Book•
Error control coding : fundamentals and applications
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.
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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
Cites methods from "Error control coding : fundamentals..."
...Characteristic two finite fields have been used extensively in connection with error-correcting codes; for example, see Berlekamp [118] and Lin and Costello [769]....
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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
Cites methods from "Error control coding : fundamentals..."
...However, the minimum distance in ARToolKitPlus considering all the BCH markers is 2, which is a low value in comparison to our method, or ARTag....
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...The mean bit transitions for all the BCH markers in ARToolKitPlus is 15.0 which is also below our method....
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...The last known version of ARToolKitPlus employs a binary BCH [25] code for 36 bits markers which presents a minimun Hamming distance of two....
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...As a consequence, ARToolKitPlus BCH markers can detect a maximun error of one bit and cannot perform error correction....
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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
TL;DR: The results show that a reliable link-layer protocol that is TCP-aware provides very good performance and it is possible to achieve good performance without splitting the end-to-end connection at the base station.
Abstract: Reliable transport protocols such as TCP are tuned to perform well in traditional networks where packet losses occur mostly because of congestion. However, networks with wireless and other lossy links also suffer from significant losses due to bit errors and handoffs. TCP responds to all losses by invoking congestion control and avoidance algorithms, resulting in degraded end-to end performance in wireless and lossy systems. We compare several schemes designed to improve the performance of TCP in such networks. We classify these schemes into three broad categories: end-to-end protocols, where loss recovery is performed by the sender; link-layer protocols that provide local reliability; and split-connection protocols that break the end-to-end connection into two parts at the base station. We present the results of several experiments performed in both LAN and WAN environments, using throughput and goodput as the metrics for comparison. Our results show that a reliable link-layer protocol that is TCP-aware provides very good performance. Furthermore, it is possible to achieve good performance without splitting the end-to-end connection at the base station. We also demonstrate that selective acknowledgments and explicit loss notifications result in significant performance improvements.
1,325 citations
Cites background from "Error control coding : fundamentals..."
...These protocols attempt to hide link-related losses from the TCP sender by using local retransmissions and perhaps forward error correction (e.g., [ 18 ]) over the wireless link....
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