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143
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.
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 considered. In low signaltonoise regions, performance analysis uses simulations of typical turbo coding systems. For higher signaltonoise 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 considered. In low signaltonoise regions, performance analysis uses simulations of typical turbo coding systems. For higher signaltonoise 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.
Iterative Channel Estimation and Decoding of Pilot Symbol Assisted Turbo Codes Over FlatFading Channels
 IEEE Journal on Selected Areas in Communications
, 2001
"... A method for coherently detecting and decoding turbo coded binary phase shift keying (BPSK) signals transmitted over frequencyflat fading channels is discussed. Estimates of the complex channel gain and variance of the additive noise are derived first from known pilot symbols and an estimation fi ..."
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Cited by 81 (3 self)
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A method for coherently detecting and decoding turbo coded binary phase shift keying (BPSK) signals transmitted over frequencyflat fading channels is discussed. Estimates of the complex channel gain and variance of the additive noise are derived first from known pilot symbols and an estimation filter. After each iteration of turbo decoding, the channel estimates are refined using information fed back from the decoder. Both harddecision and softdecision feedback are considered and compared with three baseline turbocoded systems: 1) a BPSK system that has perfect channel estimates; 2) a system that uses differential phase shift keying and hence needs no estimates; and 3) a system that performs channel estimation using pilot symbols but has no feedback path from decoder to estimator. Performance can be further improved by borrowing channel estimates from the previously decoded frame. Simulation results show the influence of pilot symbol spacing, estimation filter size and type, and fade rate. Performance within 0.49 and 1.16 dB of turbocoded BPSK with perfect coherent detection is observed at a biterror rate of 10 4 for normalized fade rates of =0005 and =002, respectively.
Transfer Function Bounds on the Performance of Turbo Codes
 Communications Systems and Research Section, R. 1. McEliece California Institute of Technology
, 1995
"... In this article, we apply transfer function bounding techniques to obtain upper bounds on the biterror rate for maximumlikelihood decoding of turbo codes constructed with random permutations. These techniques are applied to two turbo codes with constraint length 3 and later extended to other code ..."
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Cited by 62 (5 self)
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In this article, we apply transfer function bounding techniques to obtain upper bounds on the biterror rate for maximumlikelihood decoding of turbo codes constructed with random permutations. These techniques are applied to two turbo codes with constraint length 3 and later extended to other codes. The performance predicted by these bounds is compared with simulation results. The bounds are useful in estimating the \error °oor " that is di–cult to measure by simulation, and they provide insight on how to lower this °oor. More reflned bounds are needed for accurate performance measures at lower signaltonoise ratios. I.
On the Minimum Distance of Parallel and Serially Concatenated Codes. [Online]. Available: http://lthcwww.epfl.ch/publications/index.php
, 1997
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VLSI Architectures for Iterative Decoders in Magnetic Recording Channels
 IEEE Trans. Magnetics
, 2001
"... VLSI implementation complexities of softinput softoutput (SISO) decoders are discussed. These decoders are used in iterative algorithms based on Turbo codes or Low Density Parity Check (LDPC) codes, and promise significant bit error performance advantage over conventionally used partialresponse m ..."
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Cited by 33 (4 self)
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VLSI implementation complexities of softinput softoutput (SISO) decoders are discussed. These decoders are used in iterative algorithms based on Turbo codes or Low Density Parity Check (LDPC) codes, and promise significant bit error performance advantage over conventionally used partialresponse maximum likelihood (PRML) systems, at the expense of increased complexity. This paper analyzes the requirements for computational hardware and memory, and provides suggestions for reducedcomplexity decoding and reduced control logic. Serial concatenation of interleaved codes, using an outer block code with a partial response channel acting as an inner encoder, is of special interest for magnetic storage applications.
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 .
Upper Bound on the Minimum Distance of Turbo Codes Using a Combinatorial Approach
 IEEE Transactions on Communications
, 2000
"... By using combinatorial considerations, we derive new upper bounds on the minimum Hamming distance, which Turbo codes can maximally attain with arbitrary  including the best  interleavers. The new bounds prove that by contrast to general linear binary channel codes, the minimum Hamming distance o ..."
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Cited by 27 (1 self)
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By using combinatorial considerations, we derive new upper bounds on the minimum Hamming distance, which Turbo codes can maximally attain with arbitrary  including the best  interleavers. The new bounds prove that by contrast to general linear binary channel codes, the minimum Hamming distance of Turbo codes cannot asymptotically grow stronger than the third root of the codeword length.
On Maximum ContentionFree Interleavers and Permutation Polynomials over Integer Rings
 IEEE TRANS. ON INFORM. THEORY
, 2006
"... An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contentionfree interleavers have been recently shown to be suitable for p ..."
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Cited by 23 (3 self)
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An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contentionfree interleavers have been recently shown to be suitable for parallel decoding of turbo codes. In this correspondence, it is shown that quadratic permutation polynomials generate maximum contentionfree interleavers, i.e., every factor of the interleaver length becomes a possible degree of parallel processing of the decoder. Further, it is shown by computer simulations that turbo codes using these interleavers perform very well for the 3rd Generation Partnership Project (3GPP) standard.