低密度奇偶校驗碼：設計、構造與統(tǒng)一框架

　　Error control codes protect the accuracy of data in modern information sys-tems，including computing，communication，and storage systems. Low-density parity-check （LDPC） codes and their relatives represent the state of the art in error control coding and are renowned for their ability to perform close to the theoretical limits. This book presents recent results on various LDPC code designs，making strong connections between two prominent design approaches，the algebraic-based and the graph theoretic-based constructions. New codes and code construction techniques are presented.Most methods for constructing LDPC codes can be classified into two general categories，the algebraic-based and the graph-theoretic-based constructions. The two best-known graph-theoretic-based construction methods are the progressive edge-growth （PEG） and the protograph-based （PTG-based） methods，devised in 2001 and 2003，respectively. Both of these techniques involve computer-aided design. One of the earliest algebraic-based methods for constructing LDPC codes is the superposition （SP） construction，proposed in 2002. In this book，the algebraic-based construction method is re-interpreted from both the algebraic and the graph-theoretic perspectives. From the algebraic point of view，it is shown that the SP-construction of LDPC codes includes，as special cases，most of the major algebraic construction methods developed since 2002. From the graph-theoretic point of view，it is shown that the SP-construction also includes the PTG-based construction as a special case. Based on this PTG/SP connection，an algebraic method is developed here to construct PTG-based LDPC codes.There are advantages to putting the algebraic-based and the PTG-based constructions into a single framework，the SP framework. One advantage is that SP descriptions of codes tend to be relatively compact，enabling simple code specifications in standards and textbooks. Another advantage to studying LDPC codes under the SP framework is that students and practitioners need only learn a single code design approach rather than the myriad approaches that exist in the published literature.Both binary and nonbinary code constructions will be presented under the SP framework. The SP-construction also leads to a new class of LDPC codes with a doubly quasi-cyclic （QC） structure as well as algebraic methods for constructing spatially and globally coupled LDPC codes. The globally coupled codes will be shown to possess a highly effective burst-erasure correction capability.A good number of new LDPC codes are constructed and simulated over thebinary-input additive white Gaussian noise channel and the binary erasure channel.This book will open the door for readers to understand many topics in modern LDPC codes that are scattered in the literature. It is intended as a self-study guide for students，researchers，and engineers interested in LDPC codes and their variations. The book explains the different design methodologies in detail and provides an ample number of code constructions along with simulations. The book shows that code design and construction are more of an art rather than science.Hopefully，after reading this book，the reader may gain enough artistic experience to produce codes that not only meet required specifications but also improve upon those reported here. To make the material widely accessible，the authors have kept the presentation as clear as possible and assumed only basic knowledge of terminology and results that are commonly covered in textbooks on coding theory.

　　李娟娥（Juane Li）博士畢業(yè)于美國加州大學戴維斯分校，師從國際編碼理論權威林舒教授。她目前是美光科技公司（Micron Technology Inc.）的資深系統(tǒng)架構師。她的研究興趣包括通信和存儲系統(tǒng)的信道編碼，以及低密度奇偶校驗碼的編碼器和譯碼器的硬件實現(xiàn)。林舒（Shu Lin）是世界知名的編碼理論專家，曾擔任IEEE信息論學會主席。他本科畢業(yè)于臺灣大學，博士畢業(yè)于美國的萊斯大學，后在夏威夷大學檀香山分校、得克薩斯農(nóng)工大學、加州大學戴維斯分校等大學任教50余年。他是國際電氣與電子工程師協(xié)會的終生杰出會士（IEEE Life Fellow），獲得過洪堡研究獎（1996）、 IEEE第三千年獎章（2000）、NASA杰出公共成就獎章（2014）、馬奎斯世界名人錄終身成就獎（2019）和IEEE研究生教育獎（2020）。他在編碼理論領域撰寫過多部著作，“香農(nóng)信息科學經(jīng)典”系列里已出版了《差錯控制編碼 第2版》《信道編碼：經(jīng)典和現(xiàn)代方法》和《低密度奇偶校驗碼：設計、構造與統(tǒng)一框架》。哈立德·阿卜杜勒·加法爾（Khaled Abdel-Ghaffar）是加州大學戴維斯分校電子與計算機工程系的教授。他本科畢業(yè)于埃及亞歷山大大學，博士畢業(yè)于美國加州理工學院。他的研究興趣主要在編碼理論，發(fā)表過100多篇學術論文，并曾擔任 IEEE Transactions on Information Theory和IEEE Transactions on Communications的副主編。他和林舒教授是李娟娥博士在加州大學戴維斯分校的共同導師。威廉·瑞安（William E. Ryan）是通信理論和信道編碼領域專家，是國際電氣與電子工程師協(xié)會的杰出會士（IEEE Fellow）。他本科畢業(yè)于美國的凱斯西儲大學，博士畢業(yè)于弗吉尼亞大學，后在新墨西哥州立大學和亞利桑那大學任教近20年，他目前是澤塔聯(lián)合公司（Zeta Associates， Inc.）的高級合伙人。他的研究興趣主要在編碼和信號處理及其在數(shù)據(jù)存儲和無線數(shù)據(jù)通信中的應用，發(fā)表過100多篇學術論文，并曾擔任IEEE Transactions on Communications的副主編。他和林舒教授還一起著有《信道編碼：經(jīng)典和現(xiàn)代方法》一書。丹尼爾·科斯特洛（Daniel J. Costello， Jr.）是世界知名的編碼理論專家，曾擔任IEEE信息論學會主席。他本科畢業(yè)于西雅圖大學，博士畢業(yè)于圣母大學，后在伊利諾伊理工學院和圣母大學任教50余年，并曾擔任圣母大學電子工程系主任。他是國際電氣與電子工程師協(xié)會的終生杰出會士（IEEE Life Fellow），獲得過洪堡研究獎（1999）、IEEE第三千年獎章（2000）、IEEE信息論學會杰出服務獎（2013）和IEEE研究生教育獎（2015）。他和林舒教授還一起著有《差錯控制編碼 第2版》一書。