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313
Turbo decoding as an instance of Pearl’s belief propagation algorithm
- IEEE Journal on Selected Areas in Communications
, 1998
"... Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pear ..."
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Cited by 420 (16 self)
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Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl’s belief propagation algorithm. We shall see that if Pearl’s algorithm is applied to the “belief network ” of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his algorithm works when there are no loops, so an explanation of the excellent experimental performance of turbo decoding is still lacking. However, we shall also show that Pearl’s algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other error-control systems, including Gallager’s
Applications of Error-Control Coding
, 1998
"... An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video t ..."
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Cited by 274 (0 self)
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An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video transmission. Examples, both historical and current, are given that typify the different approaches used in each application area. Although no attempt is made to be comprehensive in our coverage, the examples chosen clearly illustrate the richness, variety, and importance of error-control coding methods in modern digital applications.
"Turbo equalization": principles and new results
, 2000
"... Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalizati ..."
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Cited by 271 (24 self)
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Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalization" approach, which can be applied to coded data transmission over channels with intersymbol interference (ISI). In the original system invented by Douillard et al., the data is protected by a convolutional code and a receiver consisting of two trellis-based detectors are used, one for the channel (the equalizer) and one for the code (the decoder). It has been shown that iterating equalization and decoding tasks can yield tremendous improvements in bit error rate (BER). We introduce new approaches to combining equalization based on linear ltering with the decoding. The result is a receiver that is capable of improving BER performance through iterations of equalization and decoding in a manner similar to turbo ...
Coded cooperation in wireless communications: space-time transmission and iterative decoding
- IEEE Trans. Signal Processing
, 2004
"... Abstract—When mobiles cannot support multiple antennas due to size or other constraints, conventional space-time coding cannot be used to provide uplink transmit diversity. To address this limitation, the concept of cooperation diversity has been introduced, where mobiles achieve uplink transmit div ..."
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Cited by 195 (3 self)
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Abstract—When mobiles cannot support multiple antennas due to size or other constraints, conventional space-time coding cannot be used to provide uplink transmit diversity. To address this limitation, the concept of cooperation diversity has been introduced, where mobiles achieve uplink transmit diversity by relaying each other’s messages. A particularly powerful variation of this principle is coded cooperation. Instead of a simple repetition relay, coded cooperation partitions the codewords of each mobile and transmits portions of each codeword through independent fading channels. This paper presents two extensions to the coded cooperation framework. First, we increase the diversity of coded cooperation in the fast-fading scenario via ideas borrowed from space-time codes. We calculate bounds for the bit- and block-error rates to demonstrate the resulting gains. Second, since cooperative coding contains two code components, it is natural to apply turbo codes to this framework. We investigate the application of turbo codes in coded cooperation and demonstrate the resulting gains via error bounds and simulations. Index Terms—Channel coding, diversity, space-time coding, user cooperation, wireless communications.
Extrinsic information transfer functions: A model and two properties
- in Proc. Conf. Info. Sci. Syst. (CISS
, 2002
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Low-density parity-check codes based on finite geometries: A rediscovery and new results
- IEEE Trans. Inform. Theory
, 2001
"... 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 thei ..."
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Cited by 182 (7 self)
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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 graphs have girth T. 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.
Error-floors of LDPC codes
- Proceedings of the 41st Annual Conference on Communication, Control and Computing
, 2003
"... We introduce a computational technique that accurately predicts performance for a given LDPC code in the error floor region. We present some results obtained by applying the technique and describe certain aspects of it. 1 ..."
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Cited by 168 (1 self)
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We introduce a computational technique that accurately predicts performance for a given LDPC code in the error floor region. We present some results obtained by applying the technique and describe certain aspects of it. 1
A distance spectrum interpretation of turbo codes
- IEEE Trans. Inform. Theory
, 1996
"... Abstract-The performance of Turbo codes is addressed by examining the code’s distance spectrum. The “error floor ” that occurs at moderate signal-to-noise ratios is shown to be a conse-quence of the relatively low free distance of the code. It is also shown that the “error floor ” can be lowered by ..."
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Cited by 110 (7 self)
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Abstract-The performance of Turbo codes is addressed by examining the code’s distance spectrum. The “error floor ” that occurs at moderate signal-to-noise ratios is shown to be a conse-quence of the relatively low free distance of the code. It is also shown that the “error floor ” can be lowered by increasing the size of the interleaver without changing the free distance of the code. Alternatively, the free distance of the code may be increased by using primitive feedback polynomials. The excellent performance of lurbo codes at low signal-to-noise ratios is explained in terms of the distance spectrum. The interleaver in the Turbo encoder is shown to reduce the number of low-weight codewords through a process called “spectral thinning. ” This thinned distance spec-trum results in the free distance asymptote being the dominant performance parameter for low and moderate signal-to-noise ratios. Index Terms-Turbo codes, convolutional codes, distance spec-trum. T I.
Design and Analysis of Turbo Codes on Rayleigh Fading Channels
- IEEE Journal of Selected Areas in Comm
, 1998
"... Abstract—The performance and design of turbo codes using coherent BPSK signaling on the Rayleigh fading channel is con-sidered. In low signal-to-noise regions, performance analysis uses simulations of typical turbo coding systems. For higher signal-to-noise regions beyond simulation capabilities, an ..."
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Cited by 87 (0 self)
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Abstract—The performance and design of turbo codes using coherent BPSK signaling on the Rayleigh fading channel is con-sidered. In low signal-to-noise regions, performance analysis uses simulations of typical turbo coding systems. For higher signal-to-noise regions beyond simulation capabilities, an average upper bound is used in which the average is over all possible interleaving schemes. Fully interleaved and exponentially correlated Rayleigh channels are explored. Furthermore, the design issues relevant to turbo codes are examined for the correlated fading channel. Turbo interleaver design criteria are developed and architectural modifications are proposed for improved performance. Index Terms — Codes, concatenated coding, fading channels, interleaved coding, Rayleigh channels. I.
SNR Mismatch and On-Line Estimation in Turbo Decoding
- IEEE Trans. Commun
, 1998
"... Iterative decoding of turbo codes, as well as other concatenated coding schemes of similar nature, requires accurate knowledge of the signal-to-noise ratio of the channel so that proper blending of the a posteriori information of the separate decoders is achieved. In this paper, we study the sensiti ..."
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Cited by 71 (0 self)
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Iterative decoding of turbo codes, as well as other concatenated coding schemes of similar nature, requires accurate knowledge of the signal-to-noise ratio of the channel so that proper blending of the a posteriori information of the separate decoders is achieved. In this paper, we study the sensitivity of decoder performance to mis-estimation of the SNR, and propose a simple on-line scheme that estimates the unknown SNR from each code block, prior to decoding. We show this scheme is sufficiently adequate in accuracy to not appreciably degrade performance. y work sponsored by NSF grant NCR-9415996 and NASA/LeRC contract NAG3-1948 1 Introduction Turbo codes and other similar constructions have captured the fancy of the error control coding community in that performance quite near the Shannon capacity limit is attainable with moderate complexity decoding. The technique uses one or more component codes, with separate decoders processing each code to estimate the a posteriori probabili...
