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24
Iterative decoding in the presence of strong phase noise
 IEEE J. ON SEL. AREAS
, 2005
"... 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 ..."
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Cited by 62 (19 self)
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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.
Joint iterative detection and decoding in the presence of phase noise and frequency offset
, 2007
"... 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 rep ..."
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Cited by 19 (6 self)
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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.
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 19 (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.
Codeaided frame synchronization and phase ambiguity resolution
 IEEE Transactions on Signal Processing
"... Abstract—This contribution deals with two hypothesis testing problems for digital receivers: frame synchronization and phase ambiguity resolution. As current receivers use powerful errorcorrecting codes and operate at low signaltonoise ratio (SNR), these problems have become increasingly challeng ..."
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Cited by 7 (2 self)
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Abstract—This contribution deals with two hypothesis testing problems for digital receivers: frame synchronization and phase ambiguity resolution. As current receivers use powerful errorcorrecting codes and operate at low signaltonoise ratio (SNR), these problems have become increasingly challenging: one is forced either to waste a part of the bandwidth on training symbols or to consider novel hypothesis testing techniques. We will consider five algorithms for hypothesis testing that exploit properties of the underlying channel code: a reencoding (REEN) technique, an algorithm we previously derived from the expectationmaximization (EM) algorithm, two recently proposed algorithms known as mode separation (MS) and pseudoML (PML), and a technique where all hypotheses are tested simultaneously by applying the sum–product algorithm (SPA) to the overall factor graph of the system. These techniques will be compared in terms of their computational complexity, the class of problems to which they can be applied and their error rate performance. Through computer simulations we show that the EMbased and the PML algorithms have excellent performance. The MS, PML, REEN, and EMbased algorithms all have similar complexity, but the latter algorithm is suitable for a much wider range of applications. The SPA has the lowest computational complexity, but might yield poor performance. Index Terms—Expectationmaximization (EM) algorithm, factor graphs, frame synchronization, turbo synchronization. I.
An iterative equalization and decoding approach for underwater acoustic communication
 IEEE J. Ocean. Eng
, 2008
"... Abstract—In this paper, we present an iterative approach for recovering information sent over a shallow underwater acoustic (UWA) communication channel. The procedure has three main tasks: estimation of channel model parameters (CMPs), channel equalization, and decoding. These tasks are performed cy ..."
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Cited by 5 (0 self)
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Abstract—In this paper, we present an iterative approach for recovering information sent over a shallow underwater acoustic (UWA) communication channel. The procedure has three main tasks: estimation of channel model parameters (CMPs), channel equalization, and decoding. These tasks are performed cyclicly until the algorithm converges. Information bits are convolutionally encoded, punctured and permuted, mapped into quaternary phaseshift keying (QPSK) symbols, linearly modulated, and transmitted through a downwardrefracting ocean waveguide. Training symbols are prepended to the transmitted sequence for initial estimation of CMPs. Our algorithm processes data from a single receive sensor. Data are received on a vertical array and the performance of the algorithm for each sensor in the array is examined. There is negligible Doppler spread in the received data. However, difference between transmitter and receiver clocks as well as slight motion of the receive array produce a nonnegligible compression of the received signals. Consequently, there is observable Doppler “shift. ” Nonuniform resampling of the data produces time series we model as the output of a linear timeinvariant system. Resampling and CMP estimation are done iteratively, in conjunction with equalization and decoding. The algorithm successfully processes the data to yield few or no information bit errors. Index Terms—Iterative equalization and decoding, linear equalization, message passing, nonuniform resampling, underwater acoustic (UWA) communication. I.
Joint synchronization and decoding exploiting the turbo principle
 in Proc. of the 38th Conference on Information Sciences and Systems, 2004
, 2004
"... Abstract — This paper investigates turbo methods for joint synchronization and decoding in pulse amplitude modulated (PAM) systems. We begin with a brief review of the turbo principle before applying it to the synchronization problem. Specifically, we propose and investigate a baud timing offset syn ..."
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Cited by 4 (0 self)
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Abstract — This paper investigates turbo methods for joint synchronization and decoding in pulse amplitude modulated (PAM) systems. We begin with a brief review of the turbo principle before applying it to the synchronization problem. Specifically, we propose and investigate a baud timing offset synchronization algorithm for error control coded systems. Unlike many previously proposed algorithms, which feed estimates for the coded symbols to the decoder, our algorithm calculates and exchanges extrinsic information values for the coded bits, as is consistent with the turbo principle. Simulations prove the algorithm’s utility and verify that it has performance near to that of an ideal synchronizer achieving the Cramer Rao lower bound on timing error estimation variance. We investigate both systems employing regular convolutional error correcting codes as well as serially concatenated convolutional turbo codes. I.
on maximumlikelihood timing synchronization
 IEEE Trans. on Comm
"... Abstract—In this letter, we address the issue of symbol timing recovery for a coded burst transmission system. As direct maximumlikelihood (ML) estimation is intractable, we resort to the expectationmaximization (EM) algorithm in order to derive a receiver that iterates between data detection and ..."
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Cited by 2 (2 self)
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Abstract—In this letter, we address the issue of symbol timing recovery for a coded burst transmission system. As direct maximumlikelihood (ML) estimation is intractable, we resort to the expectationmaximization (EM) algorithm in order to derive a receiver that iterates between data detection and synchronization. Conventional dataaided (DA) and decisiondirected (DD) synchronizers can be interpreted as special cases of the proposed algorithm. The EMbased technique takes into account code properties and is especially well suited to scenarios where conventional schemes fail to provide the detector with a reliable timing estimate. The performance of the proposed algorithm is compared with conventional techniques through computer simulations, both in terms of meansquare estimation error (MSEE) and bit error rate (BER). Index Terms—Iterative methods, maximumlikelihood estimation, synchronization.
Iterative softdecision directed timing estimation for turbo receivers
"... Abstract—The current paper addresses the issue of estimating the sampling instant in turbo receivers. More specifically, we focus on a transmitter made of bit interleaved coded modulation. The proposed synchronizer is based on the maximization of an approximation of the timing loglikelihood functio ..."
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Abstract—The current paper addresses the issue of estimating the sampling instant in turbo receivers. More specifically, we focus on a transmitter made of bit interleaved coded modulation. The proposed synchronizer is based on the maximization of an approximation of the timing loglikelihood function. In particular, we approximate the a priori probabilities in the loglikelihood function from the bit a posteriori probabilities provided by the turbo receiver. The maximization is performed by means of a NewtonRaphson method based on an earlylate implementation. Performance of the proposed synchronizer is illustrated by simulation results. The mean and the variance of the estimator as well as the bit error rate reached by the synchronized system are reported. I.
1 Expectation Maximization as Message Passing—Part I: Principles and Gaussian Messages
, 2009
"... Abstract—It is shown how expectation maximization (EM) may be viewed as a message passing algorithm in factor graphs. In particular, a new general EM message computation rule is identified. As a factor graph tool, EM may be used to break cycles in a factor graph, and “nice ” messages may in some cas ..."
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Cited by 1 (0 self)
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Abstract—It is shown how expectation maximization (EM) may be viewed as a message passing algorithm in factor graphs. In particular, a new general EM message computation rule is identified. As a factor graph tool, EM may be used to break cycles in a factor graph, and “nice ” messages may in some cases be obtained where the standard sumproduct messages are unwieldy. As an exemplary application, the paper considers linear Gaussian state space models with multipliers. Such multipliers arise naturally from unknown model coefficients. A main attraction of EM in such cases is that it results in purely Gaussian message passing algorithms. These Gaussian EM messages are tabulated for several (scalar, vector, matrix) multipliers that frequently appear in applications. I.
On the Influence of Pilot Symbol and Data Symbol Positioning on Turbo Synchronization
 In Proc. of the IEEE VTC Conf
, 2007
"... Abstract — When realizing carrier frequency offset estimation at low signaltonoise ratios, a typical feedforward synchronization unit solely relies on known pilot symbols. The importance of the position of these pilot symbols within the burst has been elaborated on in the literature. In this pap ..."
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Abstract — When realizing carrier frequency offset estimation at low signaltonoise ratios, a typical feedforward synchronization unit solely relies on known pilot symbols. The importance of the position of these pilot symbols within the burst has been elaborated on in the literature. In this paper, we discuss the importance of the pilot symbol constellation for iterative codeaided synchronization. Furthermore, we investigate the transmission order of data symbols for a turbo coded system with codeaided synchronization. I.