent reference for researchers in the wireless communication and data storage communities, as well as development/research engineers in telecoms and storage companies. Postgraduate students in these fields will also find this book of interest.

Download or read book Low complexity Decoding Algorithms and Architectures for Non binary LDPC Codes written by Fang Cai and published by . This book was released on 2013 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than their binary counterparts when the code length is moderate at the cost of higher decoding complexity. The high complexity is mainly caused by the complicated computations in the check node processing and the large memory requirement. In this thesis, three decoding algorithms and corresponding VLSI architectures are proposed for NB-LDPC codes to lower the computational complexity and memory requirement. The first design is based on the proposed relaxed Min-max decoding algorithm. A novel relaxed check node processing scheme is proposed for the Min-max NB-LDPC decoding algorithm. Each finite field element of GF(2p̂) can be uniquely represented by a linear combination of $p$ independent field elements. Making use of this property, an innovative method is developed in this paper to first find a set of the p most reliable variable-to-check messages with independent field elements, called the minimum basis. Then the check-to-variable messages are efficiently computed from the minimum basis. With very small performance loss, the complexity of the check node processing can be substantially reduced using the proposed scheme. In addition, efficient VLSI architectures are developed to implement the proposed check node processing and overall NB-LDPC decoder. Compared to the most efficient prior design, the proposed decoder for a (837, 726) NB-LDPC code over GF(25̂) can achieve 52% higher efficiency in terms of throughput-over-area ratio. The second design is based on a proposed enhanced iterative hard reliability-based majority-logic decoding. The recently developed iterative hard reliability-based majority-logic NB-LDPC decoding has better performance-complexity tradeoffs than previous algorithms. Novel schemes are proposed for the iterative hard reliability-based majority-logic decoding (IHRB-MLGD). Compared to the IHRB algorithm, our enhanced (E- )IHRB algorithm can achieve significant coding gain with small hardware overhead. Then low-complexity partial-parallel NB-LDPC decoder architectures are developed based on these two algorithms. Many existing NB-LDPC code construction methods lead to quasi-cyclic or cyclic codes. Both types of codes are considered in our design. Moreover, novel schemes are developed to keep a small proportion of messages in order to reduce the memory requirement without causing noticeable performance loss. In addition, a shift-message structure is proposed by using memories concatenated with variable node units to enable efficient partial-parallel decoding for cyclic NB-LDPC codes. Compared to previous designs based on the Min-max decoding algorithm, our proposed decoders have at least tens of times lower complexity with moderate coding gain loss. The third design is based on a proposed check node decoding scheme using power representation of finite field elements. Novel schemes are proposed for the Min-max check node processing by making use of the cyclical-shift property of the power representation of finite field elements. Compared to previous designs based on the Min-max algorithm with forward-backward scheme, the proposed check node units (CNUs) do not need the complex switching network. Moreover, the multiplications of the parity check matrix entries are efficiently incorporated. For a Min-max NB-LDPC decoder over GF(32), the proposed scheme reduces the CNU area by at least 32%, and leads to higher clock frequency.

Download or read book Adaptive Multiset Stochastic Decoding of Non binary LDPC Codes written by Alexandru Ciobanu and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Performance and Energy Efficient Decoder Design for Non Binary LDPC Codes written by Yuta Toriyama and published by . This book was released on 2016 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Binary Low-Density Parity-Check (LDPC) codes are a type of error correction code known to exhibit excellent error-correcting capabilities, and have increasingly been applied as the forward error correction solution in a multitude of systems and standards, such as wireless communications, wireline communications, and data storage systems. In the pursuit of codes with even higher coding gain, non-binary LDPC (NB-LDPC) codes defined over a Galois field of order q have risen as a strong replacement candidate. For codes defined with similar rate and length, NB-LDPC codes exhibit a significant coding gain improvement relative to that of their binary counterparts. Unfortunately, NB-LDPC codes are currently limited from practical application by the immense complexity of their decoding algorithms, because the improved error-rate performance of higher field orders comes at the cost of increasing decoding algorithm complexity. Currently available ASIC implementation solutions for NB-LDPC code decoders are simultaneously low in throughput and power-hungry, leading to a low energy efficiency. We propose several techniques at the algorithm level as well as hardware architecture level in an attempt to bring NB-LDPC codes closer to practical deployment. On the algorithm side, we propose several algorithmic modifications and analyze the corresponding hardware cost alleviation as well as impact on coding gain. We also study the quantization scheme for NB-LDPC decoders, again in the context of both the hardware and coding gain impacts, and we propose a technique that enables a good tradeoff in this space. On the hardware side, we develop a FPGA-based NB-LDPC decoder platform for architecture prototyping as well as hardware acceleration of code evaluation via error rate simulations. We also discuss the architectural techniques and innovations corresponding to our proposed algorithm for optimization of the implementation. Finally, a proof-of-concept ASIC chip is realized that integrates many of the proposed techniques. We are able to achieve a 3.7x improvement in the information throughput and 23.8x improvement in the energy efficiency over prior state-of-the-art, without sacrificing the strong error correcting capabilities of the NB-LDPC code.

Download or read book LDPC Codes Over Non binary Alphabets written by Ariel Amir and published by . This book was released on 2006 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 Analysis and Design of Protograph Based LDPC Codes and Ensembles written by Jeremy Thorpe and published by . This book was released on 2005 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book 3D Flash Memories written by Rino Micheloni and published by Springer. This book was released on 2016-05-26 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book walks the reader through the next step in the evolution of NAND flash memory technology, namely the development of 3D flash memories, in which multiple layers of memory cells are grown within the same piece of silicon. It describes their working principles, device architectures, fabrication techniques and practical implementations, and highlights why 3D flash is a brand new technology. After reviewing market trends for both NAND and solid state drives (SSDs), the book digs into the details of the flash memory cell itself, covering both floating gate and emerging charge trap technologies. There is a plethora of different materials and vertical integration schemes out there. New memory cells, new materials, new architectures (3D Stacked, BiCS and P-BiCS, 3D FG, 3D VG, 3D advanced architectures); basically, each NAND manufacturer has its own solution. Chapter 3 to chapter 7 offer a broad overview of how 3D can materialize. The 3D wave is impacting emerging memories as well and chapter 8 covers 3D RRAM (resistive RAM) crosspoint arrays. Visualizing 3D structures can be a challenge for the human brain: this is way all these chapters contain a lot of bird’s-eye views and cross sections along the 3 axes. The second part of the book is devoted to other important aspects, such as advanced packaging technology (i.e. TSV in chapter 9) and error correction codes, which have been leveraged to improve flash reliability for decades. Chapter 10 describes the evolution from legacy BCH to the most recent LDPC codes, while chapter 11 deals with some of the most recent advancements in the ECC field. Last but not least, chapter 12 looks at 3D flash memories from a system perspective. Is 14nm the last step for planar cells? Can 100 layers be integrated within the same piece of silicon? Is 4 bit/cell possible with 3D? Will 3D be reliable enough for enterprise and datacenter applications? These are some of the questions that this book helps answering by providing insights into 3D flash memory design, process technology and applications.