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18
Iterative decoding in the presence of strong phase noise,” submitted to
 IEEE J. on Sel. Areas
"... Abstract—We present two new iterative decoding algorithms for channels affected by strong phase noise and compare them with the best existing algorithms proposed in the literature. The proposed algorithms are obtained as an application of the sumproduct algorithm to the factor graph representing th ..."
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Cited by 61 (19 self)
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Abstract—We present two new iterative decoding algorithms for channels affected by strong phase noise and compare them with the best existing algorithms proposed in the literature. The proposed algorithms are obtained as an application of the sumproduct algorithm to the factor graph representing the joint a posteriori probability mass function of the information bits given the channel output. In order to overcome the problems due to the presence in the factor graph of continuous random variables, we apply the method of canonical distributions. Several choices of canonical distributions have been considered in the literature. Wellknown approaches consist of discretizing continuous variables or treating them as jointly Gaussian, thus obtaining a Kalman estimator. Our first new approach, based on the Fourier series expansion of the phase probability density function, yields better complexity/performance tradeoff with respect to the usual discretizedphase method. Our second new approach, based on the Tikhonov canonical distribution, yields nearoptimal performance at very low complexity and is shown to be much more robust than the Kalman method to the placement of pilot symbols in the coded frame. We present numerical results for binary LDPC codes and LDPCcoded modulation, with particular reference to some phasenoise models and codedmodulation formats standardized in the nextgeneration satellite Digital Video Broadcasting (DVBS2). These results show that our algorithms achieve nearcoherent performance at very low complexity without requiring any change to the existing DVBS2 standard. Index Terms—Channels with memory, factor graphs (FGs), iterative detection/decoding, lowdensity paritycheck (LDPC) codes, phasenoise, sumproduct algorithm (SPA), Tikhonov parameterization. I.
On the application of factor graphs and the sumproduct algorithm to ISI channels
 IEEE Trans. Commun
, 2005
"... Abstract—In this paper, based on the application of the sum–product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative softinput softoutput (SISO) detection schemes for intersymbol interference (ISI) chan ..."
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Cited by 31 (5 self)
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Abstract—In this paper, based on the application of the sum–product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative softinput softoutput (SISO) detection schemes for intersymbol interference (ISI) channels. We have verified by computer simulations that the SP algorithm converges to a good approximation of the exact marginal APPs of the transmitted symbols if the FG has girth at least 6. For ISI channels whose corresponding FG has girth 4, the application of a stretching technique allows us to obtain an equivalent girth6 graph. For sparse ISI channels, the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm. They also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction. The application to joint detection and decoding of lowdensity paritycheck (LDPC) codes is also considered and results are shown for some partialresponse magnetic channels. Also in these cases, we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal “serial ” BCJR algorithm is used for detection. Therefore, for their parallel implementation, they represent a favorable alternative to the modified “parallel ” BCJR algorithm proposed in the literature for the application to magnetic channels. Index Terms—Factor graphs, intersymbol interference (ISI) channels, iterative detection, lowdensity paritycheck (LDPC) codes, partialresponse channels, sum–product (SP) algorithm. I.
Joint iterative detection and decoding in the presence of phase noise and frequency offset
 in Proc. IEEE Intern. Conf. Commun
, 2005
"... Abstract—We present a new algorithm for joint detection and decoding of iteratively decodable codes transmitted over channels affected by a timevarying phase noise (PN) and a constant frequency offset. The proposed algorithm is obtained as an application of the sumproduct algorithm to the factor g ..."
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Cited by 19 (6 self)
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Abstract—We present a new algorithm for joint detection and decoding of iteratively decodable codes transmitted over channels affected by a timevarying phase noise (PN) and a constant frequency offset. The proposed algorithm is obtained as an application of the sumproduct algorithm to the factor graph representing the joint a posteriori distribution of the information symbols and the channel parameters given the channel output. The resulting algorithm employs the softoutput information on the coded symbols provided by the decoder and performs forward– backward recursions, taking into account the joint probability distribution of phase and frequency offset. We present simulation results for highorder coded modulation schemes based on lowdensity paritycheck codes and serially concatenated convolutional codes, showing that, despite its low complexity, the algorithm is able to cope with a strong PN and a significant uncompensated frequency offset, thus avoiding the use of complicated dataaided frequencyestimation schemes operating on a known preamble. The robustness of the algorithm in the presence of a timevarying frequency offset is also discussed. Index Terms—Detection and decoding in the presence of phase noise and frequency offset, factor graphs (FGs), iterative detection and decoding, lowdensity paritycheck (LDPC) codes, serially concatenated convolutional codes (SCCCs), sumproduct algorithm (SPA), turbo codes (TCs). I.
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.
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.
Iterative Detection for Channels With Memory
, 2007
"... In this paper, we present an overview on the design of algorithms for iterative detection over channels with memory. The starting point for all the algorithms is the implementation of softinput softouput maximum a posteriori (MAP) symbol detection strategies for transmissions over channels encom ..."
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Cited by 4 (1 self)
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In this paper, we present an overview on the design of algorithms for iterative detection over channels with memory. The starting point for all the algorithms is the implementation of softinput softouput maximum a posteriori (MAP) symbol detection strategies for transmissions over channels encompassing unknown parameters, either stochastic or deterministic. The proposed solutions represent effective ways to reach this goal. The described algorithms are grouped into three categories: i) we first introduce algorithms for adaptive iterative detection, where the unknown channel parameters are explicitly estimated; ii) then, we consider finitememory iterative detection algorithms, based on ad hoc truncation of the channel memory and often interpretable as based on an implicit estimation of the channel parameters; and iii) finally, we present a general detectiontheoretic approach to derive optimal detection algorithms with polynomial complexity. A few illustrative numerical results are also presented.
Impact of Phase Noise and Compensation Techniques in Coherent Optical Systems
"... Abstract—One of the most severe impairments that affect coherent optical systems employing highorder modulation formats is phase noise due to transmit and receive lasers. This is especially detrimental in uncompensated links, where an ideal compensator for channel distortions and laser phase noise ..."
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Cited by 2 (0 self)
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Abstract—One of the most severe impairments that affect coherent optical systems employing highorder modulation formats is phase noise due to transmit and receive lasers. This is especially detrimental in uncompensated links, where an ideal compensator for channel distortions and laser phase noise should first eliminate receive phase noise, then equalize channel distortions, and only later compensate for transmit phase noise. Unfortunately, the simultaneous presence of transmit and receive phase noise makes very difficult to discriminate between them, even in the presence of a pilot tone. Moreover, the picture is different for optical systems using singlecarrier or orthogonal frequency divisionmultiplexing, where transmit and receive phase noise components may have a different impact. All these aspects are analyzed and discussed in this paper. A novel digital coherence enhancement (DCE) technique, able to significantly reduce the phase noise of transmit or receive lasers by using an interferometric device plus a very simple electronic processing, is also described. The performance of this technique and the statistical properties of the residual phase noise are analytically derived and verified by simulations, showing a high increase of the maximum bitratedistance product. The practical implementation of DCE is finally discussed and some alternative implementation schemes are presented. Index Terms—Coherent detection, group velocity dispersion (GVD), optical communication, orthogonal frequency division multiplexing (OFDM), phase noise. I.
On linear predictive detection for communications with phase noise and frequency offset
 IEEE Trans. Veh. Techol
, 2007
"... Abstract—In this paper, by applying the concept of linear prediction, which is widely used for fading channels, to phaseuncertain communications, we generalize existing linear predictive detection algorithms for transmission over channels with phase noise and frequency offset. This approach leads to ..."
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Abstract—In this paper, by applying the concept of linear prediction, which is widely used for fading channels, to phaseuncertain communications, we generalize existing linear predictive detection algorithms for transmission over channels with phase noise and frequency offset. This approach leads to the derivation of detection algorithms, which are referred to as phasor linear predictive (pLP), for trellisbased maximum a posteriori (MAP) sequence detection (based on the Viterbi algorithm) and MAP symbol detection: trellisbased (using the forward– backward algorithm) and graphbased (using the sum–product algorithm). The effectiveness of the proposed pLP detection algorithms is evaluated for several communication schemes. The derived algorithms outperform previously appeared finitememory detection solutions in terms of robustness against fast channel dynamics. Moreover, the proposed detection strategy lends itself to attractive extensions to adaptive schemes. Index Terms—Finitememory detection, forward–backward (FB) algorithm, graphbased detection, iterative detection, linear prediction, maximum a posteriori (MAP) sequence/symbol detection, minimum mean square error (MMSE) estimation, sum– product (SP) algorithm, Viterbi algorithm (VA). I.
Softoutput detection of differentially encoded MPSK over channels with phase noise
 in Proc. European Signal Processing Conf. (EUSIPCO
, 2006
"... Abstract — We consider a differentially encoded MPSK signal transmitted over a channel affected by phase noise. For this problem, we derive the exact maximum a posteriori (MAP) symbol detection algorithm. By analyzing its properties, we demonstrate that it can be implemented by a forwardbackward e ..."
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Abstract — We consider a differentially encoded MPSK signal transmitted over a channel affected by phase noise. For this problem, we derive the exact maximum a posteriori (MAP) symbol detection algorithm. By analyzing its properties, we demonstrate that it can be implemented by a forwardbackward estimator of the phase probability density function, followed by a symbolbysymbol completion to produce the a posteriori probabilities of the information symbols. To practically implement the forwardbackward phase estimator, we propose a couple of schemes with different complexity. The resulting algorithms exhibit an excellent performance and, in one case, only a slight complexity increase with respect to the algorithm which perfectly knows the channel phase. The application of the proposed algorithms to repeat and accumulate codes is assessed in the numerical results. I.
1LDPC Decoding Over NonBinary QueueBased Burst Noise Channels
"... Abstract—Iterative decoding based on the sumproduct algorithm (SPA) is examined for sending lowdensity parity check (LDPC) codes over a discrete nonbinary queuebased Markovian burst noise channel. This channel model is adopted due to its analytically tractability and its recently demonstrated c ..."
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Abstract—Iterative decoding based on the sumproduct algorithm (SPA) is examined for sending lowdensity parity check (LDPC) codes over a discrete nonbinary queuebased Markovian burst noise channel. This channel model is adopted due to its analytically tractability and its recently demonstrated capability in accurately representing correlated flat Rayleigh fading channels under antipodal signaling and either hard or soft output quantization. SPA equations are derived in closedform for this model in terms of its parameters. It is then numerically observed that potentially large coding gains can be realized with respect to the Shannon limit by exploiting channel memory as opposed to ignoring it via interleaving. Finally, the LDPC decoding performance under both matched and mismatched decoding regimes is evaluated. It is shown that the Markovian model provides noticeable gains over channel interleaving and that it can effectively capture the underlying fading channels behavior when decoding LDPC codes. Index Terms—Burst Noise, finitestate Markov channels, modeling correlated Rayleigh fading channels, Shannon limit, matched and mismatched decoding, hard and softdecision demodulation, channel interleaving, lowdensity paritycheck codes, iterative decoding. I.