Shu LinTalk Title: Collective Encoding and Soft-Decision Decoding of Cyclic Codes in Galois-Fourier Transform Domain


This paper presents a novel coding scheme for collective encoding and iterative soft-decision decoding of cyclic codes of prime lengths. The encoding of a cyclic code is performed on a collection of codewords. This collection of codewords is mapped through Galois-Fourier transform into a codeword in an LDPC code for transmission. The parity-check matrix of the LDPC code is binary and its associated Tanner graph has girth at least 6. The received codewords in a collection are decoded jointly in binary based on the binary LDPC matrix using a binary iterative soft-decision decoding algorithm. The joint-decoding allows information sharing among the received codewords in a collection during the iterative decoding process. The binary iterative decoding can be performed efficiently and reduces the decoding complexity significantly. For decoding Reed-Solomon, BCH, Reed-Muller and quadratic residue codes of prime lengths, the proposed coding scheme not only requires much less decoding complexity than other soft-decision decoding algorithms for these codes, but also yields far superior performance. The proposed scheme can also achieve a joint-decoding gain over the maximum likelihood decoding of a code decoded individually.


Shu Lin (S’62-M’65-SM’78-F’80-LF’00) received the B.S.E.E. degree from the National Taiwan University, Taipei, Taiwan, in 1959, and the M.S. and Ph.D. degrees in electrical engineering from Rice University, Houston, TX, in 1964 and 1965, respectively.

In 1965, he joined the Faculty of the University of Hawaii, Honolulu, as an Assistant Professor of Electrical Engineering. He became an Associate Professor in 1969 and a Professor in 1973. In 1986, he joined Texas A \& M University, College Station, as the Irma Runyon Chair Professor of Electrical Engineering. In 1987, he returned to the University of Hawaii. From 1978 to 1979, he was a Visiting Scientist at the IBM Thomas J. Watson Research Center, Yorktown Heights, NY, where he worked on error control protocols for data communication systems. He spent the academic year of 1996-1997 as a Visiting Professor at the Technical University of Munich, Munich, Germany. He retired from University of Hawaii in 1999 and he is currently an Adjunct Professor at University of California, Davis. He has published numerous technical papers in IEEE Transactions and other refereed journals. He is the author of the book, An Introduction to Error-Correcting Codes (Englewood Cliff, NJ: Prentice-Hall, 1970). He also co-authored (with D. J. Costello) the book, Error Control Coding: Fundamentals and Applications (Upper Saddle River, NJ: Prentice-Hall, 1st edition, 1982, 2nd edition, 2004), (with T. Kasami, T. Fujiwara, and M. Fossorier) the book, Trellises and Trellis-Based Decoding Algorithms, (Boston, MA: Kluwer Academic, 1998), (with W. E. Ryan) the book, Channel Codes: Classical and Modern (Cambridge University Press, 2009), and (with J. Li, K. Abdel-Ghaffar, W. E. Ryan, and D. J. Costello, Jr. ) the book, LDPC Code Designs, Constructions, and Unification (Cambridge University Press, 2017). His current research areas include algebraic coding theory, coded modulation, error control systems, and satellite communications. He has served as the Principle Investigator on 32 research grants.

Dr. Lin is a Member of the IEEE Information Theory Society and the Communication Society. He served as the Associate Editor for Algebraic Coding Theory for the IEEE TRANSACTIONS ON INFORMATION THEORY from 1976 to 1978, and as the Program Co-Chairman of the IEEE International Symposium of Information Theory held in Kobe, Japan, in June 1988. He was the President of the IEEE Information Theory Society in 1991. In 1996, he was a recipient of the Alexander von Humboldt Research Prize for U.S. Senior Scientists and a recipient of the IEEE Third-Millennium Medal, 2000. In 2007, he was a recipient of The Communications Society Stephen O. Rice Prize in the Field of Communications Theory. In 2014, he was awarded the NASA Exceptional Public Achievement Medal.