Finite Channel Research Articles

Adaptive fuzzy finite‐time formation asymptotic tracking control for nonholonomic multirobot systems with inputs quantization

SummaryThis paper investigates the finite‐time formation tracking control problem for nonholonomic multirobot systems with inputs quantization. The fuzzy logic systems (FLSs) and adaptive method are introduced to approximate unknown nonlinear functions and parameters. Multirobot needs to keep safe and effective communicating range, the barrier function and prescribed performance method are employed to ensure collision avoidance and connectivity maintenance. Then, in order to make each robot more precisely and quickly track referenced leader's trajectory and consider the finite channel bandwidth in practical applications, the travel range of robots can be maintained at more secure region and formation can operate normally within the given bandwidth. By combining the command filter and finite‐time theory, a novel decentralized finite‐time formation asymptotic tracking (FTFAT) control strategy is further proposed based on inputs quantization technology, it guarantees that all signals are bounded and the formation tracking errors asymptotically converge to zero in finite‐time. Finally, the practicability of FTFAT strategy is demonstrated absolutely for nonholonomic multirobot systems.

Sedimentation of particles with various shapes and orientations in a closed channel using smoothed particle hydrodynamics

The sedimentation of particles with various shapes and orientations in a closed channel using smoothed particle hydrodynamics is investigated in this paper. The continuity and momentum equations of both fluid and solid are discretized using kernel approximation in the Lagrangian frame. The sedimentation behavior of different general shapes, including circle, pentagon, square, ellipse, rectangle, and triangle, at various initial orientations in the suspending fluid is simulated. The stable equilibrium orientation (SEO) of these shapes is examined, excluding the circle which serves as a validation case. Specifically, the major axis of the ellipse and rectangle tends to align horizontally, whereas the orientations of the pentagon and square seem to be random due to the lack of a major axis and the finite channel height. The settling behavior of the three types of triangles is also discussed, and the von Mises stress of these shapes during their settling is presented. This study offers valuable insights into fluid-particle interactions, specifically regarding the SEO and internal stress of settling particles with varying shapes and orientations.

Resource Allocation for Cell-Free Massive MIMO-Enabled URLLC Downlink Systems

Ultra-Reliable and low-latency communication (URLLC) is a pivotal technique for enabling the wireless control over industrial Internet-of-Things (IIoT) devices. By deploying distributed access points (APs), cell-free massive multiple-input and multiple-output (CF mMIMO) has great potential to provide URLLC services for IIoT devices. In this paper, we investigate CF mMIMO-enabled URLLC in a smart factory. Lower bounds (LBs) of downlink ergodic data rate under finite channel blocklength (FCBL) with imperfect channel state information (CSI) are derived for maximum-ratio transmission (MRT), full-pilot zero-forcing (FZF), and local zero-forcing (LZF) precoding schemes. Meanwhile, the weighted sum rate is maximized by jointly optimizing the pilot power and transmission power based on the derived LBs. Specifically, we first provide the globally optimal solution of the pilot power, and then introduce some approximations to transform the original problems into a series of subproblems, which can be expressed in a geometric programming (GP) form that can be readily solved. Finally, an iterative algorithm is proposed to optimize the power allocation based on various precoding schemes. Simulation results demonstrate that the proposed algorithm is superior to the existing algorithms, and that the quality of URLLC services will benefit by deploying more APs, except for the FZF precoding scheme.

Noncryogenic Quantum Repeaters with hot Hybrid Alkali-Noble Gases

We propose a quantum repeater architecture that can operate without cryogenics. Each node in our architecture builds on a cell of hot alkali atoms and noble-gas spins that offer an hours-long storage time. Such a cell of hybrid gases is placed in a ring cavity, which allows us to suppress the detrimental four-wave-mixing noise in the system. We investigate the protocol based on a single-photon source made of an ensemble of the same hot alkali atoms. A single photon emitted from the source is either stored in the memory or transmitted to the central station to be detected. We quantify the fidelity and success probability of generating entanglement between two remote ensembles of noble-gas spins by taking into account finite memory efficiency, channel loss, and dark counts in detectors. We describe how the entanglement can be extended to long distances via entanglement swapping operations by retrieving the stored signal. Moreover, we quantify the performance of this proposed repeater architecture in terms of repeater rates and overall entanglement fidelities and compare it to another recently proposed noncryogenic quantum repeater architecture based on nitrogen-vacancy (N-V) centers and optomechanical spin-photon interfaces. As the system requires a relatively simple setup, it is easier to perform multiplexing, which enables achieving rates comparable to the rates of repeaters with N-V centers and optomechanics, while the overall entanglement fidelities of the present scheme are higher than the fidelities of the previous scheme. Our work shows that a scalable long-distance quantum network made of hot hybrid atomic gases is within reach of current technological capabilities.

Hall viscosity and hydrodynamic inverse Nernst effect in graphene

Motivated by Hall viscosity measurements in graphene sheets, we study hydrodynamic transport of electrons in a channel of finite width in external electric and magnetic fields. We consider electric charge densities varying from close to the Dirac point up to the Fermi-liquid regime. We find two competing contributions to the hydrodynamic Hall and inverse Nernst signals that originate from the Hall viscous and Lorentz forces. This competition leads to a nonlinear dependence of the full signals on the magnetic field and even a cancellation at different critical field values for both signals. In particular, the hydrodynamic inverse Nernst signal in the Fermi-liquid regime is dominated by the Hall viscous contribution. We further show that a finite channel width leads to a suppression of the Lorenz ratio, while the magnetic field enhances this ratio. All of these effects are predicted in parameter regimes accessible in experiments.

Low regularity solutions for the Vlasov–Poisson–Landau/Boltzmann system

In the paper, we are concerned with the nonlinear Cauchy problem on the Vlasov–Poisson–Landau/Boltzmann system around global Maxwellians in a torus or a finite channel. The main goal is to establish the global existence and large time behaviour of small amplitude solutions for a class of low regularity initial data. The molecular interaction type is restricted to the case of hard potentials for two classical collision operators because of the effect of the self-consistent forces. The result extends the one by Duan–Liu–Sakamoto-Strain (Duan et al 2021 Commun. Pure Appl. Math. 74 932–1020) for the pure Landau/Boltzmann equation to the case of the VPL and VPB systems.

Self-Triggered Stabilization of Discrete-Time Linear Systems With Quantized State Measurements

We study the self-triggered stabilization of discrete-time linear systems with quantized state measurements. In the networked control system we consider, sensors may be spatially distributed and be connected to a self-triggering mechanism through finite data-rate channels. Each sensor independently encodes its measurements and sends them to the self-triggering mechanism. The self-triggering mechanism integrates quantized measurement data and then computes sampling times. Assuming that the closed-loop system is stable in the absence of quantization and self-triggered sampling, we propose a joint design method of an encoding scheme and a self-triggering mechanism for stabilization. To deal with data inaccuracy due to quantization, the proposed self-triggering mechanism uses not only quantized data but also an upper bound of quantization errors, which is shared with a decoder.

Correcting bandwidth depolarization by extreme Faraday rotation

ABSTRACT Measurements of the polarization of radio emission are subject to a number of depolarization effects such as bandwidth depolarization, which is caused by the averaging effect of a finite channel bandwidth combined with the frequency-dependent polarization caused by Faraday rotation. There have been very few mathematical treatments of bandwidth depolarization, especially in the context of the rotation measure (RM) synthesis method for analysing radio polarization data. We have found a simple equation for predicting if bandwidth depolarization is significant for a given observational configuration. We have derived and tested three methods of modifying RM synthesis to correct for bandwidth depolarization. From these tests we have developed a new algorithm that can detect bandwidth-depolarized signals with higher signal-to-noise ratio than conventional RM synthesis and recover the correct source polarization properties (RM and polarized intensity). We have verified that this algorithm works as expected with real data from the LOw-Frequency ARray (LOFAR) Two-metre Sky Survey. To make this algorithm available to the community, we have added it as a new tool in the RM-Tools polarization analysis package.

No-go theorem and a universal decomposition strategy for quantum channel compilation

We rigorously prove a no-go theorem that, in sharp contrast to the case of compiling unitary gates, it is impossible to compile an arbitrary channel to arbitrary precision with any given finite elementary channel set, regardless of the length of the decomposition sequence. However, for a fixed error bound $\ensuremath{\epsilon}$, we find a general and systematic strategy to compile arbitrary quantum channels. We construct a universal set with a constant number of $\ensuremath{\epsilon}$-dependent elementary channels, such that an arbitrary quantum channel can be decomposed into a sequence of these elementary channels followed by a unitary gate, with the sequence length bounded by $O(\frac{1}{\ensuremath{\epsilon}}log\frac{1}{\ensuremath{\epsilon}})$ in the worst case. We further optimize this approach by exploiting proximal policy optimization---a powerful deep reinforcement learning algorithm for the gate compilation. We numerically evaluate the performance of our algorithm concerning topological compiling of Majorana fermions, and we show that our algorithm can conveniently and effectively reduce the use of expensive elementary operations.

Online Bayesian Meta-Learning for Cognitive Tracking Radar

A key component of cognitive radar is the ability to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">generalize</i> , or achieve consistent performance across a range of sensing environments, since aspects of the physical scene may vary over time. This presents a challenge for learning-based waveform selection approaches, since transmission policies which are effective in one scene may be highly suboptimal in another. We address this problem by strategically <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">biasing</i> a learning algorithm by exploiting high-level structure across tracking instances, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">meta-learning</i> . In this work, we develop an online meta-learning approach for waveform-agile tracking. This approach uses information gained from previous target tracks to speed up and enhance learning in new tracking instances. This results in sample-efficient learning across a class of finite state target channels by exploiting inherent similarity across tracking scenes, attributed to common physical elements such as target type or clutter statistics. We formulate the online waveform selection problem within the framework of Bayesian learning, and provide prior-dependent performance bounds for the meta-learning problem using Probability Approximately Correct (PAC)-Bayes theory. We present a computationally feasible meta-posterior sampling algorithm and study the performance in a simulation study consisting of diverse scenes. Finally, we examine the potential performance benefits and practical challenges associated with online meta-learning for waveform-agile tracking.

Tighter sum uncertainty relations via metric-adjusted skew information

In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special cases as Wigner-Yanase-Dyson skew information. In quantifying the uncertainty of channels, we discuss two types of lower bounds and compare the tightness between them, meanwhile, a tight lower bound is given. The uncertainty relations obtained by us are stronger than the existing ones. To illustrate our results, we give several specific examples.

Complexity curtailed MLSE equalizer based on a compact look-up-table for C-band DSB IM/DD transmission.

Chromatic dispersion appears to be a major performance limiting problem in optical intensity modulation direct detection (IM/DD) transmission systems, especially for a double-sideband (DSB) signal. We propose a complexity-reduced look-up-table based maximum likelihood sequence estimation (LUT-MLSE) for DSB C-band IM/DD transmission based on pre-decision-assisted trellis compression and a path-decision-assisted Viterbi algorithm. To further compress the size of the LUT and reduce the length of the training sequence, we proposed a finite impulse response (FIR) and LUT hybrid channel model for the LUT-MLSE. For PAM-6 and PAM-4, the proposed methods can compress the size of the LUT into 1/6 and 1/4, and reduce the number of multipliers by 98.1% and 86.6% with slight performance degradation. We successfully demonstrate a 20-km 100-Gb/s PAM-6 and a 30-km 80-Gb/s PAM-4 C-band transmission over dispersion-uncompensated links.

Asymptotic stability for two-dimensional Boussinesq systems around the Couette flow in a finite channel

In this paper, we study the asymptotic stability for the two-dimensional Navier-Stokes Boussinesq system around the Couette flow with small viscosity ν and small thermal diffusion μ in a finite channel. In particular, we prove that if the initial velocity and initial temperature (vin,ρin) satisfies ‖vin−(y,0)‖Hx,y2≤ε0min⁡{ν,μ}12 and ‖ρin−1‖Hx1Ly2≤ε1min⁡{ν,μ}1112 for some small ε0,ε1 independent of ν,μ, then for the solution of the two-dimensional Navier-Stokes Boussinesq system, the velocity remains within O(min⁡{ν,μ}12) of the Couette flow, and approaches to Couette flow as t→∞; the temperature remains within O(min⁡{ν,μ}1112) of the constant 1, and approaches to 1 as t→∞.

Statistical CSI-Based Design for RIS-Assisted Communication Systems

Reconfigurable intelligent surfaces (RISs) have attracted considerable attention over the past years. A RIS can smartly adjust the phase of incident wavefronts and create anomalous reflections towards desired directions. In this letter, we consider a RIS-assisted large antenna system and investigate the ergodic spectral efficiency (SE). By considering a finite dimensional channel, we derive an upper bound on the ergodic SE. Based on this upper bound, we propose an optimal phase shift design by exploiting statistical channel state information. Specifically, we develop a semidefinite relaxation technique and Gaussian randomization procedure for continous phase shift design. Furthermore, an alternating optimization algorithm is applied to the discrete case. Numerical results verify the tightness of the upper bound and the effectiveness of our phase shift design. Considering hardware limitations, we find that a RIS of 2-bit phase adjustable elements achieves the same ergodic SE as the continous phase shift architecture.

Existence of a solitary planar bubble in symmetric channels

Two-dimensional steady ideal fluids with gravity in finite height symmetric channels are considered. This model is well-known, but the existence results seem rare in the literature. For suitable incoming vertical velocity and the divergent nozzles, there exists a solitary bubble starting at the symmetric axis and extending downwards without limit. Finally, the inclination angle at the vertex of this bubble is investigated.

Feedback Capacity of Ising Channels With Large Alphabet via Reinforcement Learning

We propose a new method to compute the feedback capacity of unifilar finite state channels (FSCs) with memory using reinforcement learning (RL). The feedback capacity was previously estimated using its formulation as a Markov decision process (MDP) with dynamic programming (DP) algorithms. However, their computational complexity grows exponentially with the channel alphabet size. Therefore, we use RL, and specifically, its ability to parameterize value functions and policies with neural networks, to evaluate numerically the feedback capacity of channels with a large alphabet size. The outcome of the RL algorithm is a numerical lower bound on the feedback capacity, which is used to reveal the structure of the optimal solution. The structure is modeled by a graph-based auxiliary random variable that is utilized to derive an analytic upper bound on the feedback capacity with the duality bound. The capacity computation is concluded by verifying the tightness of the upper bound by testing whether it is Bahl-Cocke-Jelinek-Raviv (BCJR) invariant. We demonstrate this method on the Ising channel with an arbitrary alphabet size. For an alphabet size smaller than or equal to 8, we derive the analytic solution of the capacity. Next, the structure of the numerical solution is used to deduce a simple coding scheme that achieves the feedback capacity and serves as a lower bound for larger alphabets. For an alphabet size greater than 8, we present an upper bound on the feedback capacity. For an asymptotically large alphabet size, we present an asymptotic optimal coding scheme.

Skew information-based coherence generating power of quantum channels

We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. We define the measure of coherence generating power (CGP) for a generic quantum channel to be the average coherence generated by the quantum channel acting on a uniform ensemble of incoherent states based on the skew information-based coherence measure. We present explicitly the analytical formulae of the CGP for any arbitrary finite dimensional unitary channels. We derive the mean value of the CGP over the unitary groups and investigate the typicality of the normalized CGP. Furthermore, we give an upper bound of the CGP for the convex combinations of unitary channels. Detailed examples are provided to calculate exactly the values of the CGP for the unitary channels related to specific quantum gates and for some qubit channels.

Ising and XY paramagnons in two-dimensional 2H−NbSe2

Paramagnons are the collective modes that govern the spin response of nearly magnetic conductors. In some cases they mediate electron pairing leading to superconductivity. This scenario may occur in 2H-NbSe$_2$ monolayers, that feature spin-valley coupling on account of spin-orbit interactions and their lack of inversion symmetry. Here we explore spin anisotropy of paramagnons both for non-centrosymmetric Kane-Mele-Hubbard models for 2H-NbSe$_2$ monolayers described with a DFT-derived tight-binding model. In the infinite wavelength limit we find spatially uniform paramagnons with energies around $1$~meV that feature a colossal off-plane uniaxial magnetic anisotropy, with quenched transversal spin response. At finite wave vectors, longitudinal and transverse channels reverse roles: XY fluctuations dominate within a significant portion of the Brillouin zone. Our results show that 2H-NbSe$_2$ is close to a Coulomb-driven in-plane (XY) spin density wave instability.

Enhanced dissipation and transition threshold for the 2-D plane Poiseuille flow via resolvent estimate

In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow (1−y2,0) in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized operator around the Poiseuille flow, we first establish the enhanced dissipation estimates for the linearized Navier-Stokes equations with a sharp decay rate e−cνt. As an application, we prove that if the initial perturbation of vorticity satisfies‖ω0‖L2≤c0ν34 for some small constant c0>0 independent of the viscosity ν, then the solution does not transition away from the Poiseuille flow for any time.

Complete Entropic Inequalities for Quantum Markov Chains

We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we prove that every finite dimensional GNS-symmetric quantum channel satisfies a strong data processing inequality with respect to its decoherence free part. Moreover, we establish the first general approximate tensorization property of the relative entropy. This extends the famous strong subadditivity of the quantum entropy (SSA) of two subsystems to the general setting of two subalgebras. All three results are independent of the size of the environment and hence satisfy the tensorization property. They are obtained via a common, conceptually simple method for proving entropic inequalities via spectral or L_2-estimates. As an application, we combine our results on the modified log-Sobolev inequality and approximate tensorization to derive tight bounds for local generators.