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62
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 404 (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
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 112 (8 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 89 (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.
Soft-output decoding algorithms in iterative decoding of turbo codes
- JPL TDA Progress Report 42124
, 1996
"... In this article, we present two versions of a simplifled maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring cod ..."
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Cited by 53 (5 self)
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In this article, we present two versions of a simplifled maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplifled a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed. I. Introduction and Motivations The broad framework of this analysis encompasses digital transmission systems where the received signal is a sequence of wave forms whose correlation extends well beyond T, the signaling period. There can be many reasons for this correlation, such as coding, intersymbol interference, or correlated fading. It
On the Minimum Distance of Parallel and Serially Concatenated Codes. [Online]. Available: http://lthcwww.epfl.ch/publications/index.php
, 1997
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Serial and hybrid concatenated codes with applications
- Proc. Intl. Symp. Turbo Codes and Appls
, 1997
"... Abstract — Analytical bounds on the performance of concatenated codes on a tree structure are obtained. Analytical results are applied to examples of parallel concatenation of two codes (turbo codes), serial concatenation of two codes, hybrid concatenation of three codes, and self concatenated codes ..."
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Cited by 28 (1 self)
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Abstract — Analytical bounds on the performance of concatenated codes on a tree structure are obtained. Analytical results are applied to examples of parallel concatenation of two codes (turbo codes), serial concatenation of two codes, hybrid concatenation of three codes, and self concatenated codes, over AWGN and fading channels. Based on the analysis, design criteria for the selection of component codes are presented. Asymptotic results for large interleavers are extended to MPSK modulations over AWGN and Rayleigh fading channels. Simulation results are only given for examples of coded modulation and fading channels. 1.
Combined Turbo Codes and Interleaver Design
- IEEE Transactions on Communications
, 1999
"... Abstract—In this letter the impact of the distance spectrum and interleaver structure on the bit error probability of turbo codes is considered. A new turbo code design method for Gaussian channels is presented. The proposed method combines a search for good component codes with interleaver design. ..."
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Cited by 23 (1 self)
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Abstract—In this letter the impact of the distance spectrum and interleaver structure on the bit error probability of turbo codes is considered. A new turbo code design method for Gaussian channels is presented. The proposed method combines a search for good component codes with interleaver design. The optimal distance spectrum is used as the design criterion to construct good turbo component codes at low signal-to-noise ratios (SNR’s). In addition, an interleaver design method is proposed. This design improves the code performance at high SNR. Search for good component codes at low SNR is combined with a code matched interleaver design. This results in new turbo codes with a superior error performance relative to the best known codes at both low and high SNR. The performance is verified by both analysis and simulation. Index Terms — Concatenated codes, distance spectrum, turbo codes.
Some High-Rate Near Capacity Codecs for the Gaussian Channel
- 34th Allerton Conference on Communications, Control and Computing
, 1996
"... We present a construction of high-rate linear error-correcting codes based on random bipartite graphs. In contrast to other researchers, our approach uses these graphs to produce generator matrices. A distributive parallel decoding algorithm based on the principle of belief propagation is presented. ..."
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Cited by 23 (2 self)
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We present a construction of high-rate linear error-correcting codes based on random bipartite graphs. In contrast to other researchers, our approach uses these graphs to produce generator matrices. A distributive parallel decoding algorithm based on the principle of belief propagation is presented. These new codes are then shown to be linear-time encodable and decodable. Experimental results further show the performances of these new systems to be approach the channel capacities of the Gaussian channels with binary or multilevel signal constellations. 1 Introduction The introduction of multi-stage iterative decoding with exchange of soft information [3] has recently attracted substantial research interests and reperesents a genuine breakthrough in coding theory. This methodology has been applied to parallel concatenated convolutional (turbo) codes [5, 11, 12, 17, 22], parallel concatenated block codes [17], serial concatenated convolutional codes [2], and generalized concatenated con...
Hybrid concatenated codes and iterative decoding
- in Proc. ISIT’97
, 1997
"... A hybrid concatenated code with two interleavers is the parallel concatenation of an encoder, which accepts the permuted version of the information sequence as its ..."
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Cited by 18 (0 self)
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A hybrid concatenated code with two interleavers is the parallel concatenation of an encoder, which accepts the permuted version of the information sequence as its
Turbo Codes for Noncoherent FH-SS with Partial-Band Interference
- IEEE Trans. Commun
, 1998
"... In this paper, turbo codes are investigated in a slow frequency-hopped spread spectrum (FH-SS) system with partialband jamming. In addition, full-band thermal noise is present. The channel model is that of a partial-band jammer in which a fraction of the frequency band is jammed and the remaining fr ..."
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Cited by 15 (5 self)
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In this paper, turbo codes are investigated in a slow frequency-hopped spread spectrum (FH-SS) system with partialband jamming. In addition, full-band thermal noise is present. The channel model is that of a partial-band jammer in which a fraction of the frequency band is jammed and the remaining fraction is unjammed. This paper focuses on the implemention and performance of a modified turbo decoder for this model. We refer to the knowledge that each transmitted bit is jammed as channel state information. We consider cases of known or unknown channel state and variable number of bits per hop. Our approach is to modify the calculation of branch transition probabilities inherent in the original turbo decoder. For the cases with no side information and multiple bits per hop, we iteratively calculate channel state estimates. Analytical bounds are derived and simulation is performed for noncoherent demodulation. The performance of turbo codes is compared with a Reed--Solomon and a concatenated code comprised of a convolutional inner code and Reed--Solomon outer code.
