Near Shannon limit performance of low density parity check codes
TL;DR: The authors report the empirical performance of Gallager's low density parity check codes on Gaussian channels, showing that performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Abstract: The authors report the empirical performance of Gallager's low density parity check codes on Gaussian channels. They show that performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed the performance is almost as close to the Shannon limit as that of turbo codes.
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Book•
06 Oct 2003
TL;DR: A fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
Abstract: Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
8,091 citations
Cites background from "Near Shannon limit performance of l..."
...Publications on Gallager codes contributing to their 1990s rebirth include (Wiberg et al., 1995; MacKay and Neal, 1995; MacKay and Neal, 1996; Wiberg, 1996; MacKay, 1999b; Spielman, 1996; Sipser and Spielman, 1996)....
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Proceedings Article•
01 Jan 2005
TL;DR: This book aims to provide a chronology of key events and individuals involved in the development of microelectronics technology over the past 50 years and some of the individuals involved have been identified and named.
Abstract: Alhussein Abouzeid Rensselaer Polytechnic Institute Raviraj Adve University of Toronto Dharma Agrawal University of Cincinnati Walid Ahmed Tyco M/A-COM Sonia Aissa University of Quebec, INRSEMT Huseyin Arslan University of South Florida Nallanathan Arumugam National University of Singapore Saewoong Bahk Seoul National University Claus Bauer Dolby Laboratories Brahim Bensaou Hong Kong University of Science and Technology Rick Blum Lehigh University Michael Buehrer Virginia Tech Antonio Capone Politecnico di Milano Javier Gómez Castellanos National University of Mexico Claude Castelluccia INRIA Henry Chan The Hong Kong Polytechnic University Ajit Chaturvedi Indian Institute of Technology Kanpur Jyh-Cheng Chen National Tsing Hua University Yong Huat Chew Institute for Infocomm Research Tricia Chigan Michigan Tech Dong-Ho Cho Korea Advanced Institute of Science and Tech. Jinho Choi University of New South Wales Carlos Cordeiro Philips Research USA Laurie Cuthbert Queen Mary University of London Arek Dadej University of South Australia Sajal Das University of Texas at Arlington Franco Davoli DIST University of Genoa Xiaodai Dong, University of Alberta Hassan El-sallabi Helsinki University of Technology Ozgur Ercetin Sabanci University Elza Erkip Polytechnic University Romano Fantacci University of Florence Frank Fitzek Aalborg University Mario Freire University of Beira Interior Vincent Gaudet University of Alberta Jairo Gutierrez University of Auckland Michael Hadjitheodosiou University of Maryland Zhu Han University of Maryland College Park Christian Hartmann Technische Universitat Munchen Hossam Hassanein Queen's University Soong Boon Hee Nanyang Technological University Paul Ho Simon Fraser University Antonio Iera University "Mediterranea" of Reggio Calabria Markku Juntti University of Oulu Stefan Kaiser DoCoMo Euro-Labs Nei Kato Tohoku University Dongkyun Kim Kyungpook National University Ryuji Kohno Yokohama National University Bhaskar Krishnamachari University of Southern California Giridhar Krishnamurthy Indian Institute of Technology Madras Lutz Lampe University of British Columbia Bjorn Landfeldt The University of Sydney Peter Langendoerfer IHP Microelectronics Technologies Eddie Law Ryerson University in Toronto
7,826 citations
Cites background or methods from "Near Shannon limit performance of l..."
...9 Ultrawideband Radios Ultrawideband (UWB) radios are extremely wideband radios with very high potential data rates [18, 6]....
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...This model can be extended to more than two regions [18]....
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...The data is correctly received if the instantaneous received SNR is greater than or equal to γmin [17, 18]....
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...They have also been used for system design and system performance analysis in [18, 19]....
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...3 dB of power at the expense of increased complexity in the constellation map [18]....
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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
Book•
30 Nov 2008TL;DR: The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.
Abstract: Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.
2,098 citations
Cites background from "Near Shannon limit performance of l..."
...The discovery of turbo codes [11] and the re-discovery of low-density parity-check (LDPC) codes [38, 69] with their corresponding iterative decoding algorithms marked a new era in Coding Theory....
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...4 Bounds and Approximations Above the Cutoff Rate Spurred by the appearance of turbo-codes [11] and the rediscovery of LDPC codes [69], there has been renewed interest in the past decade in the derivation of improved bounds for a region above the cutoff rate....
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References
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Book•
01 Jan 1988TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Abstract: From the Publisher:
Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information.
Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
15,671 citations
Book•
01 Jan 1963TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Abstract: A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.
11,592 citations
"Near Shannon limit performance of l..." refers background in this paper
...A linear code may be described in terms of a generator matrix G or in terms of a parity check matrix H, which satises Hx = 0 for all codewords x. In 1962, Gallager reported work on binary codes dened in terms of low density parity check matrices (abbreviated ‘GL codes’) [ 5 , 6]. The matrix H was dened in a non-systematic form; each column of H had a small weight (e.g., 3) and the weight per row was also uniform; the matrix H was constructed ......
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Proceedings Article•
01 Jan 1993
7,742 citations
23 May 1993
TL;DR: In this article, a new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed.
Abstract: A new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed. The turbo-code encoder is built using a parallel concatenation of two recursive systematic convolutional codes, and the associated decoder, using a feedback decoding rule, is implemented as P pipelined identical elementary decoders. >
5,963 citations
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