Low-density Parity-check Codes with Erasures and Puncturing
Low-density Parity-check Codes with Erasures and Puncturing

Author: Jeongseok Ha Ha

Publisher:

Published: 2003

Total Pages:

ISBN-13:

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In this thesis, we extend applications of Low-Density Parity-Check (LDPC) codes to a combination of constituent sub-channels, which is a mixture of Gaussian channels with erasures. This model, for example, represents a common channel in magnetic recordings where thermal asperities in the system are detected and represented at the decoder as erasures. Although this channel is practically useful, we cannot find any previous work that evaluates performance of LDPC codes over this channel. We are also interested in practical issues such as designing robust LDPC codes for the mixture channel and predicting performance variations due to erasure patterns (random and burst), and finite block lengths. On time varying channels, a common error control strategy is to adapt the coding rate according to available channel state information (CSI). An effective way to realize this coding strategy is to use a single code and puncture it in a rate-compatible fashion, a so-called rate-compatible punctured code (RCPC). We are interested in the existence of good puncturing patterns for rate-changes that minimize performance loss. We show the existence of good puncturing patterns with analysis and verify the results with simulations. Universality of a channel code across a broad range of coding rates is a theoretically interesting topic. We are interested in the possibility of using the puncturing technique proposed in this thesis for designing universal LDPC codes. We also consider how to design high rate LDPC codes by puncturing low rate LDPC codes. The new design method can take advantage of longer effect block lengths, sparser parity-check matrices, and larger minimum distances of low rate LDPC codes.

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.

Essentials of Error-Control Coding
Essentials of Error-Control Coding

Author: Jorge Castiñeira Moreira

Publisher: John Wiley & Sons

Published: 2006-08-04

Total Pages: 388

ISBN-13: 0470035714

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Rapid advances in electronic and optical technology have enabled the implementation of powerful error-control codes, which are now used in almost the entire range of information systems with close to optimal performance. These codes and decoding methods are required for the detection and correction of the errors and erasures which inevitably occur in digital information during transmission, storage and processing because of noise, interference and other imperfections. Error-control coding is a complex, novel and unfamiliar area, not yet widely understood and appreciated. This book sets out to provide a clear description of the essentials of the subject, with comprehensive and up-to-date coverage of the most useful codes and their decoding algorithms. A practical engineering and information technology emphasis, as well as relevant background material and fundamental theoretical aspects, provides an in-depth guide to the essentials of Error-Control Coding. Provides extensive and detailed coverage of Block, Cyclic, BCH, Reed-Solomon, Convolutional, Turbo, and Low Density Parity Check (LDPC) codes, together with relevant aspects of Information Theory EXIT chart performance analysis for iteratively decoded error-control techniques Heavily illustrated with tables, diagrams, graphs, worked examples, and exercises Invaluable companion website features slides of figures, algorithm software, updates and solutions to problems Offering a complete overview of Error Control Coding, this book is an indispensable resource for students, engineers and researchers in the areas of telecommunications engineering, communication networks, electronic engineering, computer science, information systems and technology, digital signal processing and applied mathematics.

OFDM Baseband Receiver Design for Wireless Communications
OFDM Baseband Receiver Design for Wireless Communications

Author: Tzi-Dar Chiueh

Publisher: John Wiley & Sons

Published: 2008-04-15

Total Pages: 278

ISBN-13: 0470822481

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Orthogonal frequency-division multiplexing (OFDM) access schemes are becoming more prevalent among cellular and wireless broadband systems, accelerating the need for smaller, more energy efficient receiver solutions. Up to now the majority of OFDM texts have dealt with signal processing aspects. To address the current gap in OFDM integrated circuit (IC) instruction, Chiueh and Tsai have produced this timely text on baseband design. OFDM Baseband Receiver Design for Wireless Communications covers the gamut of OFDM technology, from theories and algorithms to architectures and circuits. Chiueh and Tsai give a concise yet comprehensive look at digital communications fundamentals before explaining modulation and signal processing algorithms in OFDM receivers. Moreover, the authors give detailed treatment of hardware issues -- from design methodology to physical IC implementation. Closes the gap between OFDM theory and implementation Enables the reader to transfer communication receiver concepts into hardware design wireless receivers with acceptable implementation loss achieve low-power designs Contains numerous figures to illustrate techniques Features concrete design examples of MC-CDMA systems and cognitive radio applications Presents theoretical discussions that focus on concepts rather than mathematical derivation Provides a much-needed single source of material from numerous papers Based on course materials for a class in digital communication IC design, this book is ideal for advanced undergraduate or post-graduate students from either VLSI design or signal processing backgrounds. New and experienced engineers in industry working on algorithms or hardware for wireless communications devices will also find this book to be a key reference.

Coding Theory and Applications
Coding Theory and Applications

Author: Ángela I. Barbero

Publisher: Springer

Published: 2017-08-22

Total Pages: 306

ISBN-13: 3319662783

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This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017. The 24 full papers presented were carefully reviewed and selected for inclusion in this volume. The papers cover relevant research areas in modern coding theory, including codes and combinatorial structures, algebraic geometric codes, group codes, convolutional codes, network coding, other applications to communications, and applications of coding theory in cryptography.

Algebraic Low-density Parity-check Codes
Algebraic Low-density Parity-check Codes

Author: Qiuju Diao

Publisher:

Published: 2013

Total Pages:

ISBN-13: 9781303442414

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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.