Spatially Coupled LDPC Codes: Is This What Shannon Had In Mind?

Following a review of the development of coding theory since the time of Shannon and the basic concepts of low-density parity-check (LDPC) block codes, we examine spatially coupled LDPC codes from several different perspectives. First, asymptotic ensemble average properties are presented, including both iterative decoding thresholds and minimum distance growth rates. Protograph-based code ensembles form the basis for this discussion. Next, finite-length code properties, such as bit-error-rate (BER) performance, decoding latency, and decoding complexity are reviewed. With sliding window decoding, we see that spatially coupled codes achieve a BER performance advantage compared to block codes for fixed decoding latency and practical block (window) lengths, and decoding complexity results are presented for both binary and non-binary codes. Finally, the BER performance advantages of spatially coupled codes are shown to also hold when puncturing is employed to achieve higher code rates.

Daniel J. Costello, Jr. is the Bettex Professor Emeritus of Electrical Engineering at the University of Notre Dame, where he has been since 1985, and where he was department chair from 1989 to 1998. His research interests are in digital communications, with special emphasis on error control coding and coded modulation. He has numerous publications, and in 1983 he co-authored the textbook "error Control Coding: Fundamentals and Applications" , the 2nd edition of which was published in 2004. Dr. Costello is a Fellow of the IEEE and has received many awards, including the IEEE Donald G. Fink Prize Paper Award, the Joint IEEE Information Theory Society/Communications Society Prize Paper Award, the IEEE Information Theory Society Aaron D. Wyner Distinguished Service Award, and the IEEE Kirchmayer Graduate Teaching Award.