On the advances in message-passing algorithms and practical iterative receiver design
Résumé
Tutorial presented at the EUSIPCO 2024 conference https://eusipcolyon.sciencesconf.org/resource/page/id/28. In recent years, we witnessed a renewed interest of the wireless communications and signal processing research communities about iterative algorithms based on approximate Bayesian inference and message passing. Such techniques have previously shined through the success of probabilistic channel decoding algorithms throughout the 90s, leading to the widespread investigations on the “turbo principle” and on the belief propagation (BP) algorithm in early 2000s, in many digital receiver design problems involving estimation, equalization, detection and decoding. A decade later, the increased popularity of expectation propagation (EP) for handling intractable variational inference problems and other emerging practical approximate message passing (AMP) techniques have led to novel iterative signal estimation algorithms with attractive complexity-performance trade-offs. In particular, these algorithms are able to produce signal estimates uncorrelated with the observations and the priors, a property which considerably reduces error propagation in the iterative estimation process, and whose performance in the asymptotic regime can be accurately predicted. Reinforced with other practical variational inference techniques such as the expectation maximization (EM) or mean-field (MF), and with emerging deep learning aided design approaches, advanced iterative algorithm design remains a hot-topic in various signal processing and machine learning communities. Indeed, researchers have been proposing competing strategies such as the sparse Bayesian learning (SBL), expectation consistent optimisation framework, memory AMP (MAMP), orthogonal AMP (OAMP) or vector AMP (VAMP) and many others to seek nearoptimal estimation performance, with significant variations both in algorithmic complexity and in the underlying theoretical backgrounds. Consequently, it has become significantly more difficult to get a grasp on this rapidly developing literature, which incorporates many closely-related contributions as well as some important overlooked developments. Our tutorial aims to provide a synthetic view on the major developments on variational Bayesian inference techniques, mainly from a message-passing algorithm perspective, and to assess the capabilities of this arsenal based on EP and other related AMP techniques for addressing stochastic signal processing problems. In particular, in the context of digital communication receiver design, we make emphasis on the importance of factor graph assumptions and scheduling strategies, for achieving reasonable performance-complexity tradeoff. Indeed, recent years have shown that these techniques lead to the practical implementation of iterative receivers for non-orthogonal multiple access (NOMA), for multiple-input multiple-output (MIMO) and singlecarrier (SC) systems among others. With the help of additional optimization through deep unfolding, and with optimized channel code design, such techniques can be expected to play an important role in next-generation communications transceivers.
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