Author
Shu Lin
Other affiliations: University of Hawaii, University of Utah
Bio: Shu Lin is an academic researcher from University of California, Davis. The author has contributed to research in topics: Block code & Low-density parity-check code. The author has an hindex of 44, co-authored 257 publications receiving 14144 citations. Previous affiliations of Shu Lin include University of Hawaii & University of Utah.
Papers published on a yearly basis
Papers
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Book•
01 Jan 1983
TL;DR: This book explains coding for Reliable Digital Transmission and Storage using Trellis-Based Soft-Decision Decoding Algorithms for Linear Block Codes and Convolutional Codes, and some of the techniques used in this work.
Abstract: 1. Coding for Reliable Digital Transmission and Storage. 2. Introduction to Algebra. 3. Linear Block Codes. 4. Important Linear Block Codes. 5. Cyclic Codes. 6. Binary BCH Codes. 7. Nonbinary BCH Codes, Reed-Solomon Codes, and Decoding Algorithms. 8. Majority-Logic Decodable Codes. 9. Trellises for Linear Block Codes. 10. Reliability-Based Soft-Decision Decoding Algorithms for Linear Block Codes. 11. Convolutional Codes. 12. Trellis-Based Decoding Algorithms for Convolutional Codes. 13. Sequential and Threshold Decoding of Convolutional Codes. 14. Trellis-Based Soft-Decision Algorithms for Linear Block Codes. 15. Concatenated Coding, Code Decomposition ad Multistage Decoding. 16. Turbo Coding. 17. Low Density Parity Check Codes. 18. Trellis Coded Modulation. 19. Block Coded Modulation. 20. Burst-Error-Correcting Codes. 21. Automatic-Repeat-Request Strategies.
3,848 citations
TL;DR: Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
Abstract: This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
1,401 citations
Book•
30 Oct 2009TL;DR: The design of LDPC codes based on combinatorial designs, graphs, and superposition and their application to LDPC code applications and advanced topics are described.
Abstract: Channel coding lies at the heart of digital communication and data storage, and this detailed introduction describes the core theory as well as decoding algorithms, implementation details, and performance analyses. In this book, Professors Ryan and Lin provide clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes. They also present detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, and product codes, providing a one-stop resource for both classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design. 250 varied and stimulating end-of-chapter problems are also included to test and enhance learning, making this an essential resource for students and practitioners alike.
846 citations
27 Jun 1994
TL;DR: A novel approach to soft decision decoding for binary linear block codes that achieves a desired error performance progressively in a number of stages and is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved.
Abstract: Presents a novel approach to soft decision decoding for binary linear block codes. The basic idea is to achieve a desired error performance progressively in a number of stages. For each decoding stage, the error performance is tightly bounded and the decoding is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved. As a result, more flexibility in the tradeoff between performance and decoding complexity is provided. The decoding is based on the reordering of the received symbols according to their reliability measure. The statistics of the noise after ordering are evaluated. Based on these statistics, two monotonic properties which dictate the reprocessing strategy are derived. Each codeword is decoded in two steps: (1) hard-decision decoding based on reliability information and (2) reprocessing of the hard-decision-decoded codeword in successive stages until the desired performance is achieved. The reprocessing is based on the monotonic properties of the ordering and is carried out using a cost function. A new resource test tightly related to the reprocessing strategy is introduced to reduce the number of computations at each reprocessing stage. For short codes of lengths N/spl les/32 or medium codes with 32 >
636 citations
TL;DR: It is shown that the encoding complexity of a QC-LDPC code is linearly proportional to the number of parity bits of the code for serial encoding, and to the length of thecode for high-speed parallel encoding.
Abstract: Efficient Encoding of Quasi-Cyclic Low-Density Parity-Check Codes Quasi-cyclic (QC) low-density parity-check (LDPC) codes form an important subclass of LDPC codes. These codes have encoding advantage over other types of LDPC codes. This paper addresses the issue of efficient encoding of QC-LDPC codes. Two methods are presented to find the generator matrices of QC-LDPC codes in systematic-circulant form from their parity-check matrices given in circulant form. Based on the systematic-circulation form of the generator matrix of a QC-LDPC code, various types of encoding circuits using simple shift registers are devised. It is shown that the encoding complexity of a QC-LDPC code is linearly proportional to the number of parity bits of the code for serial encoding, and to the length of the code for high-speed parallel encoding.
559 citations
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Book•
01 Jan 1996TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
Abstract: From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.
13,597 citations
TL;DR: A fiducial marker system specially appropriated for camera pose estimation in applications such as augmented reality and robot localization is presented and an algorithm for generating configurable marker dictionaries following a criterion to maximize the inter-marker distance and the number of bit transitions is proposed.
1,758 citations
IBM1
TL;DR: Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.
Abstract: We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.
1,507 citations
TL;DR: Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
Abstract: This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
1,401 citations
TL;DR: Certain notorious nonlinear binary codes contain more codewords than any known linear code and can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes).
Abstract: Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson (1967), Kerdock (1972), Preparata (1968), Goethals (1974), and Delsarte-Goethals (1975). It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z/sub 4/ domain implies that the binary images have dual weight distributions. The Kerdock and "Preparata" codes are duals over Z/sub 4/-and the Nordstrom-Robinson code is self-dual-which explains why their weight distributions are dual to each other. The Kerdock and "Preparata" codes are Z/sub 4/-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z/sub 4/, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the "Preparata" code and a Hadamard-transform soft-decision decoding algorithm for the I(Kerdock code. Binary first- and second-order Reed-Muller codes are also linear over Z/sub 4/, but extended Hamming codes of length n/spl ges/32 and the Golay code are not. Using Z/sub 4/-linearity, a new family of distance regular graphs are constructed on the cosets of the "Preparata" code. >
1,347 citations