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Author: Keke Liu
Publisher:
ISBN: 9781321806663
Category :
Languages : en
Pages :
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Book Description
The algebraic low-density parity-check (LDPC) codes have received great attention in the practical applications to communication and data storage systems due to their fruitful structural properties and excellent overall performances. This dissertation investigates the following topics regarding the construction, analysis and decoding of the algebraic LDPC codes.The first contribution is a comprehensive rank analysis of the algebraic quasi-cyclic (QC) LDPC (QC-LDPC) codes constructed based on two arbitrary subsets of a finite field, which generalizes the rank analysis results in the previous literature. Also investigated is a flexible algebraic construction of QC-LDPC codes with large row redundancy based on field partitions. This construction results in a large class of binary regular QC-LDPC codes with flexible choices of rates and lengths that are shown to perform well over the additive white Gaussian noise (AWGN) channel. Secondly, to resolve the issue of decoder complexity caused by relatively high density of the parity-check matrices of algebraic LDPC codes, an effective revolving iterative decoding (RID) scheme is developed for algebraic cyclic and QC-LDPC codes. The proposed RID scheme significantly reduces the hardware implementation complexities. Also presented is a variation of the RID scheme, called merry-go-round (MGR) decoding scheme, which maintains the circulant permutation matrix (CPM) structure that is desirable for the hardware implementation but lost in the RID scheme, while preserving the merits of reducing decoder complexity. The proposed RID and MGR decoding schemes may enhance the applications of algebraic LDPC codes.Lastly, a general algebraic construction of QC-LDPC convolutional codes, also called spatially coupled (SC) QC-LDPC codes, is proposed. Simulation results show that the constructed algebraic SC-QC-LDPC codes can outperform their non-algebraic counterparts. Also investigated is the rate compatibility of the constructed SC-QC-LDPC codes using the regular puncturing scheme.
Author: Keke Liu
Publisher:
ISBN: 9781321806663
Category :
Languages : en
Pages :
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Book Description
The algebraic low-density parity-check (LDPC) codes have received great attention in the practical applications to communication and data storage systems due to their fruitful structural properties and excellent overall performances. This dissertation investigates the following topics regarding the construction, analysis and decoding of the algebraic LDPC codes.The first contribution is a comprehensive rank analysis of the algebraic quasi-cyclic (QC) LDPC (QC-LDPC) codes constructed based on two arbitrary subsets of a finite field, which generalizes the rank analysis results in the previous literature. Also investigated is a flexible algebraic construction of QC-LDPC codes with large row redundancy based on field partitions. This construction results in a large class of binary regular QC-LDPC codes with flexible choices of rates and lengths that are shown to perform well over the additive white Gaussian noise (AWGN) channel. Secondly, to resolve the issue of decoder complexity caused by relatively high density of the parity-check matrices of algebraic LDPC codes, an effective revolving iterative decoding (RID) scheme is developed for algebraic cyclic and QC-LDPC codes. The proposed RID scheme significantly reduces the hardware implementation complexities. Also presented is a variation of the RID scheme, called merry-go-round (MGR) decoding scheme, which maintains the circulant permutation matrix (CPM) structure that is desirable for the hardware implementation but lost in the RID scheme, while preserving the merits of reducing decoder complexity. The proposed RID and MGR decoding schemes may enhance the applications of algebraic LDPC codes.Lastly, a general algebraic construction of QC-LDPC convolutional codes, also called spatially coupled (SC) QC-LDPC codes, is proposed. Simulation results show that the constructed algebraic SC-QC-LDPC codes can outperform their non-algebraic counterparts. Also investigated is the rate compatibility of the constructed SC-QC-LDPC codes using the regular puncturing scheme.
Author: Ivana Djurdjevic
Publisher:
ISBN:
Category :
Languages : en
Pages : 320
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Book Description
Author: Bo Zhou
Publisher:
ISBN:
Category :
Languages : en
Pages : 292
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Book Description
Author: Dave K. Kythe
Publisher: CRC Press
ISBN: 1466505621
Category : Computers
Languages : en
Pages : 507
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Book Description
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.
Author: Lingqi Zeng
Publisher:
ISBN:
Category :
Languages : en
Pages : 328
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Author: Lan Lan
Publisher:
ISBN:
Category :
Languages : en
Pages : 340
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Book Description
Author: Edgar Martinez-Moro
Publisher: World Scientific
ISBN: 9814335754
Category : Computers
Languages : en
Pages : 334
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Book Description
Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.
Author: Qiuju Diao
Publisher:
ISBN: 9781303442414
Category :
Languages : en
Pages :
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Book Description
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.
Author: Martin Tomlinson
Publisher: Springer
ISBN: 3319511033
Category : Technology & Engineering
Languages : en
Pages : 527
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Book Description
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.
Author: Simeon Ball
Publisher: Springer Nature
ISBN: 3030411532
Category : Mathematics
Languages : en
Pages : 185
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Book Description
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.
