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Asynchronous physicallayer network coding,” technical report. Available: http://arxiv.org/abs/1105.3144
"... Abstract—A key issue in physicallayer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrierphase offset. ..."
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Abstract—A key issue in physicallayer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrierphase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannelcoded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For QPSK unchannelcoded PNC, with a half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channelcoded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channelcoded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannelcoded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC. Index Terms—Physicallayer network coding, network coding, synchronization. I.
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 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.
On the CramerRao bound for carrier frequency estimation in the presence of phase noise
, 2007
"... We consider the carrier frequency offset estimation in a digital burstmode satellite transmission affected by phase noise. The corresponding CramerRao lower bound is analyzed for linear modulations under a Wiener phase noise model and in the hypothesis of knowledge of the transmitted data. Even i ..."
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Cited by 5 (4 self)
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We consider the carrier frequency offset estimation in a digital burstmode satellite transmission affected by phase noise. The corresponding CramerRao lower bound is analyzed for linear modulations under a Wiener phase noise model and in the hypothesis of knowledge of the transmitted data. Even if we resort to a Monte Carlo average, from a computational point of view the evaluation of the CramerRao bound is very hard. We introduce a simple but very accurate approximation that allows to carry out this task in a very easy way. As it will be shown, the presence of the phase noise produces a remarkable performance degradation of the frequency estimation accuracy. In addition, we provide asymptotic expressions of the CramerRao bound, from which the effect of the phase noise and the dependence on the system parameters of the frequency offset estimation accuracy clearly result. Finally, as a byproduct of our derivations and approximations, we derive a couple of estimators specifically tailored for the phase noise channel that will be compared with the classical Rife and Boorstyn algorithm, gaining in this way some important hints on the estimators to be used in this scenario.
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.
Iterative codeaided phase noise synchronization based on the LMMSE criterion
 in Proc. IEEE Workshop on Signal Process. Adv. Wireless Commun
, 2007
"... In this paper, we examine codeaided synchronization in the presence of carrier frequency uncertainties and phase noise. As codeaided synchronization can only achieve high estimation accuracy if the initial parameter offset is sufficiently small, we employ a dataaided coarse synchronization unit ..."
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Cited by 3 (1 self)
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In this paper, we examine codeaided synchronization in the presence of carrier frequency uncertainties and phase noise. As codeaided synchronization can only achieve high estimation accuracy if the initial parameter offset is sufficiently small, we employ a dataaided coarse synchronization unit comprising a feedforward frequency estimator and a LMMSE estimator for precompensating frequency offsets and phase noise. Furthermore, we make use of known iterative synchronization techniques for frequency and phase offsets. We here extend the concept of iterative synchronization to iterative phase noise compensation and we show analytically under which circumstances our approach can achieve a worthwhile improvement in terms of estimation accuracy. 1.
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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Cited by 2 (0 self)
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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.
Chapter 13 Factor Graphs and Message Passing Algorithms
"... Complex modern day systems are often characterized by the presence of many interacting variables that govern the dynamics of the system. Statistical inference in such systems requires efficient algorithms that offer an ease of implementation while delivering the prespecified performance guarantees ..."
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Complex modern day systems are often characterized by the presence of many interacting variables that govern the dynamics of the system. Statistical inference in such systems requires efficient algorithms that offer an ease of implementation while delivering the prespecified performance guarantees. In developing an algorithm for a sophisticated system, accurate and representative modeling of the underlying system is often the first step. The use of graphical models to explain the