Abstract:
Spatially coupled (SC) low-density parity-check (LDPC) codes can achieve capacity approaching performance with low message recovery latency when using sliding window (SW)...Show MoreMetadata
Abstract:
Spatially coupled (SC) low-density parity-check (LDPC) codes can achieve capacity approaching performance with low message recovery latency when using sliding window (SW) decoding. An SC-LDPC code constructed from a protograph can be generated by first coupling a chain of block protographs and then lifting the coupled protograph using permutation matrices. In this paper, we introduce a systematic design to eliminate 4-cycles in a coupled protograph. Further using a quasi-cyclic (QC) lifting, we introduce a procedure for constructing QC-SC-LDPC codes of girth at least eight. This can be interpreted as a multi-stage graph lifting process that yields a greater flexibility in designing QC-SC-LDPC codes with a large girth than previous approaches. Simulation results show the design leads to improved decoding performance, particularly in the error floor, compared to random constructions. Finally, we determine the minimum coupling width required to eliminate 4-cycles in a coupled protograph.
Published in: IEEE Transactions on Communications ( Volume: 68, Issue: 9, September 2020)
Funding Agency:

School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China
Shiyuan Mo (Member, IEEE) received the B.Sc. degree in software engineering and the M.Sc. degree in information and communication engineering from Sun Yat-sen University, Guangzhou, China, in 2015 and 2018, respectively. His research interests include channel coding and data communications.
Shiyuan Mo (Member, IEEE) received the B.Sc. degree in software engineering and the M.Sc. degree in information and communication engineering from Sun Yat-sen University, Guangzhou, China, in 2015 and 2018, respectively. His research interests include channel coding and data communications.View more

School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China
Li Chen (Senior Member, IEEE) received the B.Sc. degree in applied physics from Jinan University, China, in 2003, and the M.Sc. degree in communications and signal processing and the Ph.D. degree in communications engineering from Newcastle University, U.K., in 2004 and 2008, respectively. From 2007 to 2010, he was a Research Associate with Newcastle University. In 2010, he returned China as a Lecturer with the School of ...Show More
Li Chen (Senior Member, IEEE) received the B.Sc. degree in applied physics from Jinan University, China, in 2003, and the M.Sc. degree in communications and signal processing and the Ph.D. degree in communications engineering from Newcastle University, U.K., in 2004 and 2008, respectively. From 2007 to 2010, he was a Research Associate with Newcastle University. In 2010, he returned China as a Lecturer with the School of ...View more

Department of Electrical Engineering, University of Notre Dame, Notre Dame, USA
Daniel J. Costello, Jr. (Life Fellow, IEEE) received the B.S.E.E. degree from Seattle University in 1964 and the M.S. and Ph.D. degrees in electrical engineering from the University of Notre Dame in 1966 and 1969, respectively.
He joined the Illinois Institute of Technology in 1969 as a Faculty Member. In 1985, he became a Professor of electrical engineering with the University of Notre Dame, where he served as the Departm...Show More
Daniel J. Costello, Jr. (Life Fellow, IEEE) received the B.S.E.E. degree from Seattle University in 1964 and the M.S. and Ph.D. degrees in electrical engineering from the University of Notre Dame in 1966 and 1969, respectively.
He joined the Illinois Institute of Technology in 1969 as a Faculty Member. In 1985, he became a Professor of electrical engineering with the University of Notre Dame, where he served as the Departm...View more

Klipsch School of Electrical and Computer Engineering, New Mexico State University, Las Cruces, USA
David G. M. Mitchell (Senior Member, IEEE) received the Ph.D. degree in electrical engineering from the University of Edinburgh, U.K., in 2009. From 2009 to 2015, he held Post-Doctoral Research Associate and then Visiting Assistant Professor positions at the Department of Electrical Engineering, University of Notre Dame, USA. Since 2015, he has been an Assistant Professor with the Klipsch School of Electrical and Computer...Show More
David G. M. Mitchell (Senior Member, IEEE) received the Ph.D. degree in electrical engineering from the University of Edinburgh, U.K., in 2009. From 2009 to 2015, he held Post-Doctoral Research Associate and then Visiting Assistant Professor positions at the Department of Electrical Engineering, University of Notre Dame, USA. Since 2015, he has been an Assistant Professor with the Klipsch School of Electrical and Computer...View more

Department of Electrical Engineering, University of Notre Dame, Notre Dame, USA
Department of Mathematics, University of Notre Dame, Notre Dame, USA
Roxana Smarandache (Senior Member, IEEE) received the B.S. degree in mathematics with a thesis in number theory from the University of Bucharest, Bucharest, Romania, in 1996, and the M.Sc. degree and the Ph.D. degree in mathematics with a thesis in coding theory from the University of Notre Dame, Notre Dame, IN, USA, in 1997 and 2001, respectively. She is currently a Professor of mathematics and electrical engineering wit...Show More
Roxana Smarandache (Senior Member, IEEE) received the B.S. degree in mathematics with a thesis in number theory from the University of Bucharest, Bucharest, Romania, in 1996, and the M.Sc. degree and the Ph.D. degree in mathematics with a thesis in coding theory from the University of Notre Dame, Notre Dame, IN, USA, in 1997 and 2001, respectively. She is currently a Professor of mathematics and electrical engineering wit...View more

School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China
Jie Qiu received the B.Sc. degree in communication engineering from the Hefei University of Technology, Hefei, China, in 2017. She is currently pursuing the M.Sc. degree in information and communication engineering with Sun Yat-sen University, Guangzhou, China. Her research interests include channel coding and data communications.
Jie Qiu received the B.Sc. degree in communication engineering from the Hefei University of Technology, Hefei, China, in 2017. She is currently pursuing the M.Sc. degree in information and communication engineering with Sun Yat-sen University, Guangzhou, China. Her research interests include channel coding and data communications.View more

School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China
Shiyuan Mo (Member, IEEE) received the B.Sc. degree in software engineering and the M.Sc. degree in information and communication engineering from Sun Yat-sen University, Guangzhou, China, in 2015 and 2018, respectively. His research interests include channel coding and data communications.
Shiyuan Mo (Member, IEEE) received the B.Sc. degree in software engineering and the M.Sc. degree in information and communication engineering from Sun Yat-sen University, Guangzhou, China, in 2015 and 2018, respectively. His research interests include channel coding and data communications.View more

School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China
Li Chen (Senior Member, IEEE) received the B.Sc. degree in applied physics from Jinan University, China, in 2003, and the M.Sc. degree in communications and signal processing and the Ph.D. degree in communications engineering from Newcastle University, U.K., in 2004 and 2008, respectively. From 2007 to 2010, he was a Research Associate with Newcastle University. In 2010, he returned China as a Lecturer with the School of Information Science and Technology, Sun Yat-sen University, Guangzhou. From 2011 to 2016, he became an Associate Professor and a Professor with Sun Yat-sen University, respectively. In 2013, he became an Associate Head of the Department of Electronic and Communication Engineering (ECE). From 2017 to 2020, he was the Deputy Dean of the School of Electronics and Communication Engineering. From 2011 to 2012, he was a Visiting Researcher with the Institute of Network Coding, the Chinese University of Hong Kong. From July 2015 to October 2015, he was a Visitor with the Institute of Communications Engineering, Ulm University, Germany. From October 2015 to June 2016, he was a Visiting Associate Professor with the Department of Electrical Engineering, University of Notre Dame, USA. His research interests include information theory, error-correction codes, and data communications. He likes reading and photography. He is currently a Senior Member of the Chinese Institute of Electronics (CIE). He is also a member of the IEEE Information Theory Society Board of Governors Conference Committee and a Committee Member of the CIE Information Theory Society. He has been involved in organizing several international conferences, including the 2018 IEEE Information Theory Workshop (ITW) at Guangzhou, for which he was the General Co-Chair. He is also the Chair of the IEEE Information Theory Society Guangzhou Chapter. He is serving as an Associate Editor for IEEE Transactions on Communications.
Li Chen (Senior Member, IEEE) received the B.Sc. degree in applied physics from Jinan University, China, in 2003, and the M.Sc. degree in communications and signal processing and the Ph.D. degree in communications engineering from Newcastle University, U.K., in 2004 and 2008, respectively. From 2007 to 2010, he was a Research Associate with Newcastle University. In 2010, he returned China as a Lecturer with the School of Information Science and Technology, Sun Yat-sen University, Guangzhou. From 2011 to 2016, he became an Associate Professor and a Professor with Sun Yat-sen University, respectively. In 2013, he became an Associate Head of the Department of Electronic and Communication Engineering (ECE). From 2017 to 2020, he was the Deputy Dean of the School of Electronics and Communication Engineering. From 2011 to 2012, he was a Visiting Researcher with the Institute of Network Coding, the Chinese University of Hong Kong. From July 2015 to October 2015, he was a Visitor with the Institute of Communications Engineering, Ulm University, Germany. From October 2015 to June 2016, he was a Visiting Associate Professor with the Department of Electrical Engineering, University of Notre Dame, USA. His research interests include information theory, error-correction codes, and data communications. He likes reading and photography. He is currently a Senior Member of the Chinese Institute of Electronics (CIE). He is also a member of the IEEE Information Theory Society Board of Governors Conference Committee and a Committee Member of the CIE Information Theory Society. He has been involved in organizing several international conferences, including the 2018 IEEE Information Theory Workshop (ITW) at Guangzhou, for which he was the General Co-Chair. He is also the Chair of the IEEE Information Theory Society Guangzhou Chapter. He is serving as an Associate Editor for IEEE Transactions on Communications.View more

Department of Electrical Engineering, University of Notre Dame, Notre Dame, USA
Daniel J. Costello, Jr. (Life Fellow, IEEE) received the B.S.E.E. degree from Seattle University in 1964 and the M.S. and Ph.D. degrees in electrical engineering from the University of Notre Dame in 1966 and 1969, respectively.
He joined the Illinois Institute of Technology in 1969 as a Faculty Member. In 1985, he became a Professor of electrical engineering with the University of Notre Dame, where he served as the Department Chair from 1989 to 1998. He has more than 400 technical publications in his field. In 1983, he coauthored a popular textbook entitled Error Control Coding: Fundamentals and Applications (Second Edition, 2004). His research interests include digital communications, with a special emphasis on error control coding and information theory. In 1999, he received the Humboldt Research Prize from the German Government, and in 2000, he was named the Leonard Bettex Professor of electrical engineering at Notre Dame.
Dr. Costello was elected as a fellow of the IEEE in 1985. He served 18 years as a member of the IEEE Information Theory Society Board of Governors; in 1986, he was the President of the IT Society BOG; and in 2000, he received the Third-Millennium Medal from the IT Society. He was a co-recipient of the Donald G. Fink Prize Paper Award in 2009 and the joint IT Society/COM Society Prize Paper Award in 2012. He also received the Aaron D. Wyner Distinguished Service Award from the IT Society in 2013 and the IEEE Leon K. Kirchmayer Graduate Teaching Award in 2015.
Daniel J. Costello, Jr. (Life Fellow, IEEE) received the B.S.E.E. degree from Seattle University in 1964 and the M.S. and Ph.D. degrees in electrical engineering from the University of Notre Dame in 1966 and 1969, respectively.
He joined the Illinois Institute of Technology in 1969 as a Faculty Member. In 1985, he became a Professor of electrical engineering with the University of Notre Dame, where he served as the Department Chair from 1989 to 1998. He has more than 400 technical publications in his field. In 1983, he coauthored a popular textbook entitled Error Control Coding: Fundamentals and Applications (Second Edition, 2004). His research interests include digital communications, with a special emphasis on error control coding and information theory. In 1999, he received the Humboldt Research Prize from the German Government, and in 2000, he was named the Leonard Bettex Professor of electrical engineering at Notre Dame.
Dr. Costello was elected as a fellow of the IEEE in 1985. He served 18 years as a member of the IEEE Information Theory Society Board of Governors; in 1986, he was the President of the IT Society BOG; and in 2000, he received the Third-Millennium Medal from the IT Society. He was a co-recipient of the Donald G. Fink Prize Paper Award in 2009 and the joint IT Society/COM Society Prize Paper Award in 2012. He also received the Aaron D. Wyner Distinguished Service Award from the IT Society in 2013 and the IEEE Leon K. Kirchmayer Graduate Teaching Award in 2015.View more

Klipsch School of Electrical and Computer Engineering, New Mexico State University, Las Cruces, USA
David G. M. Mitchell (Senior Member, IEEE) received the Ph.D. degree in electrical engineering from the University of Edinburgh, U.K., in 2009. From 2009 to 2015, he held Post-Doctoral Research Associate and then Visiting Assistant Professor positions at the Department of Electrical Engineering, University of Notre Dame, USA. Since 2015, he has been an Assistant Professor with the Klipsch School of Electrical and Computer Engineering, New Mexico State University, USA. His research interests are in the area of digital communications, with an emphasis on coding and information theory.
David G. M. Mitchell (Senior Member, IEEE) received the Ph.D. degree in electrical engineering from the University of Edinburgh, U.K., in 2009. From 2009 to 2015, he held Post-Doctoral Research Associate and then Visiting Assistant Professor positions at the Department of Electrical Engineering, University of Notre Dame, USA. Since 2015, he has been an Assistant Professor with the Klipsch School of Electrical and Computer Engineering, New Mexico State University, USA. His research interests are in the area of digital communications, with an emphasis on coding and information theory.View more

Department of Electrical Engineering, University of Notre Dame, Notre Dame, USA
Department of Mathematics, University of Notre Dame, Notre Dame, USA
Roxana Smarandache (Senior Member, IEEE) received the B.S. degree in mathematics with a thesis in number theory from the University of Bucharest, Bucharest, Romania, in 1996, and the M.Sc. degree and the Ph.D. degree in mathematics with a thesis in coding theory from the University of Notre Dame, Notre Dame, IN, USA, in 1997 and 2001, respectively. She is currently a Professor of mathematics and electrical engineering with the University of Notre Dame. After spending 11 years on the faculty of San Diego State University, she joined the University of Notre Dame in 2012, where she has a joint appointment in mathematics and electrical engineering. Her research interests include coding theory, combinatorics, and graph theory. In particular, she focuses on low-density parity check codes, iterative and linear programming decoding, and convolutional codes. She has been an Associate Editor of the Advances in Mathematics of Communications (AMC) journal and IEEE Transactions on Information Theory from 2013 to 2014 and from 2014 to 2017, respectively.
Roxana Smarandache (Senior Member, IEEE) received the B.S. degree in mathematics with a thesis in number theory from the University of Bucharest, Bucharest, Romania, in 1996, and the M.Sc. degree and the Ph.D. degree in mathematics with a thesis in coding theory from the University of Notre Dame, Notre Dame, IN, USA, in 1997 and 2001, respectively. She is currently a Professor of mathematics and electrical engineering with the University of Notre Dame. After spending 11 years on the faculty of San Diego State University, she joined the University of Notre Dame in 2012, where she has a joint appointment in mathematics and electrical engineering. Her research interests include coding theory, combinatorics, and graph theory. In particular, she focuses on low-density parity check codes, iterative and linear programming decoding, and convolutional codes. She has been an Associate Editor of the Advances in Mathematics of Communications (AMC) journal and IEEE Transactions on Information Theory from 2013 to 2014 and from 2014 to 2017, respectively.View more

School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China
Jie Qiu received the B.Sc. degree in communication engineering from the Hefei University of Technology, Hefei, China, in 2017. She is currently pursuing the M.Sc. degree in information and communication engineering with Sun Yat-sen University, Guangzhou, China. Her research interests include channel coding and data communications.
Jie Qiu received the B.Sc. degree in communication engineering from the Hefei University of Technology, Hefei, China, in 2017. She is currently pursuing the M.Sc. degree in information and communication engineering with Sun Yat-sen University, Guangzhou, China. Her research interests include channel coding and data communications.View more