In this paper, we investigate capacities of two types of the multiple-input multiple-output (MIMO) optical intensity channel (OIC) under per-antenna peak- and average-intensity constraints, called the equal-cost constrained OIC (EC-OIC) and the bounded-cost constrained OIC (BC-OIC). The average intensities of input in the EC-OIC are required to be equal to preassigned constants, while in the BC-OIC those intensities are no larger than preassigned constants. We first consider a general vector Gaussian channel under moment constraints and prove that its high-SNR capacity is determined by the maximum differential entropy with some mild conditions. Then three capacity expressions are derived for the rank-one EC-OIC, the rank-one BC-OIC and the EC-OIC of rank being the number of transmit antennas minus one, respectively, based on which we obtain the results that : 1) either a rank-one EC-OIC and a rank-one BC-OIC is equivalent to some SISO OIC with an amplitude constraint and several moment constraints; 2) by asymptotic results on the moment-constrained vector Gaussian channel, both high-SNR asymptotic capacities of the EC-OIC and the BC-OIC of rank being the number of transmit antennas minus one are characterized. Furthermore, we focus on low-SNR capacity slopes for the general MIMO BC-OIC, and prove properties of the optimal intensity allocation, which simplify the involved nonsmooth optimization problem.
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This paper proposes a cascade blockage model for analyzing the vision that a user has of a wireless network. This model, inspired by the classical multiplicative cascade models, has a radial structure meant to analyze blockages seen by the receiver at the origin in different angular sectors. The main novelty is that it is based on the geometry of obstacles and takes the joint blockage phenomenon into account. We show on a couple of simple instances that the Laplace transforms of total interference satisfies a functional equation that can be solved efficiently by an iterative scheme. This is used to analyze the coverage probability of the receiver and the effect of blockage correlation and penetration loss in both dense and sparse blockage environments. Furthermore, this model is used to investigate the effect of blockage correlation on user beamforming techniques. Another functional equation and its associated iterative algorithm are proposed to derive the coverage performance of the best beam selection in this context. In addition, the conditional coverage probability is also derived to evaluate the effect of beam switching. The results not only show that beam selection is quite efficient for multi-beam terminals, but also show how the correlation brought by blockages can be leveraged to accelerate beam sweeping and pairing.
We consider the extra degree of freedom offered by the rotation of the reconfigurable intelligent surface (RIS) plane and investigate its potential in improving the performance of RIS-assisted wireless communication systems. By considering radiation pattern modeling at all involved nodes, we first derive the composite channel gain and present a closed-form upper bound for the system ergodic capacity over cascade Rician fading channels. Then, we reconstruct the composite channel gain by taking the rotations at the RIS plane, transmit antenna, and receive antenna into account, and extract the optimal rotation angles after investigating their impacts on the capacity. Moreover, we present a location-dependent expression of the ergodic capacity and investigate the RIS deployment strategy, i.e. the joint rotation adjustment and location selection. Finally, simulation results verify the accuracy of the theoretical analyses and deployment strategy. Although the RIS location has a big impact on the performance, our results showcase that the RIS rotation plays a more important role. In other words, we can obtain a considerable improvement by properly rotating the RIS rather than moving it over a wide area. For instance, we can achieve more than 200\% performance improvement through rotating the RIS by 42.14$^{\circ}$, while an 150\% improvement is obtained by shifting the RIS over 400 meters.
In recent years, there has been a growing interest in exploring the application of single-photon avalanche diode (SPAD) in optical wireless communication (OWC). As a photon counting detector, SPAD can provide much higher sensitivity compared to the other commonly used photodetectors. However, SPAD-based receivers suffer from significant dead-time-induced non-linear distortion and signal dependent noise. In this work, we propose a novel SPAD-based OWC system in which the non-linear distortion caused by dead time can be successfully eliminated by the pre-distortion of the signal at the transmitter. In addition, another system with joint pre-distortion and noise normalization functionality is proposed. Thanks to the additional noise normalization process, for the transformed signal at the receiver, the originally signal dependent noise becomes signal independent so that the conventional signal detection techniques designed for AWGN channels can be employed to decode the signal. Our numerical results demonstrate the superiority of the proposed SPAD-based systems compared to the existing systems in terms of BER performance and achievable data rate.
The stabilizer rank of a quantum state $\psi$ is the minimal $r$ such that $\left| \psi \right \rangle = \sum_{j=1}^r c_j \left|\varphi_j \right\rangle$ for $c_j \in \mathbb{C}$ and stabilizer states $\varphi_j$. The running time of several classical simulation methods for quantum circuits is determined by the stabilizer rank of the $n$-th tensor power of single-qubit magic states. We prove a lower bound of $\Omega(n)$ on the stabilizer rank of such states, improving a previous lower bound of $\Omega(\sqrt{n})$ of Bravyi, Smith and Smolin (arXiv:1506.01396). Further, we prove that for a sufficiently small constant $\delta$, the stabilizer rank of any state which is $\delta$-close to those states is $\Omega(\sqrt{n}/\log n)$. This is the first non-trivial lower bound for approximate stabilizer rank. Our techniques rely on the representation of stabilizer states as quadratic functions over affine subspaces of $\mathbb{F}_2^n$, and we use tools from analysis of boolean functions and complexity theory. The proof of the first result involves a careful analysis of directional derivatives of quadratic polynomials, whereas the proof of the second result uses Razborov-Smolensky low degree polynomial approximations and correlation bounds against the majority function.
We consider a wireless uplink network consisting of multiple end devices and an access point (AP). Each device monitors a physical process with stochastic arrival of status updates and sends these updates to the AP over a shared channel. The AP aims to schedule the transmissions of these devices to optimize the network-wide information freshness, quantified by the Age of Information (AoI) metric. Due to the stochastic arrival of the status updates at the devices, the AP only has partial observations of system times of the latest status updates at the devices when making scheduling decisions. We formulate such a decision-making problem as a belief Markov Decision Process (belief-MDP). The belief-MDP in its original form is difficult to solve as the dimension of its states can go to infinity and its belief space is uncountable. By leveraging the properties of the status update arrival (i.e., Bernoulli) processes, we manage to simplify the feasible states of the belief-MDP to two-dimensional vectors. Built on that, we devise a low-complexity scheduling policy. We derive upper bounds for the AoI performance of the low-complexity policy and analyze the performance guarantee by comparing its performance with a universal lower bound. Numerical results validate our analyses.
The construction of polar codes with code length $n=2^m$ involves $m$ layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the polarization process. More precisely, if the previous bit is more reliable than its next bit under the successive decoder, then switching the decoding order of these two adjacent bits will make the reliable bit even more reliable and the noisy bit even noisier. Based on this observation, we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes. We add a permutation layer after each polar transform layer in the construction of the ABS polar codes. In order to choose which pairs of adjacent bits to swap in the permutation layers, we rely on a new polar transform that combines two independent channels with $4$-ary inputs. This new polar transform allows us to track the evolution of every pair of adjacent bits through different layers of polar transforms, and it also plays an essential role in the Successive Cancellation List (SCL) decoder for the ABS polar codes. Extensive simulation results show that ABS polar codes consistently outperform standard polar codes by 0.15dB -- 0.6dB when we use CRC-aided SCL decoder with list size $32$ for both codes. The implementations of all the algorithms in this paper are available at //github.com/PlumJelly/ABS-Polar
A rate-distortion-perception (RDP) tradeoff has recently been proposed by Blau and Michaeli and also Matsumoto. Focusing on the case of perfect realism, which coincides with the problem of distribution-preserving lossy compression studied by Li et al., a coding theorem for the RDP tradeoff that allows for a specified amount of common randomness between the encoder and decoder is provided. The existing RDP tradeoff is recovered by allowing for the amount of common randomness to be infinite. The quadratic Gaussian case is examined in detail.
Optical wireless communication (OWC) has the potential to provide high communication speeds that support the massive use of the Internet that is expected in the near future. In OWC, optical access points (APs) are deployed on the celling to serve multiple users. In this context, efficient multiple access schemes are required to share the resources among the users and align multi-user interference. Recently, non-orthogonal multiple access (NOMA) has been studied to serve multiple users simultaneously using the same resources, while a different power level is allocated to each user. Despite the acceptable performance of NOMA, users might experience a high packet loss due to high noise, which results from the use of successive interference cancelation (SIC). In this work, random linear network coding (RLNC) is proposed to enhance the performance of NOMA in an optical wireless network where users are divided into multicast groups, and each group contains users that slightly differ in their channel gains. Moreover, a fixed power allocation (FPA) strategy is considered among these groups to avoid complexity. The performance of the proposed scheme is evaluated in terms of total packet success probability. The results show that the proposed scheme is more suitable for the network considered compared to other benchmark schemes such as traditional NOMA and orthogonal transmission schemes. Moreover, the total packet success probability is highly affected by the level of power allocated to each group in all the scenarios.
Many practical problems need the output of a machine learning model to satisfy a set of constraints, $K$. Nevertheless, there is no known guarantee that classical neural network architectures can exactly encode constraints while simultaneously achieving universality. We provide a quantitative constrained universal approximation theorem which guarantees that for any non-convex compact set $K$ and any continuous function $f:\mathbb{R}^n\rightarrow K$, there is a probabilistic transformer $\hat{F}$ whose randomized outputs all lie in $K$ and whose expected output uniformly approximates $f$. Our second main result is a "deep neural version" of Berge's Maximum Theorem (1963). The result guarantees that given an objective function $L$, a constraint set $K$, and a family of soft constraint sets, there is a probabilistic transformer $\hat{F}$ that approximately minimizes $L$ and whose outputs belong to $K$; moreover, $\hat{F}$ approximately satisfies the soft constraints. Our results imply the first universal approximation theorem for classical transformers with exact convex constraint satisfaction. They also yield that a chart-free universal approximation theorem for Riemannian manifold-valued functions subject to suitable geodesically convex constraints.
We study constrained reinforcement learning (CRL) from a novel perspective by setting constraints directly on state density functions, rather than the value functions considered by previous works. State density has a clear physical and mathematical interpretation, and is able to express a wide variety of constraints such as resource limits and safety requirements. Density constraints can also avoid the time-consuming process of designing and tuning cost functions required by value function-based constraints to encode system specifications. We leverage the duality between density functions and Q functions to develop an effective algorithm to solve the density constrained RL problem optimally and the constrains are guaranteed to be satisfied. We prove that the proposed algorithm converges to a near-optimal solution with a bounded error even when the policy update is imperfect. We use a set of comprehensive experiments to demonstrate the advantages of our approach over state-of-the-art CRL methods, with a wide range of density constrained tasks as well as standard CRL benchmarks such as Safety-Gym.
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