Error-Correction Coding and Decoding
Error-Correction Coding and Decoding

Author: Martin Tomlinson

Publisher: Springer

Published: 2017-02-21

Total Pages: 527

ISBN-13: 3319511033

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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.

Design of Rate-compatible Structured Low-density Parity-check Codes
Design of Rate-compatible Structured Low-density Parity-check Codes

Author: Jaehong Kim

Publisher:

Published: 2006

Total Pages:

ISBN-13:

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The main objective of our research is to design practical low-density parity-check (LDPC) codes which provide a wide range of code rates in a rate-compatible fashion. To this end, we first propose a rate-compatible puncturing algorithm for LDPC codes at short block lengths (up to several thousand symbols). The proposed algorithm is based on the claim that a punctured LDPC code with a smaller level of recoverability has better performance. The proposed algorithm is verified by comparing performance of intentionally punctured LDPC codes (using the proposed algorithm) with randomly punctured LDPC codes. The intentionally punctured LDPC codes show better bit error rate (BER) performances at practically short block lengths. Even though the proposed puncturing algorithm shows excellent performance, several problems are still remained for our research objective. First, how to design an LDPC code of which structure is well suited for the puncturing algorithm. Second, how to provide a wide range of rates since there is a puncturing limitation with the proposed puncturing algorithm. To attack these problems, we propose a new class of LDPC codes, called efficiently-encodable rate-compatible (E2RC) codes, in which the proposed puncturing algorithm concept is imbedded. The E2RC codes have several strong points. First, the codes can be efficiently encoded. We present low-complexity encoder implementation with shift-register circuits. In addition, we show that a simple erasure decoder can also be used for the linear-time encoding of these codes. Thus, we can share a message-passing decoder for both encoding and decoding in transceiver systems that require an encoder/decoder pair. Second, we show that the non-systematic parts of the parity-check matrix are cycle-free, which ensures good code characteristics. Finally, the E2RC codes having a systematic rate-compatible puncturing structure show better puncturing performance than any other LDPC codes in all ranges of code rates.

Construction of Low Density Parity Check Codes Without Short Cycles
Construction of Low Density Parity Check Codes Without Short Cycles

Author: Lizhi Wu

Publisher:

Published: 2003

Total Pages: 0

ISBN-13:

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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.

Resource Efficient LDPC Decoders
Resource Efficient LDPC Decoders

Author: Vikram Arkalgud Chandrasetty

Publisher: Academic Press

Published: 2017-12-05

Total Pages: 192

ISBN-13: 0128112565

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This book takes a practical hands-on approach to developing low complexity algorithms and transforming them into working hardware. It follows a complete design approach – from algorithms to hardware architectures - and addresses some of the challenges associated with their design, providing insight into implementing innovative architectures based on low complexity algorithms.The reader will learn: Modern techniques to design, model and analyze low complexity LDPC algorithms as well as their hardware implementation How to reduce computational complexity and power consumption using computer aided design techniques All aspects of the design spectrum from algorithms to hardware implementation and performance trade-offs Provides extensive treatment of LDPC decoding algorithms and hardware implementations Gives a systematic guidance, giving a basic understanding of LDPC codes and decoding algorithms and providing practical skills in implementing efficient LDPC decoders in hardware Companion website containing C-Programs and MATLAB models for simulating the algorithms, and Verilog HDL codes for hardware modeling and synthesis

A Study of Low Density Parity-Check Codes Using Systematic Repeat-Accumulate Codes
A Study of Low Density Parity-Check Codes Using Systematic Repeat-Accumulate Codes

Author:

Publisher:

Published: 2015

Total Pages: 82

ISBN-13:

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Low Density Parity-Check, or LDPC, codes have been a popular error correction choice in the recent years. Its use of soft-decision decoding through a message-passing algorithm and its channel-capacity approaching performance has made LDPC codes a strong alternative to that of Turbo codes. However, its disadvantages, such as encoding complexity, discourages designers from implementing these codes. This thesis will present a type of error correction code which can be considered as a subset of LDPC codes. These codes are called Repeat-Accumulate codes and are named such because of their encoder structure. These codes is seen as a type of LDPC codes that has a simple encoding method similar to Turbo codes. What makes these codes special is that they can have a simple encoding process and work well with a soft-decision decoder. At the same time, RA codes have been proven to be codes that will work well at short to medium lengths if they are systematic. Therefore, this thesis will argue that LDPC codes can avoid some of its encoding disadvantage by becoming LDPC codes with systematic RA codes. This thesis will also show in detail how RA codes are good LDPC codes by comparing its bit error performance against other LDPC simulation results tested at short to medium code lengths and with different LDPC parity-check matrix constructions. With an RA parity-check matrix describing our LDPC code, we will see how changing the interleaver structure from a random construction to that of a structured can lead to improved performance. Therefore, this thesis will experiment using three different types of interleavers which still maintain the simplicity of encoding complexity of the encoder but at the same time show potential improvement of bit error performance compared to what has been previously seen with regular LDPC codes.

Codes and turbo codes
Codes and turbo codes

Author: Claude Berrou

Publisher: Springer Science & Business Media

Published: 2011-01-27

Total Pages: 400

ISBN-13: 2817800397

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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.

Linear-time Encodable Low-density Parity-check Codes
Linear-time Encodable Low-density Parity-check Codes

Author: Amir Meidan

Publisher:

Published: 1998

Total Pages:

ISBN-13:

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In this thesis, a class of Low-Density Parity-Check codes with the property that encoding can be performed in time linearly proportional to block length, is presented. These codes were named Linear-Time Encodable Low-Density Parity-Check codes (LE-LDPC). The necessary background theory is examined, concentrating on factor graphs and APP iterative decoding algorithms. Furthermore, the various details of the construction of LE-LDPC codes are also examined. A number of algorithmic modifications which yielded significant improvement in decoding performance are proposed. Simulation results are presented wherein code performance is examined as a function of a variety of construction parameters such as block size and graph structure. Lastly, LE-LDPC codes are shown to perform well compared with similar codes; even at the relatively short block lengths necessary for application in personal communication systems.

Channel Codes
Channel Codes

Author: William Ryan

Publisher: Cambridge University Press

Published: 2009-09-17

Total Pages: 709

ISBN-13: 1139483013

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Channel coding lies at the heart of digital communication and data storage, and this detailed introduction describes the core theory as well as decoding algorithms, implementation details, and performance analyses. In this book, Professors Ryan and Lin provide clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes. They also present detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, and product codes, providing a one-stop resource for both classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design. 250 varied and stimulating end-of-chapter problems are also included to test and enhance learning, making this an essential resource for students and practitioners alike.