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Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding
 IEEE Trans. Inform. Theory
, 1996
"... A serially concatenated code with an interleaver consists of the cascade of an outer code... ..."
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Cited by 372 (32 self)
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A serially concatenated code with an interleaver consists of the cascade of an outer code...
Unveiling Turbo Codes: Some Results on Parallel Concatenated Coding Schemes
, 1995
"... A parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver. The input bits to the first encoder are scrambled by the interleaver before entering the second encoder. The codeword of the parallel concatenated code consists of the input bits to ..."
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Cited by 314 (6 self)
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A parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver. The input bits to the first encoder are scrambled by the interleaver before entering the second encoder. The codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders. This construction can be generalized to any number of constituent codes. Parallel concatenated schemes employing two convolutional codes as constituent codes, in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes, have been recently shown to yield remarkable coding gains close to theoretical limits. They have been named, and are known as, "turbo codes". We propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length. The analytical bounding technique is then used to s...
Design of parallel concatenated convolutional codes
 IEEE Transactions on Communications
, 1996
"... Abstract. ’ parallel concatenated convolutional coding scheme consists of two constituent systematic convolutional encoders linked by an interleaver. The information bits at the input of the first encoder are scrambled by the interleaver before entering the second encoder. The codewords of the para ..."
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Cited by 130 (10 self)
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Abstract. ’ parallel concatenated convolutional coding scheme consists of two constituent systematic convolutional encoders linked by an interleaver. The information bits at the input of the first encoder are scrambled by the interleaver before entering the second encoder. The codewords of the parallel concatenated code consist of the information bits followed by the parity check bits of both encoders. Parallel concatenated codes (turbo codes), decoded through an iterative decoding algorithm of relatively low complexity, have recently been shown to yield remarkable coding gains close to theoretical limits. In this paper, we characterize the separate contributions that the interleaver length and constituent codes give to the overall performance of the parallel concatenated code, and present some guidelines for the optimal design of the constituent convolutional codes. Zndex Terms Iterative decoding, concatenated codes, turbo codes. I.
A distance spectrum interpretation of turbo codes
 IEEE Trans. Inform. Theory
, 1996
"... AbstractThe performance of Turbo codes is addressed by examining the code’s distance spectrum. The “error floor ” that occurs at moderate signaltonoise ratios is shown to be a consequence 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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AbstractThe performance of Turbo codes is addressed by examining the code’s distance spectrum. The “error floor ” that occurs at moderate signaltonoise ratios is shown to be a consequence 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 signaltonoise ratios is explained in terms of the distance spectrum. The interleaver in the Turbo encoder is shown to reduce the number of lowweight codewords through a process called “spectral thinning. ” This thinned distance spectrum results in the free distance asymptote being the dominant performance parameter for low and moderate signaltonoise ratios. Index TermsTurbo codes, convolutional codes, distance spectrum. T I.
Multiple Turbo Codes for DeepSpace Communications , It TDA
, 1995
"... In this article, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) ..."
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Cited by 85 (4 self)
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In this article, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP)
SNR Mismatch and OnLine 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 signaltonoise 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 signaltonoise 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 misestimation of the SNR, and propose a simple online 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 NCR9415996 and NASA/LeRC contract NAG31948 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...
Softoutput 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
Improved Upper Bounds on the ML Decoding Error Probability of Parallel and Serial Concatenated Turbo Codes via Their Ensemble Distance Spectrum
 IEEE Trans. on Information Theory
, 2000
"... The ensemble performance of parallel and serial concatenated turbo codes is considered, where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time varying recursive systematic convolutional codes. Following the derivation of the input ..."
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Cited by 35 (4 self)
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The ensemble performance of parallel and serial concatenated turbo codes is considered, where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time varying recursive systematic convolutional codes. Following the derivation of the inputoutput weight enumeration functions of the ensembles of random parallel and serial concatenated turbo codes,the tangential sphere upper bound is employed to provide improved upper bounds on the block and bit error probabilities of these ensembles of codes for the binaryinput additive white Gaussian noise channel, based on coherent detection of equienergy antipodal signals and maximum likelihood decoding. The influence of the interleaver length and the memory length of the component codes are investigated. The improved bounding technique proposed here is compared to the conventional union bound and to a recent alternative bounding technique by Duman and Salehi which incorporates modified Gallager bounds. The advantage of the derived bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random recursive systematic convolutional component codes, and it is especially pronounced in the region exceeding the cutoff rate, where the performance of turbo codes is most appealing. These upper bounds are also compared to simulation results of the iterative decoding algorithm. Keywords:
Analysis, Design, and Iterative Decoding of Double Serially Concatenated Codes with Interleavers
 IEEE J. Select. Areas Commun
, 1998
"... A double serially concatenated code with two interleavers consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits, and an inner encoder whose input words are the permuted middle codewords. ..."
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Cited by 28 (1 self)
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A double serially concatenated code with two interleavers consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits, and an inner encoder whose input words are the permuted middle codewords. The construction can be generalized to h cascaded encoders separated by h 0 1 interleavers, where h?3: We obtain upper bounds to the average maximum likelihood biterror probability of double serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer, middle, and inner codes that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a lowcomplexity iterative decoding algorithm. Comparisons with parallel concatenated convolutional codes, known as "turbo codes," and with the recently proposed serially concatenated convolutional codes are also presented, showing that in some cases, t...
Wireless Image Transmission Using Turbo Codes and Optimal Unequal Error Protection
 IN PROC. IEEE INT. CONFERENCE ON IMAGE PROCESSING
, 2003
"... A novel image transmission scheme is proposed for the communication of set partitioning in hierarchical trees image streams over wireless channels. The proposed scheme employs turbo codes and Reed–Solomon codes in order to deal effectively with burst errors. An algorithm for the optimal unequal err ..."
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Cited by 25 (7 self)
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A novel image transmission scheme is proposed for the communication of set partitioning in hierarchical trees image streams over wireless channels. The proposed scheme employs turbo codes and Reed–Solomon codes in order to deal effectively with burst errors. An algorithm for the optimal unequal error protection of the compressed bitstream is also proposed and applied in conjunction with an inherently more efficient technique for product code decoding. The resulting scheme is tested for the transmission of images over wireless channels. Experimental evaluation clearly demonstrates the superiority of the proposed transmission system in comparison to wellknown robust coding schemes.