Message passing algorithms, in particular approximate message passing (AMP) and vector approximate message passing (VAMP) are versatile, low-complexity approaches for solving a variety of problems in communications. In most cases, real-valued data is treated. However, in communications and other applications that use electromagnetic waves, complex signals are of interest. Moreover, quaternionic signal processing is an area of increasing interest that is useful whenever two complex signals are treated jointly. In this talk, we discuss a concise method for calculating complex and quaternionic minimum mean-squared error (MMSE) estimators in the case of additive Gaussian noise, or more generally, noise from an exponential family. To that end, it must be noted that quaternion algebra has some peculiarities. Nevertheless, we show that, formally, the results in the complex and quaternionic cases are identical to those in real settings, provided that the gradients of complex and quaternionic functions are suitably defined.

In this talk, we present a signal recovery framework for a multi-user uplink communication system where U users transmit simultaneously to a base station using random precoding. After cyclic-prefix removal, the received signal is modeled as y = sum_{u=1..U} H_u Xi_u s_u + n, where n is circularly symmetric complex Gaussian noise with covariance sigma^2 I_L, s_u is the information-bearing signal of user u, Xi_u is a random precoding matrix, and H_u is the effective discrete-time channel matrix. We consider a general setting in which H_u and Xi_u are independent random matrices with bounded spectral norms with high probability, and Xi_u is right-unitarily invariant. We first analyze the associated static inference problem via the replica-symmetry (RS) ansatz. Guided by the RS predictions, we propose an OAMP-type algorithm that jointly processes the user-specific effective dictionaries H_u Xi_u. We provide a rigorous finite-sample analysis for generic non-separable (coded) systems, allowing s_u to follow general (not necessarily i.i.d.) distributions. The RS analysis and the finite-sample characterization yield the same decoupling principle, implying that, under the validity of the RS ansatz, the proposed algorithm achieves asymptotically Bayes-optimal performance.

On Gaussian vector channels the joint statistics of any pair of input and output component converge under weak conditions to a limit distribution as the dimensions of the channel grow large. To those vector channels, an equivalent scalar channel can be constructed. This scalar channel shows the same behavior as the vector channel for various performance measures. The equivalent scalar channel, often to referred as the "decoupled channel“ for short, allows for a simplified analysis of the vector channel and gives insight into the properties of the vector channel. In many cases, the decoupled channel is a scalar AWGN channel with an increased noise variance that accounts for the crosstalk that remains after interference mitigation on the vector channel. In other cases, the decoupled channel is scalar and noise is additive, but the noise is neither Gaussian nor independent from the channel input. Which of these cases occurs, depends on whether the replica symmetry of the vector channel is broken or not. An introduction into replica symmetry breaking is given and an intuitive explanation for this case distinction is given. It is also pointed out that replica symmetry breaking provides a subclassification of the complexity of exhaustive search problems. Some can be well approximated by message passing algorithms, others cannot.

Designing efficient compressors that provably achieve the optimal rate-distortion tradeoff is a long standing goal in information theory. Sparse regression codes asymptotically achieve the optimal tradeoff with a simple encoder, but their gap from the optimal curve can be significant at finite block lengths. An encoding algorithm based on Approximate Message Passing (AMP) by Wu et al. was recently shown to improve the finite-length distortion. In this talk, we theoretically characterize the performance of this algorithm, and show how it can be used within diffusion sampling to obtain an enhanced compressor whose performance can be rigorously characterized. Joint work with Galen Reeves, George Ardeleanu, and Pablo Pascual Cobo.

Many real-world datasets are inherently graph-structured, with nodes representing entities and edges capturing relationships. Such graphs arise in applications such as anti-money laundering, supply chains, energy grids, communication networks, and cybersecurity, and are often distributed across multiple entities that each own an interconnected subgraph. Learning from these distributed graphs requires leveraging cross-client connections under strict privacy constraints.

We propose FedLap, a framework for subgraph federated learning that injects global structural information via Laplacian smoothing in the spectral domain, enabling effective learning over interconnected subgraphs without exchanging sensitive embeddings. We provide a formal privacy analysis establishing strong privacy guarantees for FedLap; to the best of our knowledge, FedLap is the first subgraph FL approach with formal privacy guarantees. We further demonstrate that FedLap achieves competitive or improved utility relative to prior approaches across several graph datasets.

In the last decade, two sets of empirical observations have been put forth to try to understand and model how neural networks learn: spectral properties of the learned weights, and scaling laws for the generalization error. Current theoretical models fail at predicting and understanding such observations in the feature learning regime, i.e. when the networks learn high-dimensional internal representation of the high-dimensional input data. In this talk I will introduce a solvable class of models, bilinear index models, in which both spectra and scaling laws can be analytically studied in the feature learning regime. This class of models includes one-hidden-layer extensive-width neural networks with quadratic activations and softmax attention layers as used in transformers, allowing to explore analytically spectra and scaling laws in non-trivial architectures.

Representation learning often imposes geometric inductive biases on latent representations, in particular by increasing separation on the hypersphere. Prototypical learning is an attractive framework to control these biases while still allowing degrees of freedom to preserve input data structure. Although such methods have seen empirical success, it is difficult to systematically assess the importance of inducing separation compared to preserving relevant structure of the input data. In this paper, we address this gap in the understanding of prototypical learning and provide new insights into which properties promote good performance. Firstly, we collect both empirical and theoretical evidence indicating that separation is not sufficient to guarantee good performance. Secondly, to investigate the roles of structure-inducing and structure-preserving learning, we introduce a principled framework that combines fixed hyperspherical prototypes with controllable separation with learnable prototype labels. Thirdly, we give a full characterisation of the optimal feature separation, both through theoretical analysis and achievable practical schemes with near-optimal separation. Results show that even though prototype separation contributes to performance, especially in low dimension, performance gains obtained by matching the prototype labels to the input data structure are more significant, and it is possible to compensate for poor separation by optimising the prototype labels.

Achieving reliable connectivity in future wireless networks requires understanding how statistical dependencies between links affect end-to-end performance. While traditional analyses assume independent link failures, real networks exhibit correlated outages due to shared interference, environmental effects, or cascading faults. This talk presents a unified reliability framework for statistically dependent networks that characterizes worst- and best-case performance without requiring full knowledge of the joint link-state distribution. We introduce analytical reliability bounds for arbitrary dependency structures, generalizing classical results to multihop networks with correlated links and expressing connectivity via minimal path compositions. To handle complex shared-edge topologies, we develop a linear programming formulation that yields exact worst- and best-case reliability, together with a scalable graph-decomposition method. Building on this framework, we analyze multi-connectivity strategies—packet duplication and load balancing—in dependent diamond networks, deriving closed-form relations among rate, SNR, and reliability. A key insight is that load balancing can outperform packet duplication under worst-case dependencies. The framework is further extended to intermittent networks and to joint reliability–resource allocation problems, enabling the identification of optimal connectivity strategies under power constraints. Overall, the presented tools provide a principled basis for designing and evaluating resilient wireless networks under dependency uncertainty.

The talk is based on Z. Ge and E. A. Jorswieck, "Reliability in Statistically Dependent Networks: Bounds, Linear Programming, and Scalability," in IEEE Transactions on Communications, vol. 74, pp. 2731-2746, 2026, doi: 10.1109/TCOMM.2025.3648972.

There has been growing interest in the transmission of short packets in wireless communications. In this regime, asymptotic metrics such as channel capacity or outage capacity no longer provide accurate performance benchmarks, and a more refined characterization of the maximum coding rate as a function of the blocklength is required. Over the past fifteen years, significant effort has therefore been devoted to developing accurate benchmarks for short-packet wireless communications using finite-blocklength information theory.

Existing results can be broadly classified into two categories: (i) nonasymptotic bounds on the maximum coding rate, which are highly accurate but typically require numerically intensive and computationally demanding evaluations; and (ii) refined asymptotic approximations of the maximum coding rate or error probability—such as normal approximations and error exponents—which become accurate as the blocklength increases. Bridging these two approaches are saddlepoint approximations, which achieve near-nonasymptotic accuracy while remaining computationally efficient.

In this talk, I will review key advances in the application of finite-blocklength information theory to fading channels, considering both coherent and noncoherent settings. I will then present our latest result: a high-SNR normal approximation for noncoherent MIMO block-fading channels. This approximation complements existing nonasymptotic bounds in the literature, whose evaluation is often computationally prohibitive, and provides a theoretical foundation for the analytical study of the fundamental tradeoff among diversity, multiplexing, and channel-estimation cost at finite blocklength and finite SNR.

We consider a prediction-powered communication setting, in which transceivers, equipped with pre-trained predictors, communicate under zero-delay constraints with strict distortion guarantees that hold for every sequence. Specifically, we propose zero-delay compression algorithms leveraging online conformal prediction to provide per-sequence guarantees on the distortion of reconstructed sequences over error-free and packet-erasure channels with feedback. For erasure channels, we introduce a doubly-adaptive conformal update to compensate for channel-induced errors and derive sufficient conditions on erasure statistics to ensure distortion constraints.

Suppose that you wish to guess the true value of a discrete random variable through a sequence of queries. The number of queries required to do so is known as the guessing effort, or guesswork. Quantifying the expected guesswork, as well as its higher moments, is the subject of information-theoretic guessing. In this talk, I will review fundamental results in information-theoretic guessing. I will then discuss the central role of guessing in analyzing the performance of optimal lossless source encoders, as well as its role in an emerging class of guessing-based channel decoders.

We present a novel interpretation of the multi-linear spreading approach to random access from [Decurninge et al, WCL 2021] as a coded modulation for the case where M -state phase-shift keying (M -PSK) symbols are used. While the resulting code structure is not new, we show that thanks to the continuous relaxation of the M-PSK to the unit circle proposed in [Suresh et al,, IZS 2026], FEC decoding can be implemented directly in a continuous domain, and parametric beliefs taking the form of von Mises distributions replace beliefs about the M discrete states of each variable. This decoding approach is adapted to cases where parallel interference cancelation is peformed among many users and where multiple nuisance channel parameters (phase and frequency offset, fading channel gain, etc.) need to be accounted for.