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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...
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.
VLSI Architectures for Turbo Codes
 IEEE Transactions on VLSI Systems
, 1999
"... A great interest has been gained in recent years by a new errorcorrecting code technique, known as "turbo coding," which has been proven to offer performance closer to the Shannon's limit than traditional concatenated codes. In this paper, several very large scale integration (VLSI) ..."
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Cited by 64 (2 self)
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A great interest has been gained in recent years by a new errorcorrecting code technique, known as "turbo coding," which has been proven to offer performance closer to the Shannon's limit than traditional concatenated codes. In this paper, several very large scale integration (VLSI) architectures suitable for turbo decoder implementation are proposed and compared in terms of complexity and performance; the impact on the VLSI complexity of system parameters like the state number, number of iterations, and code rate are evaluated for the different solutions. The results of this architectural study have then been exploited for the design of a specific decoder, implementing a serial concatenation scheme with 2/3 and 3/4 codes; the designed circuit occupies 35 mm , supports a 2Mb/s data rate, and for a bit error probability of 10 06 , yields a coding gain larger than 7 dB, with ten iterations.
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
A search for good convolutional codes to be used in the construction of turbo codes
 IEEE Transactions on Communications
, 1998
"... Abstract — Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the “best ” recursive s ..."
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Cited by 51 (5 self)
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Abstract — Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the “best ” recursive systematic convolutional encoders found are presented for various rates, together with the average biterror probability performances of some turbo codes using them. Index Terms—Concatenated coding, convolutional codes, encoders, turbo codes. I.
On the Minimum Distance of Parallel and Serially Concatenated Codes. [Online]. Available: http://lthcwww.epfl.ch/publications/index.php
, 1997
"... ..."
Comparative Study of Turbo Decoding Techniques: An Overview
, 2000
"... In this contribution, we provide an overview of the novel class of channel codes referred to as turbo codes, which have been shown to be capable of performing close to the Shannon Limit. We commence with a brief discussion on turbo encoding, and then move on to describing the form of the iterative d ..."
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Cited by 43 (2 self)
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In this contribution, we provide an overview of the novel class of channel codes referred to as turbo codes, which have been shown to be capable of performing close to the Shannon Limit. We commence with a brief discussion on turbo encoding, and then move on to describing the form of the iterative decoder most commonly used to decode turbo codes. We then elaborate on various decoding algorithms that can be used in an iterative decoder, and give an example of the operation of such a decoder using the socalled Soft Output Viterbi Algorithm (SOVA). Lastly, the effect of a range of system parameters is investigated in a systematic fashion, in order to gauge their performance ramifications.
Interleaver design for turbo codes
 IEEE J. Select. Areas Commun
, 2001
"... The performance of a Turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder correspondi ..."
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Cited by 32 (0 self)
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The performance of a Turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits. This paper describes a new interleaver design for Turbo codes with short block length based on these two criteria. A deterministic interleaver suitable for Turbo codes is also described. Simulation results compare the new interleaver design to different existing interleavers. 1
New Deterministic Interleaver Designs for Turbo Codes
 IEEE Trans. on Inform. Theory
"... It is well known that an interleaver with random properties, quite often generated by pseudorandom algorithms, is one of the essential building blocks of turbo codes. However, randomly generated interleavers have two major drawbacks: lack of an adequate analysis that guarantees their performance an ..."
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Cited by 27 (4 self)
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It is well known that an interleaver with random properties, quite often generated by pseudorandom algorithms, is one of the essential building blocks of turbo codes. However, randomly generated interleavers have two major drawbacks: lack of an adequate analysis that guarantees their performance and lack of a compact representation that leads to a simple implementation. In this paper we present several new classes of deterministic interleavers of length , with construction complexity ( ), that permute a sequence of bits with nearly the same statistical distribution as a random interleaver and perform as well as or better than the average of a set of random interleavers. The new classes of deterministic interleavers have a very simple representation based on quadratic congruences and hence have a structure that allows the possibility of analysis as well as a straightforward implementation. Using the new interleavers, a turbo code of length 16384 that is only 0.7 dB away from capacy at a biterror rate (BER) of 10 5 is constructed. We also generalize the theory of previously known deterministic interleavers that are based on block interleavers, and we apply this theory to the construction of a nonrandom turbo code of length 16384 with a very regular structure whose performance is only 1.1 dB away from capacity at a BER of 10 5 .