Capacity approaching codes, iterative decoding ... - IEEE Xplore

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CAPACITY

APPROACHING CODES,

ITERATIVE DECODING ALGORITHMS, AND THEIRAPPLICATIONS Marc Fossorier

Sedat Olqer

xactly 10 years’ago, Berrou, Glavieux, and Thitimajshima introduced a novel approach to error control coding that revolutionalized coding theory and techniques. Their breakthrough, called turbo codes by analogy with the turbo engine and its efficient use of feedback, at once capped 50 years of research toward coding techniques that are both powerful enough to approach the ultimate performance limits and amenable to practical implementations. The improvements achieved were so unexpected - and the techniques involved so foreign to conventional wisdom - that it took several years to gain a satisfactory understanding of the new turbo coding and related concepts. During this period, it was realized that “capacity-approaching” coding and decoding techniques are not limited to turbo or turbo-like codes, but encompass a significantly larger class of codes. These advances had a tremendous impact not only in the field of coding, but also in other areas such as channel equalization, interference cancellation, and multi-user detection, where the “turbo principle” can also be applied. The first article herein, by Benedetto, Divsalar, and Montorsi, is deyoted to explaining the key concepts of the turbo principle and its generalizations, often referred to as concatenation with interleaving. Drawing on conventional coding theory concepts, this article helps us understand why information was lost in similar earlier schemes and how the turbo coding technique, although still suboptimum, is able to largely avoid performance loss during the decoding phase. Turbo coding soon attracted enormous interest for practical applications also. Efforts to include turbo and turbo-like coding techniques in various communications standards rapidly became an industry trend. In the second article, Berrou describes the potential and applications of these codes for commercial systems. He discusses powerlimited and bandwidth-limited systems and addresses issues such as decoding complexity, latency, and versatility. Turbo decoding can readily be modeled as an iterative information passing technique on a graph. This modeling

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was recently extended to the decoding of many other classes of linear codes. In the third article, Kschischang covers graphical representations in detail and explains the main iterative decoding algorithms in terms of efficient message passing techniques. “ C o d e s defined on graphs” h a s emerged as a fundamental concept for all these coding techniques, for both code construction and decoding. The vast research activity generated by the discovery and success of turbo codes also resurrected earlier work on’ iterative decoding, the most prominent of which appears to be that of Gallager on low-density parity-check (LDPC) codes. In fact, Gallager’s Ph.D. thesis contains a wealth of new concepts of fundamental importance for capacityapproaching coding. Although analytical tools such as expandors or belief propagation algorithms were unavailable to him, their application to coding could already be found in his thesis. Richardson and Urbanke present a tutorial on LDPC codes, their generalizations, and their decoding algorithms within the modern framework of codes o n graphs. They address the s t a t e of the a r t of LDPC code design, and provide an overview of current commercial or experimental products employing LDPC codes. Once the communications community recognized the great potential of capacity-approaching codes, it realized that new architectural designs were needed to implement these coding and decoding techniques efficiently. Yeo, Nikolic, and Anantharan address the VLSI implementation of turbo and LDPC codes. They compare serial and parallel realizations, discuss constraints inherent to hardware implementations such as area limitation, power consumption, minimum throughput, and complexity, and present the most effective solutions found. As turbo codes and other iteratively decodable codes are being adopted in a growing number of communications systems, a natural question is whether much is left to be done in error control coding. We believe that the answer is still yes, from both theoretical and practical viewpoints. For example, most of the theory is based on representa-

IEEE Communications Magazine

August 2003

tions on graphs without cycles. Although this theory works well for long codes, this is not true for codes of moderate to small length, for which a satisfactory theory is still lacking. Furthermore, many of these new coding and decoding techniques achieve large performance gains and outperform the more classical coding schemes, and as such may appear to be satisfactory. It is nevertheless worthwhile to determine how far the new codes are from the best achievable performance. In other words, with restrictions on the code length (and possibly the decoding complexity or other design constraints) as are required in many commercial systems, it is highly probable that better codes and corresponding iterative decoding algorithms can be found in the future. The objective of this Feature Topic is to provide a historical perspective on capacity-approaching codes and introduce their state of the art. The articles gathered herein may be more mathematically oriented than is customary for IEEE Communications Magazine. Nevertheless, we hope they will find a large audience and arouse interest in this exciting field. Finally, we thank all the authors and anonymous reviewers who contributed to this Feature Topic.

BIOGRAPHIES MARCP C FOSSORIER[S'90, M'95, SM'OO] received a B E degree from the National Institute of Applied Sciences, Lyon, France, in 1987, and M S and Ph D degrees from the Unrversity of Hawaii at Manoa, Honolulu, in 1991 and 1994, all in electrical engineerin'g In 1996 he joined the faculty of the

University of Hawaii, Honolulu, .as an assistant professor of electrical engineering. He was promoted t o associate professor in 1999. In 2002 he was a visiting professor at Ecole Nationale des Telecommunications, Paris, France, and is currently visiting the University of Tokyo, Japan. His research interests include decoding techniques f o r linear codes, communication algorithms, and.statistics. He co-authored (with S. Lin, T. Kasami, and.T. Fujiwara) the book Trellises and Trellis-Based Decoding Algorithms (Kluwer, 1998). He i s a recipient of a 1998 NSF Career Development award. He has served as Editor for /E€€ Transactions on Communications since 1996 and for /€E€ Communications Letters since 1999, and is current1y.Treasurer of the IEEE Information Theory Society. Since 2002 he has also been a member of the Board of Governors of the IEEE Information Theory Society. He was Program Co-chairman for the 2000 International Symposium on Information Theory and I t s Applications and Editor of the Proceedings of the 2003 and 1999 Symposium on Applied Algebra, Algebraic Algorithms and Error Correcting Codes. He is a member of the IEEE Information Theory and Communications Societies. SEDAT OLCER [SMI received a Diploma of electrical engineering and a Ph.D. degree from the Swiss Federal Institute o f Technology, Lausanne, in 1978 and 1982, respectively. From 1982 t o 1984 he was a research associate at the Information Systems Laboratory of Stanford University, California, and Yale University, New Haven, Connecticut: In 1984 he joined the IBM Zurich Research Laboratory, Ruschlikon, Switzerland, where he has been working on digital transmission techniques for magnetic recording channels, and high-speed data communications for local area networking and network access. He participated and contributed t o the work of several standards bodies including ITU-T, IEEE802, ATM Forum, and ANSI T I E l . From 1995 t o 1996 he was co-editor of the 100BASE-T2 Fast Ethernet standard. His research interests are in digital communications, signal processing, and coding with applications.to broadband network access and storage systems. In 1994 he was Guest Editor for a Special Issue.of Computer Networks o n Broadband Access Networks, and in 2000 he served as Guest Editor of the / € E € Communication Magazine Feature Topic on Very High-speed Digital Subscriber Lines. He was a Guest Editor of the June 2002 issue of /€€€Journal on Selected Areas in Communications entitled "Twisted Pair Transmission - Ever Increasing Performances on Ancient Telephone Wires." He was a co-recipient of the 2003 Leonard G. Abraham prize paper award. He is currently a Technical Editor of /€E€ Communications Magazine.

l+ Location: Dallas, TX, USA l+ http://w.opticomm.org Fourth Annual Optical Networking and Communications Conference

C0-Sponsored by: SPIE-International Society for Optical Engineering,

NSF, Intel Corporation, IEEE Dallas section, Infotrends USA In Co-operation with: IEEE Technical Committee on Gigabit Networks (TCGN), and

IEEE TC on Transmission, Access and Optical Systems (TCTAOS), and SPIE Technical Group on Optical Networks Building on the 2000 inaugural success, the fourth OptiComm Conference returns to Dallas, TX. OptiComm 2003 will bc held on October 13-17, 2003 in the heart of Telecom Corridor. OptiComm will once again bring together researchers, developers, an( business strategists for presentations and discussions on cutting-edge technologies, and the future of optical and broadband communication. Conference Program includes: Two parallel tracks of peer reviewed articles, with keynote presentations from Cisco and Alcatel, four,expert panels on topics including 40 Gbps Networks, Wi-OTMOptical Broadband and Fiber-to-the-X and a poster presentation session. Tutorials on topics including IP-Optical Networking, NGN Metro Optical Networks, Protection/Restorationand Optical Switching. A featured day-long Industry Watch with a keynote presentation from Intel and presentations and discussions from. several industr) leaders on topics including 1O+ Gigabit Ethemet, Network Processors in Optical Networking and Optical Network Recovery. Two full-day Workshops on Optical Burst Switching (OBS) and Community Networks (including FTTH and FTTP). Organizers: General Chairs: Dr. Nasir Ghani and Prof. Krishna Sivalingam TPC Chairs: Prof. Arun Somani and Dr. Zhensheng Zhang Important: NSF Sponsored Student Travel Grants available €or qualified US-based Graduate Students For complete'details and registration please visit our website: httr,://www.opticomm.or~ For Sponsorship and Exhibits Opportunities contact the General'Chairs or visit the web site.

IEEE Communications Magazine

August 2003

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