Channel coding is vital for reliable sixth-generation (6G) data transmission, employing diverse error correction codes for various application scenarios. Traditional decoders require dedicated hardware for each code, leading to high hardware costs. Recently, artificial intelligence (AI)-driven approaches, such as the error correction code Transformer (ECCT) and its enhanced version, the foundation error correction code Transformer (FECCT), have been proposed to reduce the hardware cost by leveraging the Transformer to decode multiple codes. However, their excessively high computational complexity ofO(N2) due to the self-attention mechanism in the Transformer limits scalability, whereNrepresents the sequence length. To reduce computational complexity, we propose a unified Transformer-based decoder that handles multiple linear block codes within a single framework. Specifically, a standardized unit is employed to align code length and code rate across different code types, while a redesigned low-rank unified attention module, with computational complexity ofO(N), is shared across various heads in the Transformer. Additionally, a sparse mask, derived from the parity-check matrix’s sparsity, is introduced to enhance the decoder’s ability to capture inherent constraints between information and parity-check bits, improving decoding accuracy and further reducing computational complexity by 86%. Extensive experimental results demonstrate that the proposed unified Transformer-based decoder outperforms existing methods and provides a high-performance, low-complexity solution for next-generation wireless communication systems.

Electromagnetic information theory (EIT) is an interdisciplinary subject that serves to integrate deterministic electromagnetic theory with stochastic Shannon's information theory. Existing EIT analysis operates in the continuous space domain, which is not aligned with the practical algorithms working in the discrete space domain. This mismatch leads to a significant difficulty in application of EIT methodologies to practical discrete space systems, which is called as thediscrete-continuous gapin this paper. To bridge this gap, we establish the discrete-continuous correspondence with a prolate spheroidal wave function (PSWF)-based ergodic capacity analysis framework. Specifically, we state and prove some discrete-continuous correspondence lemmas to establish a firm theoretical connection between discrete information-theoretic quantities to their continuous counterparts. With these lemmas, we apply the PSWF ergodic capacity bound to advanced MIMO architectures such as continuous-aperture MIMO (CAP-MIMO) and extremely large-scale MIMO (XL-MIMO). From this PSWF capacity bound, we discover the capacity saturation phenomenon both theoretically and empirically. Although the growth of MIMO performance is fundamentally limited in this EIT-based analysis framework, we reveal new opportunities in MIMO channel estimation by exploiting the EIT knowledge about the channel. Inspired by the PSWF capacity bound, we utilize continuous PSWFs to improve the pilot design of discrete MIMO channel estimators, which is called as the PSWF channel estimator (PSWF-CE). Simulation results demonstrate improved performance of the proposed PSWF-CE, compared to traditional minimum mean squared error (MMSE) and compressed sensing-based estimators.

Electromagnetic information theory (EIT) is one of the emerging topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, one of the most important research directions is degree of freedom (DoF) analysis. Existing research works on DoF analysis for EIT focus on asymptotic conclusions of DoF, which do not well fit the practical wireless communication systems with finite spatial regions and finite frequency bandwidth. In this paper, we provide mathematical definitions of the DoF for continuous electromagnetic fields. Moreover, we theoretically prove that the channel DoF is upper-bounded by the proposed functional DoF of electromagnetic fields. Furthermore, we use the theoretical analyzing tools from the Slepian concentration problem and extend them to three-dimensional space domains and four-dimensional space-time domains under electromagnetic constraints. Then we provide asymptotic DoF conclusions and non-asymptotic DoF analyzing scheme, which suits practical scenarios better, under different scenarios like three-dimensional antenna array. Finally, we use numerical analysis to provide some insights about the optimal spatial sampling interval of the antenna array, the DoF of three-dimensional antenna array, the impact of unequal antenna spacing, the orthogonal space-time patterns, etc.

Channel estimation in reconfigurable intelligent surface (RIS) assisted communications requires high pilot overhead due to numerous RIS elements incapable of signal processing. Recently, research on sensing RIS has provided a dimension-independent channel estimation scheme with merely three pilots. Nevertheless, it assumes that the BS-RIS channel is perfectly known to the RIS and remains invariant over a prolonged period, while inducing high hardware and power consumption. To address these issues, this paper introduces a generalized approximate message passing (GAMP) based channel estimation framework to achieve dimension-independent estimation of separate channels, without the assumption of known BS-RIS channel. Specifically, we first formulate the channel estimation problem in RIS assisted communications as a compressive phase retrieval problem. Based on the phaseless power observations, we leverage the GAMP algorithm to retrieve original sparse signals, which inherently supports the sparse-sampling sensing RIS architecture. Furthermore, by exploiting the intrinsic mapping between the sparse representations of the channels and the power observations in the angular domain, we propose a learned GAMP network to enhance the convergence stability and estimation accuracy. Finally, simulation results demonstrate that the proposed approach can efficiently estimate both the BS-RIS and UE-RIS channels with four pilots, while eliminating the requirement for prior knowledge of the BS-RIS channel and significantly reducing hardware and power consumption.

Accurate channel prediction is essential for addressing channel aging caused by user mobility. However, the actual channel variations over time are highly complex in high-mobility scenarios, which makes it difficult for existing predictors to obtain future channels accurately. The low accuracy of channel predictors leads to difficulties in supporting reliable communication. To overcome this challenge, we propose a channel predictor based on spatio-temporal electromagnetic (EM) kernel learning (STEM-KL). Specifically, inspired by recent advancements in electromagnetic information theory (EIT), the STEM kernel function is derived. The velocity and the concentration kernel parameters are designed to reflect the time-varying propagation of the wireless signal. We obtain the parameters through kernel learning. Then, the future channels are predicted by computing their Bayesian posterior, with the STEM kernel acting as the prior. To further improve the stability and model expressibility, we propose a grid-based EM mixed kernel learning (GEM-KL) scheme. We design the mixed kernel to be a convex combination of multiple sub-kernels, where each sub-kernel corresponds to a grid point in the set of pre-selected parameters. This approach transforms the non-convex STEM kernel learning problem into a convex grid-based problem that can be easily solved by weight optimization. Finally, simulation results verify that the proposed STEM-KL and GEM-KL schemes can achieve more accurate channel prediction. This indicates that EIT can improve the performance of wireless systems efficiently.

To satisfy the increasing demands for wireless transmission rates, it is necessary to exploit spatial resources of electromagnetic (EM) waves. In this context, EM information theory (EIT) has emerged as a hot topic by integrating the theoretical framework of deterministic mathematics and stochastic statistics to explore the transmission mechanisms of continuous EM waves. However, the previous studies were primarily focused on the analysis of the spatial degrees of freedom, with limited exploration of a comprehensive understanding of the essential physical characteristics of EIT. In this paper, a three-dimensional (3D) line-of-sight channel capacity formula is proposed, which captures the vector EM physics and accommodates both near- and far-field scenes. A novel channel model is established based on the rigorous mathematical equation and the physical mechanism of fast multipole algorithm, and it is revealed that the scattered EM waves have finite angular spectral bandwidth, which determines the eigenvalue distributions of the communication system. Furthermore, a series of orthogonal basis are constructed for the currents on the transmitter and the fields on the receiving aperture, thus supporting the optimal design of the spatial precoder and combiner. Comprehensive analyses are made to investigate the relationship among the noise, transmitted power, and spatial degree of freedom, thereby establishing a rigorous upper bound of channel capacity. Finally, a series of simulations are conducted to validate the theoretical model and numerical method. This work offers a novel perspective and methodology for comprehending and leveraging spatial resources of wireless channels, and provides a theoretical foundation for the design and optimization of the holographic communications.

Rydberg atomic receivers represent a transformative approach to achieving high-sensitivity, broadband, and miniaturized radio frequency (RF) reception. However, existing static signal models for Rydberg atomic receivers rely on the steady-state assumption of atomic quantum states, which cannot fully describe the signal reception process of dynamic signals. To fill in this gap, in this paper, we present a general model to compute the dynamic signal response of Rydberg atomic receivers in closed form. Specifically, by applying small-signal perturbation techniques to the quantum master equation, we derive closed-form Laplace domain transfer functions that characterize the receiver’s dynamic responses to time-varying signal fields. To gain more insights into the quantum-based RF-photocurrent conversion process, we further introduce the concept of quantum transconductance that describes the quantum system as an equivalent classical system. By applying quantum transconductance, we quantify the influence of in-band blackbody radiation (BBR) noise on the atomic receiver sensitivity. Extensive simulations for Rydberg atomic receivers validate the proposed signal model, and demonstrate the possibility of quantum receivers to outperform classical electronic receivers through the improvement of quantum transconductance.

In wireless communication, accurate and efficient channel prediction is essential for addressing channel aging caused by user mobility. However, the actual channel variations over time are complex in high-mobility scenarios. This complexity makes it difficult for existing channel predictors to obtain future channels accurately. To overcome channel aging, we propose a channel prediction scheme based on spatial-temporal electromagnetic kernel learning (STEM-KL). Specifically, the STEM correlation function can capture the fundamental propagation characteristics of the wireless channel, making it suitable to use as a kernel function that incorporates prior information. For the channel prediction problem especially, we redesign the hyperparameters of the STEM kernel, including user velocity and concentration, which characterize the direction of the EM wave. The hyperparameters are obtained through kernel learning. Then, we use Bayesian inference to predict the future channels, employing the STEM kernel as the required covariance. To further improve the stability and model expressiveness, we propose a grid-based electromagnetic mixed kernel learning (GEM-KL) scheme. We design the mixed kernel to be a convex combination of multiple sub-kernels, where each of the sub-kernels corresponds to a grid point in the parameter space. This approach transforms the learning of concentration and speed hyperparameters into the learning of weights for different subkernels, helping the kernel learning process avoid local optima. Finally, simulation results verify that the proposed STEM-KL schemes outperform the baseline schemes.

Rydberg atomic quantum receivers represent a transformative approach to achieving high-sensitivity, broadband, and miniaturized radio frequency (RF) reception. However, existing static signal models for Rydberg atomic receivers rely on the steady-state assumption of atomic quantum states, which cannot fully describe the signal reception process of dynamic signals. To fill in this gap, in this paper, we present a transfer function-based model to compute the dynamic signal response of Rydberg atomic receivers in closed form. Specifically, by applying small-signal perturbation techniques to the quantum master equation, we derive closed-form Laplace domain transfer functions that characterize the receiver’s dynamic responses to time-varying signal fields. To gain more insights into the quantum-based RF-photocurrent conversion process, we further introduce the concept of quantum transconductance that describes the quantum system as an equivalent classical system. Simulations for Rydberg atomic receivers validate the proposed signal model, and demonstrate the possibility of quantum receivers to outperform classical electronic receivers through the improvement of quantum transconductance.

In extremely large-scale multiple-input-multiple-output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite their effectiveness, existing beam training methods suffer from significant achievable rate degradation for remote users with low signal-to-noise ratio (SNR). To tackle this challenge, leveraging the error-correcting capability of channel codes, we incorporate channel coding theory into beam training to enhance the training accuracy, thereby extending the coverage area. Specifically, we establish the duality between hierarchical beam training and channel coding, and build on it to propose a general coded beam training framework. Then, we present two specific implementations exemplified by coded beam training methods based on Hamming codes and convolutional codes, during which the beam encoding and decoding processes are refined respectively to better accommodate to the beam training problem. Simulation results have demonstrated that, the proposed coded beam training method can enable reliable beam training performance for remote users with low SNR, while keeping training overhead low.

Electromagnetic information theory (EIT) is an emerging interdisciplinary subject that integrates classical Maxwell electromagnetics and Shannon information theory. The goal of EIT is to uncover the information transmission mechanisms from an electromagnetic (EM) perspective in wireless systems. Existing works on EIT are mainly focused on the analysis of EM channel characteristics, degrees-of-freedom, and system capacity. However, these works do not clarify how to integrate EIT knowledge into the design and optimization of wireless systems. To fill in this gap, in this paper, we propose an EIT-based statistical channel model with simplified parameterization. Thanks to the simplified closed-form expression of the EMCF, it can be readily applied to various channel modeling and inference tasks. Specifically, by averaging the solutions of Maxwell’s equations over a tunable von Mises distribution, we obtain a spatio-temporal correlation function (STCF) model of the EM channel, which we name as the EMCF. Furthermore, by tuning the parameters of the EMCF, we propose an EIT-based covariance estimator (EIT-Cov) to accurately capture the channel covariance. Since classical MMSE estimators can exploit prior information contained in the channel covariance matrix, we further propose the EIT-MMSE channel estimator by substituting EMCF for the covariance matrix. Simulation results show that both the proposed EIT-Cov covariance estimator and the EIT-MMSE channel estimator outperform their baseline algorithms, thus proving that EIT is beneficial to wireless communication systems.

Fluid antenna systems (FASs) can reconfigure their antenna locations freely within a spatially continuous space. To keep favorable antenna positions, the channel state information (CSI) acquisition for FASs is essential. While some techniques have been proposed, most existing FAS channel estimators require several channel assumptions, such as slow variation and angular-domain sparsity. When these assumptions are not reasonable, the model mismatch may lead to unpredictable performance losses. In this paper, we propose the successive Bayesian reconstructor (S-BAR) as a general solution to estimate FAS channels. Unlike model-based estimators, the proposed S-BAR is prior-aided, which builds the experiential kernel for CSI acquisition. Inspired by Bayesian regression, the key idea of S-BAR is to model the FAS channels as a stochastic process, whose uncertainty can be successively eliminated by kernel-based sampling and regression. In this way, the predictive mean of the regressed stochastic process can be viewed as a Bayesian channel estimator. Simulation results verify that, in both model-mismatched and model-matched cases, the proposed S-BAR can achieve higher estimation accuracy than the existing schemes.

Electromagnetic information theory (EIT) is an emerging interdisciplinary subject that integrates classical Maxwell electromagnetics and Shannon information theory. The goal of EIT is to uncover the information transmission mechanisms from an electromagnetic (EM) perspective in wireless systems. Existing works on EIT are mainly focused on the analysis of degrees-of-freedom (DoF), system capacity, and characteristics of the electromagnetic channel. However, these works do not clarify whether EIT can improve wireless communication systems. To answer this question, in this paper, we provide a novel example of how to improve channel estimators by integrating EM knowledge into the classical MMSE channel estimator. Specifically, the EM knowledge is first encoded into a spatial correlation function (SCF) of the channel, which we term the EM kernel. This EM kernel plays the role of side information to the channel estimator. Since the EM kernel takes the form of Gaussian processes (GP), we propose the EIT-based Gaussian process regression (EIT-GPR) to derive the channel estimations. Furthermore, we propose EM kernel learning to fit the EM kernel to channel observations. Simulation results show that EIT benefits the channel estimator and enables it to outperform traditional isotropic MMSE algorithm, thus proving the practical values of EIT.

Electromagnetic information theory (EIT) is one of the important topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near-field. In this paper, we propose the near-field channel model for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the fields. Furthermore, we analyze the characteristics of the proposed channel model, including how the parameters of the scattering field affect the degrees of freedom (DoF).

Fluid antenna systems (FASs) can reconfigure their locations freely within a spatially continuous space. To keep favorable antenna positions, the channel state information (CSI) acquisition for FASs is essential. While some techniques have been proposed, most existing FAS channel estimators require several channel assumptions, such as slow variation and angular-domain sparsity. When these assumptions are not reasonable, the model mismatch may lead to unpredictable performance loss. In this paper, we propose the successive Bayesian reconstructor (S- BAR) as a general solution to estimate FAS channels. Unlike model-based estimators, the proposed S- BAR is prior-aided, which builds the experiential kernel for CSI acquisition. Inspired by Bayesian regression, the key idea of S- BAR is to model the FAS channels as a stochastic process, whose uncertainty can be successively eliminated by kernel-based sampling and regression. In this way, the predictive mean of the regressed stochastic process can be viewed as the maximum a posterior (MAP) estimator of FAS channels. Simulation results verify that, in both model-mismatched and model-matched cases, the proposed S-BAR can achieve higher estimation accuracy than the existing schemes.

Electromagnetic information theory (EIT) is one of the emerging topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near field. In this paper, we propose the near-field channel modeling scheme for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the random fields. Furthermore, we analyze the characteristics of the proposed channel model, e.g., channel degrees of freedom (DoF). Finally, we design a channel estimation scheme for near-field scenario by integrating the electromagnetic prior information of the proposed model. Numerical analysis verifies the correctness of the proposed scheme and shows that it can outperform existing schemes like least square (LS) and orthogonal matching pursuit (OMP).

The concept of continuous-aperture multiple-input multiple-output (CAP-MIMO) technology has been proposed recently, which aims at achieving high spectrum efficiency by deploying extremely dense antennas or even continuous antennas in a given aperture. The fundamental question of CAP-MIMO is whether it can achieve much better performance than the traditional discrete MIMO system. In this paper, we propose a non-asymptotic performance comparison scheme between continuous and discrete MIMO systems based on the analysis of mutual information. We show the consistency of the proposed scheme by proving that the mutual information between discretized transceivers converges to that between continuous transceivers. Numerical analysis verifies the theoretical results, and suggests that the mutual information obtained from the discrete MIMO with widely adopted half-wavelength spaced antennas almost achieves the mutual information obtained from CAP-MIMO.

Reconfigurable intelligent surface (RIS) has been envisioned as a promising research direction for future wireless communications. As an important indicator of RIS-assisted communication systems in green wireless communications, energy efficiency (EE) receives intensive research interest as an optimization target. Recently, an increasing number of works have been devoted to EE maximization in RIS-assisted systems, in which the power consumptions of the base station and RIS are jointly optimized. However, most existing works ignored the different power consumption between the ON and OFF states of the RIS elements, which mismatches the characteristics of the realworld physical components. To construct a more correct power dissipation model for EE optimization in RIS-aided systems, in this paper, we establish a novel ON-OFF aware power dissipation model for the RIS elements. Based on this new model, the EE optimization problem is re-formulated, and corresponding lowcomplexity algorithms are proposed by leveraging the mathematical structures of the problem. Simulation results verify the effectiveness of the proposed algorithms across a wide range of scenarios.

Traditional channel capacity based on the discrete spatial dimensions mismatches the continuous electromagnetic fields. For the wireless communication system in a limited region, the spatial discretization may results in information loss because the continuous field can not be perfectly recovered from the sampling points. Therefore, electromagnetic information theory based on spatially continuous electromagnetic fields becomes necessary to reveal the fundamental theoretical capacity bound of communication systems. In this paper, we propose analyzing schemes for the performance limit between continuous transceivers. Specifically, we model the communication process between two continuous regions by random fields. Then, for the white noise model, we use Mercer expansion to derive the mutual information between the source and the destination. For the close-form expression, an analytic method is introduced based on autocorrelation functions with rational spectrum. Moreover, the Fredholm determinant is used for the general autocorrelation functions to provide the numerical calculation scheme. Further works extend the white noise model to colored noise and discuss the mutual information under it. Finally, we build an ideal model with infinite-length source and destination which shows a strong correpsondence with the time-domain model in classical information theory. The mutual information and the capacity are derived through the spatial spectral density.

Reconfigurable intelligent surfaces (RISs) are envisioned as a potentially transformative technology for future wireless communications. However, RISs’ inability to process signals and the attendant increased channel dimension have brought new challenges to RIS-assisted systems, including significantly increased pilot overhead required for channel estimation. To address these problems, several prior contributions that enhance the hardware architecture of RISs or develop algorithms to exploit the channels’ mathematical properties have been made, where the required pilot overhead is reduced to be proportional to the number of RIS elements. In this paper, we propose a dimension-independent channel state information (CSI) acquisition approach in which the required pilot overhead is independent of the number of RIS elements. Specifically, in contrast to traditional signal transmission methods, where signals from the base station (BS) and the users are transmitted in different time slots, we propose a novel method in which signals are transmitted from the BS and the user simultaneously during CSI acquisition. With this method, an electromagnetic interference random field (IRF) will be induced on the RIS, and we propose the structure of sensing RIS to capture its features. Moreover, we develop three algorithms for parameter estimation in this system, in which one of the proposed vM-EM algorithm is analyzed with the fixed-point perturbation method to obtain an asymptotic achievable bound. In addition, we also derive the Cramér-Rao lower bound (CRLB) and an asymptotic expression for characterizing the best possible performance of the proposed algorithms. Simulation results verify that our proposed signal transmission method and the corresponding algorithms can achieve dimension-independent CSI acquisition for beamforming.

Shannon-Hartley theorem can accurately calculate the channel capacity when the signal observation time is infinite. However, the calculation of finite-time mutual information, which remains unknown, is essential for guiding the design of practical communication systems. In this paper, we investigate the mutual information between two correlated Gaussian processes within a finite-time observation window. We first derive the finite-time mutual information by providing a limit expression. Then we numerically compute the mutual information within a single finite-time window. We reveal that the number of bits transmitted per second within the finite-time window can exceed the mutual information averaged over the entire time axis, which is called the exceed-average phenomenon. Furthermore, we derive a finite-time mutual information formula under a typical signal autocorrelation case by utilizing the Mercer expansion of trace class operators, and reveal the connection between the finite-time mutual information problem and the operator theory. Finally, we analytically prove the existence of the exceed-average phenomenon in this typical case, and demonstrate its compatibility with the Shannon capacity.