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58
Reducedstate BCJRtype algorithms
, 2001
"... In this paper, we propose a technique to reduce the number of trellis states in BCJRtype algorithms, i.e., algorithms with a structure similar to that of the wellknown algorithm by Bahl, Cocke, Jelinek, and Raviv (BCJR). This work is inspired by reducedstate sequence detection (RSSD). The key id ..."
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Cited by 32 (10 self)
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In this paper, we propose a technique to reduce the number of trellis states in BCJRtype algorithms, i.e., algorithms with a structure similar to that of the wellknown algorithm by Bahl, Cocke, Jelinek, and Raviv (BCJR). This work is inspired by reducedstate sequence detection (RSSD). The key idea is the construction, during one of the recursions in the reducedstate trellis, of a “survivor map” to be used in the other recursion. In a more general setting, two distinct survivor maps could be determined in the two recursions and used jointly to approximate the a posteriori probabilities. Three examples of application to iterative decoding are shown: 1) coherent detection for intersymbol interference (ISI) channels; 2) noncoherent detection based on an algorithm recently proposed by the authors; and 3) detection based on linear prediction for Rayleigh fading channels. As in classical RSSD, the proposed algorithm allows significant statecomplexity reduction with limited performance degradation.
Joint noncoherent demodulation and decoding for the block fading channel: a practical framework for approaching Shannon capacity
 IEEE Transactions on Communications
, 2003
"... Abstract—This paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels, guided by explicit comparisons with informationtheoretic benchmarks. Noncoherent reception is interpreted as joint data and channel estimation, assuming that th ..."
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Cited by 30 (10 self)
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Abstract—This paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels, guided by explicit comparisons with informationtheoretic benchmarks. Noncoherent reception is interpreted as joint data and channel estimation, assuming that the channel is time varying and a priori unknown. We consider iterative decoding for a serial concatenation of a standard binary outer channel code with an inner modulation code amenable to noncoherent detection. For an information rate of about 1/2 bit per channel use, the proposed scheme, using a quaternary phaseshift keying (QPSK) alphabet, provides performance within 1.6–1.7 dB of Shannon capacity for the block fading channel, and is about 2.5–3 dB superior to standard differential demodulation in conjunction with an outer channel code. We also provide capacity computations for noncoherent communication using standard phaseshift keying (PSK) and quadrature amplitude modulation (QAM) alphabets, comparing these with the capacity with unconstrained input provides guidance as to the choice of constellation as a function of the signaltonoise ratio. These results imply that QPSK suffices to approach the unconstrained capacity for the relatively low information and fading rates considered in our performance evaluations, but that QAM is superior to PSK for higher information or fading rates, motivating further research into efficient noncoherent coded modulation with QAM alphabets. Index Terms—Capacity, coding, fading channels, noncoherent detection, wireless communications. I.
On LDPC codes over channels with memory
 IEEE Trans. Wireless Commun
, 2006
"... Abstract — The problem of detection and decoding of lowdensity paritycheck (LDPC) codes transmitted over channels with memory is addressed. A new general method to build a factor graph which takes into account both the code constraints and the channel behavior is proposed and the a posteriori proba ..."
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Cited by 18 (12 self)
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Abstract — The problem of detection and decoding of lowdensity paritycheck (LDPC) codes transmitted over channels with memory is addressed. A new general method to build a factor graph which takes into account both the code constraints and the channel behavior is proposed and the a posteriori probabilities of the information symbols, necessary to implement maximum a posteriori (MAP) symbol detection, are derived by using the sumproduct algorithm. With respect to the case of a LDPC code transmitted on a memoryless channel, the derived factor graphs have additional factor nodes taking into account the channel behavior and not the code constraints. It is shown that the function associated to the generic factor node modeling the channel is related to the basic branch metric used in the Viterbi algorithm when MAP sequence detection is applied or in the BCJR algorithm implementing MAP symbol detection. This fact suggests that all the previously proposed solutions for those algorithms can be systematically extended to LDPC codes and graphbased detection. When the sumproduct algorithm works on the derived factor graphs, the most demanding computation is in general that performed at factor nodes modeling the channel. In fact, the complexity of the computation at these factor nodes is in general exponential in a suitably defined channel memory parameter. In these cases, a technique for complexity reduction is illustrated. In some particular cases of practical relevance, the above mentioned complexity becomes linear in the channel memory. This does not happen in the same cases when detection is performed by using the Viterbi algorithm or the BCJR algorithm, suggesting that the use of factor graphs and the sumproduct algorithm might be computationally more appealing. As an example of application of the described framework, the cases of noncoherent and flat fading channels are considered. Index Terms — Factor graphs, sumproduct algorithm, channels with memory, phasenoise, flat fading, lowdensity paritycheck codes, iterative detection/decoding. I.
Noncoherent iterative (turbo) decoding
, 2000
"... Recently, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these ..."
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Cited by 18 (3 self)
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Recently, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. In this paper, we propose two noncoherent softoutput decoding algorithms. The first solution has a structure similar to that of the wellknown algorithm by Bahl et al.(BCJR), whereas the second is based on noncoherent sequence detection and a reducedstate softoutput Viterbi algorithm. Applications to the combined detection and decoding of differential or convolutional codes are considered. Further applications to noncoherent iterative decoding of turbo codes and serially concatenated interleaved codes are also considered. The proposed noncoherent detection schemes exhibit moderate performance loss with respect to corresponding coherent schemes and are very robust to phase and frequency instabilities.
Noncoherent sequence detection of continuous phase modulations
 IEEE Transactions on Communications
, 1999
"... Abstract—In this paper, noncoherent sequence detection, proposed in a companion paper [1] by Colavolpe and Raheli, is extended to the case of continuous phase modulations (CPM’s). The results in the companion paper on linear modulations with intersymbol interference (ISI) are used here because a CPM ..."
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Cited by 17 (5 self)
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Abstract—In this paper, noncoherent sequence detection, proposed in a companion paper [1] by Colavolpe and Raheli, is extended to the case of continuous phase modulations (CPM’s). The results in the companion paper on linear modulations with intersymbol interference (ISI) are used here because a CPM signal is mathematically equivalent to a sum of ISIaffected linearly modulated components, according to the Laurent decomposition. The proposed suboptimal detection schemes have a performance which approaches that of coherent detection with acceptable complexity, allow for timevarying phase models, and compare favorably with previously proposed solutions. Index Terms — Continuous phase modulation, intersymbol interference, maximumlikelihood detection, noncoherent sequence detection. I.
Theoretical analysis and performance limits of noncoherent sequence detection of coded PSK
 IEEE TRANS. INFORM. THEORY
, 2000
"... In this paper, a theoretical performance analysis of noncoherent sequence detection schemes recently proposed by the authors for combined detection and decoding of codedary phaseshift keying (PSK) is presented. A method for the numerical evaluation of the pairwise error probability—for which no c ..."
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Cited by 14 (8 self)
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In this paper, a theoretical performance analysis of noncoherent sequence detection schemes recently proposed by the authors for combined detection and decoding of codedary phaseshift keying (PSK) is presented. A method for the numerical evaluation of the pairwise error probability—for which no closedform expressions exist—is described, the classical union bound is computed, and results are compared with computer simulations. An upper bound on this pairwise error probability is also presented. This upper bound may be effectively used for the definition of an equivalent distance, which may be useful in exhaustive searches for optimal codes. Using this bound, it is proven that, in the general coded case, the considered noncoherent decoding schemes perform as close as desired to an optimal coherent receiver when a phase memory parameter is sufficiently large. In the case of differentially encodedPSK, a simple expression of the asymptotic biterror probability is derived, which is in agreement with simulations for high as well as low signaltonoise ratio (SNR).
A unified framework for finitememory detection
 IEEE J. SAC
, 2005
"... In this paper, we present a general approach to finitememory detection. From a semitutorial perspective, a number of previous results are rederived and new insights are gained within a unified framework. A probabilistic derivation of the wellknown Viterbi algorithm (VA), forwardbackward (FB), an ..."
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Cited by 10 (8 self)
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In this paper, we present a general approach to finitememory detection. From a semitutorial perspective, a number of previous results are rederived and new insights are gained within a unified framework. A probabilistic derivation of the wellknown Viterbi algorithm (VA), forwardbackward (FB), and sumproduct (SP) algorithms, shows that a basic metric emerges naturally under very general causality and finitememory conditions. This result implies that detection solutions based on one algorithm can be systematically extended to other algorithms. For stochastic channels described by a suitable parametric model, a conditional Markov property is shown to imply this finitememory condition. Unfortunately, this property is seldom met in practice and optimality cannot be claimed. We show, however, that in the case of transmission over a linear channel characterized by a single timeinvariant stochastic parameter, a finitememory detection strategy is asymptotically optimal, regardless of the particular algorithm used (VA, FB, or SP). We consider, as examples, linear predictive and noncoherent detection schemes. The final conclusion is that while asymptotic optimality for increasing complexity can often be achieved, key issues in the design of detection algorithms are the computational efficiency and the performance for limited complexity. Index Terms MAP sequence/symbol detection, iterative detection, graphbased detection, adaptive detection, finitememory detection, Viterbi algorithm, forwardbackward algorithm, sumproduct algorithm.
Blind Turbo Equalization for Wireless DPSK Systems
 in Proc. 4th Int. ITG Conf. on Source and Channel Coding
, 2002
"... A turbo equalization scheme consisting of an inner blind softin softout (SISO) equalizer and an outer SISO channel decoder is proposed and investigated. The receiver is suitable for wireless differential phase shift keying (DPSK) systems. The basic structure of the blind SISO equalizer consists of ..."
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Cited by 8 (5 self)
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A turbo equalization scheme consisting of an inner blind softin softout (SISO) equalizer and an outer SISO channel decoder is proposed and investigated. The receiver is suitable for wireless differential phase shift keying (DPSK) systems. The basic structure of the blind SISO equalizer consists of an iterative approximation of the joint maximumlikelihood (ML) solution with respect to (w.r.t.) channel estimation and sequence detection. The approximation is enhanced by adaptive channel estimation and by using a priori information delivered by the outer channel decoder. The DPSK/ISI super trellis is explicitly exploited for blind equalization rather than just doing differential decoding for resolving the problem of phase ambiguity. Phase ambiguity and shift ambiguity associated with trellisbased blind equalization are discussed for coded systems. Furthermore, new approaches are proposed to combat the phase ambiguity and the shift ambiguity.
Multilevel Optical Systems With MLSD Receivers Insensitive to GVD and PMD
"... Abstract—This paper analyzes optical transmission systems based on highorder modulations such as phaseshift keying signals and quadrature amplitude modulations. When the channel is affected by group velocity dispersion (GVD), polarization mode dispersion (PMD), and phase uncertainties due to the l ..."
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Cited by 8 (5 self)
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Abstract—This paper analyzes optical transmission systems based on highorder modulations such as phaseshift keying signals and quadrature amplitude modulations. When the channel is affected by group velocity dispersion (GVD), polarization mode dispersion (PMD), and phase uncertainties due to the laser phase noise, the optimal receiver processing based on maximumlikelihood sequence detection and its practical implementation through a Viterbi processor is described without a specific constraint on the receiver front end. The implementation issues are then faced, showing that at least a couple of widely known front ends, with proper modifications, can be used to extract the required sufficient statistics from the received signal. The aspects related to the receiver adaptivity, the complexity reduction of the Viterbi processor, and the possibility of employing polarization diversity at the transmitter end are also discussed. It is demonstrated that, as long as a sufficient number of Viterbi processor trellis states is employed, GVD and PMD entail no performance degradation with respect to the case of no channel distortions (the backtoback case). Index Terms—Differential encoding, electrical equalization, group velocity dispersion (GVD), intersymbol interference (ISI), maximumlikelihood sequence detection (MLSD), optical transmission systems, phaseshift keying (PSK), polarization mode dispersion (PMD), quadrature amplitude modulation (QAM), Viterbi algorithm (VA). I.
Robust Multilevel Coherent Optical Systems With Linear Processing at the Receiver
"... Abstract—This paper investigates optical coherent systems based on polarization multiplexing and highorder modulations such as phaseshift keying (PSK) signals and quadrature amplitude modulations (QAM). It is shown that a simple linear receiver processing is sufficient to perfectly demultiplex th ..."
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Cited by 7 (6 self)
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Abstract—This paper investigates optical coherent systems based on polarization multiplexing and highorder modulations such as phaseshift keying (PSK) signals and quadrature amplitude modulations (QAM). It is shown that a simple linear receiver processing is sufficient to perfectly demultiplex the two transmitted streams and to perfectly compensate for group velocity dispersion (GVD) and polarization mode dispersion (PMD). In addition, in the presence of a strong phase noise of the lasers at the transmitter and receiver, a symbolbysymbol detector with decision feedback is able to considerably improve the receiver robustness with a limited complexity increase. We will also discuss the channel estimation and the receiver adaptivity to timevarying channel conditions as well as the problem of the frequency acquisition and tracking. Finally, a new twodimensional (polarization/time) differential encoding rule is proposed to overcome a polarizationambiguity problem. In the numerical results, the receiver performance will be assessed versus the receiver complexity. Index Terms—Electrical equalization, group velocity dispersion (GVD), intersymbol interference (ISI), optical coherent transmission systems, phaseshift keying (PSK), polarization mode dispersion (PMD), quadrature amplitude modulation (QAM). I.