Academic literature on the topic 'Expectation Propagation (EP)'

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Multiple-input multiple-output (MIMO) technology is one of the key technical approaches to improve the spectrum efficiency of wireless communication. Modern communication systems employ MIMO and high-order quadrature amplitude modulation (QAM) to maximize spectral efficiency. However, with the increase in the number of antennas and modulation orders, it is very challenging to design a low-complexity and high-efficiency MIMO receiver. In recent years, with the rapid development of new technologies such as artificial intelligence, more and more researchers have tried to apply machine learning techniques in the field of communication to break through the performance of traditional communication algorithms. In this paper, we propose a new low-complexity MIMO detection algorithm: an artificial intelligence-assisted expectation propagation (EP) detection algorithm. Neural network models are used to learn and map some of the time-consuming steps in the EP detection algorithm, converting the complex operation process into a few matrix multiplication operations in order to reduce the complexity of the detection algorithm. It is verified that the method proposed in this paper can approximate the performance of the original EP detection algorithm with reduced complexity and is applicable in different scenarios.

The expectation propagation (EP) detector achieves significantly better performance than the linear detectors (such as minimum mean squared error detector) in massive MIMO systems, which has drawn great attention recently. EP’s approximation (EPA) algorithm simplifies the update formula of the EP algorithm by reexpressing the moment matching condition so that the number of matrix inversions in the EP algorithm is reduced to one. However, the expense is that the EPA algorithm requires higher accuracy for this inversion; otherwise, the bit-error-rate (BER) performance will suffer serious losses. To tackle this issue, the SORI iterative algorithm is introduced to obtain the high-precision result of this inversion to ensure the good BER performance of the EPA algorithm. First, the new expression of the SORI iterative algorithm is derived under the equivalent real-valued system. Second, the improved EPA-SORI algorithm is then introduced by the SORI algorithm, which is used to approximate the initial value of the EPA algorithm under the real-valued system. Finally, by designing the initial solution and the relaxation factor of the EPA-SORI iterative algorithm, the convergence rate can be quickly increased without increasing the complexity. Simulation and complexity results exhibit that in various massive MIMO system configurations, the proposed EPA-SORI algorithm can achieve the same BER performance as the Exact EP algorithm with significantly lower complexity. At the same time, compared with MMSE and the existing EPA algorithms, the proposed EPA-SORI algorithm has a better performance-complexity trade-off advantage, which is more obvious in scenarios with high modulation order and a large number of users.

This paper proposes an improved frequency domain turbo equalization (IFDTE) with iterative channel estimation and feedback to achieve both a good performance and low complexity in underwater acoustic communications (UWACs). A selective zero-attracting (SZA) improved proportionate normal least mean square (SZA-IPNLMS) algorithm is adopted by utilizing the sparsity of the UWAC channel to estimate it using a training sequence. Simultaneously, a set-membership (SM) SZA differential IPNLMS (SM SZA-DIPNLMS) with variable step size is adopted to estimate the channel status information (CSI) in the iterative channel estimation with soft feedback. In this way, the computational complexity for iterative channel estimation is reduced effectively with minimal performance loss. Different from traditional schemes in UWACs, an IFDTE with expectation propagation (EP) interference cancellation is adopted to estimate the a posteriori probability of transmitted symbols iteratively. A bidirectional IFDTE with the EP interference cancellation is proposed to further accelerate the convergence. THe simulation results show that the proposed channel estimation obtains 1.9 and 0.5 dB performance gains, when compared with those of the IPNLMS and the l0-IPNLMS at a bit error rate (BER) of 10−3. The proposed channel estimation also effectively reduces the unnecessary updating of the coefficients of the UWAC channel. Compared with traditional time-domain turbo equalization and FDTE in UWACs, the IFDTE obtains 0.5 and 1 dB gains in the environment of SPACE’08 and it obtains 0.5 and 0.4 dB gains in the environment of MACE’04 at a BER of 10−3. Therefore, the proposed scheme obtains a good BER performance and low complexity and it is suitable for efficient use in UWACs.

Accurate causal inference among time series helps to better understand the interactive scheme behind the temporal variables. For time series analysis, an unavoidable issue is the existence of time lag among different temporal variables. That is, past evidence would take some time to cause a future effect instead of an immediate response. To model this process, existing approaches commonly adopt a prefixed time window to define the lag. However, in many real-world applications, this parameter may vary among different time series, and it is hard to be predefined with a fixed value. In this letter, we propose to learn the causal relations as well as the lag among different time series simultaneously from data. Specifically, we develop a probabilistic decomposed slab-and-spike (DSS) model to perform the inference by applying a pair of decomposed spike-and-slab variables for the model coefficients, where the first variable is used to estimate the causal relationship and the second one captures the lag information among different temporal variables. For parameter inference, we propose an efficient expectation propagation (EP) algorithm to solve the DSS model. Experimental results conducted on both synthetic and real-world problems demonstrate the effectiveness of the proposed method. The revealed time lag can be well validated by the domain knowledge within the real-world applications.

In this paper, we propose a low‐complexity expectation propagation (EP) detector for orthogonal time frequency space (OTFS) system with practical rectangular waveforms. In the high‐mobility scenario, OTFS is becoming a potential scheme for the sixth‐generation (6G) wireless communication system. However, the large size of the effective delay‐Doppler (DD) domain channel matrix brings unbearable computational complexity to the signal detection algorithm based on the matrix inversion. We propose a low‐complexity EP detector based on the sparsity and the block circulant structure of the effective channel covariance matrix in the DD domain. The proposed algorithm only requires log‐linear complexity. In addition, simulation results show that the proposed algorithm not only has the advantage of low complexity but also has good performance, which achieves a tradeoff between performance and complexity.

AbstractHere, a multi‐user signal iterative detection and decoding scheme named LBEP based on block expectation propagation (BEP) is proposed for LDPC‐coded two‐phase unsourced random access (URA) scheme. In the iterative process, the approximation of matrix inversion is used to facilitate expectation propagation (EP). In addition, this idea is also applied to the double EP (DEP) scheme. The simulation results show that, in the two‐phase URA scheme, the performance of the proposed LBEP scheme is similar to the BEP scheme for LDPC codes, but the complexity of the receiver is greatly reduced.

La Propagation d'Espérance (Expectation Propagation, EP) est une technique puissante utilisée en inférence statistique pour approximer des distributions de probabilités complexes par des distributions plus simples de la famille exponentielle, grâce à un appariement des moments. Des travaux récents ont démontré que son application à la conception de récepteurs numériques offre un compromis intéressant entre complexité et performance. En affinant de manière itérative les estimations de signal via une approche de passage de messages, l'EP fournit un cadre robuste pour relever des défis dans les systèmes de communication numérique, tels que l'interférence inter-symboles (ISI) dans les canaux à large bande. Dans cette thèse, un égaliseur linéaire auto-itératif en domaine fréquentiel basé sur l'EP (Frequency Domain Self-Iterated Linear Equalizer, FD-SILE) est étudié. Il est composé d'un égaliseur, d'un démappeur souple et d'un mappeur souple. Ces composantes exploitent le retour d'information de l'EP dans un processus d'auto-itération. Bien que le FD-SILE basé sur l'EP présente un compromis complexité-performance favorable, sa complexité computationnelle reste prohibitive pour des implémentations matérielles, notamment pour des constellations d'ordre élevé. Afin de réduire cette complexité, des simplifications analytiques sont introduites pour les processus de mappage et de démappage souples. Ces simplifications permettent une réduction significative de la complexité tout en préservant les performances en termes de taux d'erreurs binaires (Bit Error Rate, BER). Dans le cadre de cette thèse, des versions en virgule fixe des mappeurs et démappeurs souples simplifiés sont développées pour permettre la conception d'architectures. Différentes architectures sont conçues pour les schémas de modulation BPSK, QPSK, 8-PSK et 16-QAM. Ces architectures sont ensuite optimisées par pipeline, ce qui réduit considérablement le nombre de cycles d'horloge par trame. Une architecture flexible et pipelinée, capable de changer dynamiquement de constellation à chaque trame, est ensuite conçue et implémentée sur un dispositif FPGA. La validation est effectuée à l'aide d'une configuration hardware-in-the-loop (HIL), qui intègre un environnement de simulation sur ordinateur avec l'architecture implémentée sur FPGA, déployée sur une plateforme Zynq MPSoC
Expectation Propagation (EP) is a powerful technique used in statistical inference to approximate complex probability distributions with simpler ones from the exponential family through moment matching. Recent works have demonstrated that its application in digital receiver design offers an attractive complexity-performance trade-off. By iteratively refining signal estimates via a message-passing approach, EP provides a robust framework for addressing challenges in digital communication systems, such as inter-symbol interference (ISI) in wideband channels. In this thesis, an EP-based Frequency Domain Self-Iterated Linear Equalizer (FD-SILE) is considered, comprising an equalizer, a soft demapper and a soft mapper. These components take advantage of EP for feedback within a self-iterating process. While the EP-based FD-SILE demonstrates favorable complexity-performance, its computational complexity remains prohibitive for hardware implementations, particularly for high-order constellations. In order to decrease this computational complexity, analytical simplifications are introduced for the soft mapping and demapping processes. These simplifications achieve substantial reductions in computational complexity while preserving bit error rate (BER) performance.As part of this thesis work, fixed-point versions of the simplified soft mapper and demapper are carried out to enable architecture design. Different architectures are designed for the modulation schemes of BPSK, QPSK, 8-PSK, and 16-QAM. These architectures are then optimized through pipelining, significantly reducing the number of clock cycles per frame. A flexible pipelined architecture, capable of dynamically switching constellations on a per-frame basis, is subsequently designed and implemented onto an FPGA device. Validation is conducted using a hardware-in-the-loop (HIL) configuration, which integrates a simulation environment on a computer with the FPGA-implemented architecture on a Zynq MPSoC platform

We address the problem of continuous stochastic optimal control in the presence of hard obstacles. Due to the non-smooth character of the obstacles, the traditional approach using dynamic programming in combination with function approximation tends to fail. We consider a recently introduced special class of control problems for which the optimal control computation is reformulated in terms of a path integral. The path integral is typically intractable, but amenable to techniques developed for approximate inference. We argue that the variational approach fails in this case due to the non-smooth cost function. Sampling techniques are simple to implement and converge to the exact results given enough samples. However, the infinite cost associated with hard obstacles renders the sampling procedures inefficient in practice. We suggest Expectation Propagation (EP) as a suitable approximation method, and compare the quality and efficiency of the resulting control with an MC sampler on a car steering task and a ball throwing task. We conclude that EP can solve these challenging problems much better than a sampling approach.