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.
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.
It has long been recognized that there are fascinating connections between cod ing theory, cryptology, and combinatorics. Therefore it seemed desirable to us to organize a conference that brings together experts from these three areas for a fruitful exchange of ideas. We decided on a venue in the Huang Shan (Yellow Mountain) region, one of the most scenic areas of China, so as to provide the additional inducement of an attractive location. The conference was planned for June 2003 with the official title Workshop on Coding, Cryptography and Combi natorics (CCC 2003). Those who are familiar with events in East Asia in the first half of 2003 can guess what happened in the end, namely the conference had to be cancelled in the interest of the health of the participants. The SARS epidemic posed too serious a threat. At the time of the cancellation, the organization of the conference was at an advanced stage: all invited speakers had been selected and all abstracts of contributed talks had been screened by the program committee. Thus, it was de cided to call on all invited speakers and presenters of accepted contributed talks to submit their manuscripts for publication in the present volume. Altogether, 39 submissions were received and subjected to another round of refereeing. After care ful scrutiny, 28 papers were accepted for publication.
Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.
Foreword by James L. Massey. Codes, Graphs, and Systems is an excellent reference for both academic researchers and professional engineers working in the fields of communications and signal processing. A collection of contributions from world-renowned experts in coding theory, information theory, and signal processing, the book provides a broad perspective on contemporary research in these areas. Survey articles are also included. Specific topics covered include convolutional codes and turbo codes; detection and equalization; modems; physics and information theory; lattices and geometry; and behaviors and codes on graphs. Codes, Graphs, and Systems is a tribute to the leadership and profound influence of G. David Forney, Jr. The 35 contributors to the volume have assembled their work in his honor.
This book introduces the theoretical elements at the basis of various classes of algorithms commonly employed in the physical layer (and, in part, in MAC layer) of wireless communications systems. It focuses on single user systems, so ignoring multiple access techniques. Moreover, emphasis is put on single-input single-output (SISO) systems, although some relevant topics about multiple-input multiple-output (MIMO) systems are also illustrated. Comprehensive wireless specific guide to algorithmic techniques Provides a detailed analysis of channel equalization and channel coding for wireless applications Unique conceptual approach focusing in single user systems Covers algebraic decoding, modulation techniques, channel coding and channel equalisation
Offers concise, practical knowledge on modern communication systems to help students transition smoothly into the workplace and beyond This book presents the most relevant concepts and technologies of today's communication systems and presents them in a concise and intuitive manner. It covers advanced topics such as Orthogonal Frequency-Division Multiplexing (OFDM) and Multiple-Input Multiple-Output (MIMO) Technology, which are enabling technologies for modern communication systems such as WiFi (including the latest enhancements) and LTE-Advanced. Following a brief introduction to the field, Digital Communication for Practicing Engineers immerses readers in the theories and technologies that engineers deal with. It starts off with Shannon Theorem and Information Theory, before moving on to basic modules of a communication system, including modulation, statistical detection, channel coding, synchronization, and equalization. The next part of the book discusses advanced topics such as OFDM and MIMO, and introduces several emerging technologies in the context of 5G cellular system radio interface. The book closes by outlining several current research areas in digital communications. In addition, this text: Breaks down the subject into self-contained lectures, which can be read individually or as a whole Focuses on the pros and cons of widely used techniques, while providing references for detailed mathematical analysis Follows the current technology trends, including advanced topics such as OFDM and MIMO Touches on content this is not usually contained in textbooks such as cyclo-stationary symbol timing recovery, adaptive self-interference canceler, and Tomlinson-Harashima precoder Includes many illustrations, homework problems, and examples Digital Communication for Practicing Engineers is an ideal guide for graduate students and professionals in digital communication looking to understand, work with, and adapt to the current and future technology.
