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Luby transform code

About: Luby transform code is a research topic. Over the lifetime, 2786 publications have been published within this topic receiving 79534 citations.


Papers
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Book
01 Jan 1977
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Abstract: Linear Codes. Nonlinear Codes, Hadamard Matrices, Designs and the Golay Code. An Introduction to BCH Codes and Finite Fields. Finite Fields. Dual Codes and Their Weight Distribution. Codes, Designs and Perfect Codes. Cyclic Codes. Cyclic Codes: Idempotents and Mattson-Solomon Polynomials. BCH Codes. Reed-Solomon and Justesen Codes. MDS Codes. Alternant, Goppa and Other Generalized BCH Codes. Reed-Muller Codes. First-Order Reed-Muller Codes. Second-Order Reed-Muller, Kerdock and Preparata Codes. Quadratic-Residue Codes. Bounds on the Size of a Code. Methods for Combining Codes. Self-dual Codes and Invariant Theory. The Golay Codes. Association Schemes. Appendix A. Tables of the Best Codes Known. Appendix B. Finite Geometries. Bibliography. Index.

10,083 citations

Journal ArticleDOI
29 Jun 1997
TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Abstract: We study two families of error-correcting codes defined in terms of very sparse matrices "MN" (MacKay-Neal (1995)) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties The decoding of both codes can be tackled with a practical sum-product algorithm We prove that these codes are "very good", in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit This result holds not only for the binary-symmetric channel but also for any channel with symmetric stationary ergodic noise We give experimental results for binary-symmetric channels and Gaussian channels demonstrating that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed, the performance of Gallager codes is almost as close to the Shannon limit as that of turbo codes

3,842 citations

Proceedings Article
16 Nov 2002
TL;DR: LT codes are introduced, the first rateless erasure codes that are very efficient as the data length grows, and are based on EMMARM code, which was introduced in version 2.0.
Abstract: We introduce LT codes, the first rateless erasure codes that are very efficient as the data length grows.

2,970 citations

Journal ArticleDOI
TL;DR: In this article, the concept of punctured convolutional codes is extended by punctuating a low-rate 1/N code periodically with period P to obtain a family of codes with rate P/(P+l), where l can be varied between 1 and (N-1)P. This allows transmission of incremental redundancy in ARQ/FEC (automatic repeat request/forward error correction) schemes and continuous rate variation to change from low to high error protection within a data frame.
Abstract: The concept of punctured convolutional codes is extended by punctuating a low-rate 1/N code periodically with period P to obtain a family of codes with rate P/(P+l), where l can be varied between 1 and (N-1)P. A rate-compatibility restriction on the puncturing tables ensures that all code bits of high rate codes are used by the lower-rate codes. This allows transmission of incremental redundancy in ARQ/FEC (automatic repeat request/forward error correction) schemes and continuous rate variation to change from low to high error protection within a data frame. Families of RCPC codes with rates between 8/9 and 1/4 are given for memories M from 3 to 6 (8 to 64 trellis states) together with the relevant distance spectra. These codes are almost as good as the best known general convolutional codes of the respective rates. It is shown that the same Viterbi decoder can be used for all RCPC codes of the same M. the application of RCPC codes to hybrid ARQ/FEC schemes is discussed for Gaussian and Rayleigh fading channels using channel-state information to optimise throughput. >

1,967 citations

Book
01 Jan 1975
TL;DR: This chapter discusses the development of soft decision and iterative decoding in linear codes, as well as some of the techniques used in convolutional codes.
Abstract: Preface 1. Basic concepts of linear codes 2. Bounds on size of codes 3. Finite fields 4. Cyclic codes 5. BCH and Reed-Soloman codes 6. Duadic codes 7. Weight distributions 8. Designs 9. Self-dual codes 10. Some favourite self-dual codes 11. Covering radius and cosets 12. Codes over Z4 13. Codes from algebraic geometry 14. Convolutional codes 15. Soft decision and iterative decoding Bibliography Index.

1,774 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
202210
202110
202011
201920
201833