Construction of Low Density Parity Check Codes Without Short Cycles PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Construction of Low Density Parity Check Codes Without Short Cycles PDF full book. Access full book title Construction of Low Density Parity Check Codes Without Short Cycles by Lizhi Wu. Download full books in PDF and EPUB format.
Author: Lizhi Wu
Publisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 0
Get Book Here
Book Description
With the rapid expansion of communication networks, there has been an increasing demand for efficient and reliable digital data transmission and storage systems. Many efficient codes have been developed. The LDPC code is one of them. In this thesis, the sum-product algorithm is used in the decoding of LDPC codes. Some schemes for encoding LDPC codes have been studied. In particular, two methods of producing regular H matrices have been attempted that include short cycles of length four with code rates of 0.5, and we present three schemes of finding regular H matrices which do not include short cycles of length four with code rate being 0.5. The effect of short cycles in the bipartite graph of regular LDPC codes has been considered. The simulation results show that the BER performances of regular H matrices that do not include short cycles of length four based on BPSK or 8PSK on AWGN channel is better than those of regular H matrices that include short cycles of length four. In conclusion, in order to obtain good performance with LDPC code, one should design H matrix related to bipartite graph without short cycles.
Author: Lizhi Wu
Publisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 0
Get Book Here
Book Description
With the rapid expansion of communication networks, there has been an increasing demand for efficient and reliable digital data transmission and storage systems. Many efficient codes have been developed. The LDPC code is one of them. In this thesis, the sum-product algorithm is used in the decoding of LDPC codes. Some schemes for encoding LDPC codes have been studied. In particular, two methods of producing regular H matrices have been attempted that include short cycles of length four with code rates of 0.5, and we present three schemes of finding regular H matrices which do not include short cycles of length four with code rate being 0.5. The effect of short cycles in the bipartite graph of regular LDPC codes has been considered. The simulation results show that the BER performances of regular H matrices that do not include short cycles of length four based on BPSK or 8PSK on AWGN channel is better than those of regular H matrices that include short cycles of length four. In conclusion, in order to obtain good performance with LDPC code, one should design H matrix related to bipartite graph without short cycles.
Author: Martin Tomlinson
Publisher: Springer
ISBN: 3319511033
Category : Technology & Engineering
Languages : en
Pages : 527
Get Book Here
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: Lei Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 340
Get Book Here
Book Description
Author: Ivana Djurdjevic
Publisher:
ISBN:
Category :
Languages : en
Pages : 320
Get Book Here
Book Description
Author: A. Donald Keedwell
Publisher: Elsevier
ISBN: 0444635580
Category : Mathematics
Languages : en
Pages : 443
Get Book Here
Book Description
Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties. Retains the organization and updated foundational material from the original edition Explores current and emerging research topics Includes the original 73 ‘Unsolved Problems’ with the current state of knowledge regarding them, as well as new Unsolved Problems for further study
Author: Sarah J. Johnson
Publisher: Cambridge University Press
ISBN: 0521871484
Category : Computers
Languages : en
Pages : 356
Get Book Here
Book Description
Presents all of the key ideas needed to understand, design, implement and analyse iterative-based error correction schemes.
Author: Juane Li
Publisher:
ISBN: 9781369201024
Category :
Languages : en
Pages :
Get Book Here
Book Description
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.
Author: Onur Osman
Publisher: CRC Press
ISBN: 1420054627
Category : Computers
Languages : en
Pages : 362
Get Book Here
Book Description
Modern error control coding methods based on turbo coding have essentially solved the problem of reliable data communications over noisy channels. Contemporary Coding Techniques and Applications for Mobile Communications provides a clear, comprehensive, and practical grounding on the subject matter, examining the fundamentals, theory, and ap
Author: Claude Berrou
Publisher: Springer Science & Business Media
ISBN: 2817800397
Category : Computers
Languages : en
Pages : 400
Get Book Here
Book Description
This book is devoted to one of the essential functions of modern telecommunications systems: channel coding or error correction coding. Its main topic is iteratively decoded algebraic codes, convolutional codes and concatenated codes.
Author: Fa-Long Luo
Publisher: Springer Science & Business Media
ISBN: 9780387782621
Category : Technology & Engineering
Languages : en
Pages : 671
Get Book Here
Book Description
Mobile multimedia broadcasting compasses a broad range of topics including radio propagation, modulation and demodulation, error control, signal compression and coding, transport and time slicing, system on chip real-time implementation in ha- ware, software and system levels. The major goal of this technology is to bring multimedia enriched contents to handheld devices such as mobile phones, portable digital assistants, and media players through radio transmission or internet pro- col (IP) based broadband networks. Research and development of mobile multi- dia broadcasting technologies are now explosively growing and regarded as new killer applications. A number of mobile multimedia broadcasting standards related to transmission, compression and multiplexing now coexist and are being ext- sively further developed. The development and implementation of mobile multi- dia broadcasting systems are very challenging tasks and require the huge efforts of the related industry, research and regulatory authorities so as to bring the success. From an implementation design and engineering practice point of view, this book aims to be the ?rst single volume to provide a comprehensive and highly coherent treatment for multiple standards of mobile multimedia broadcasting by covering basic principles, algorithms, design trade-off, and well-compared implementation system examples. This book is organized into 4 parts with 22 chapters.
