Asymptotic Capacity Research Articles

The Asymptotic Capacity of X-Secure T-Private Linear Computation With Graph Based Replicated Storage

The Asymptotic Capacity of <i>X</i>-Secure <i>T</i>-Private Linear Computation With Graph Based Replicated Storage

Beamspace Modulation for Near Field Capacity Improvement in XL-MIMO Communications

The spatial degrees of freedom (DoFs) greatly increase in the near-field region of millimeter wave or terahertz multiple-input multiple-output communications with extremely large antenna arrays (XL-MIMO). To employ the increased spatial DoFs, a beamspace modulation (BM) strategy is introduced to the near field of XL-MIMO. BM can work with a fixed small number of RF chains. It exploits the increased spatial DoFs as modulation resources for capacity improvements. The achievable spectral efficiency and its asymptotic capacity are analyzed. Both theoretical and simulation results show that the proposed BM strategy considerably outperforms the existing benchmark that only selects the best beamspace for data transmission in terms of spectral efficiency.

On the Asymptotic Capacity of Information-Theoretic Privacy-Preserving Epidemiological Data Collection.

The paradigm-shifting developments of cryptography and information theory have focused on the privacy of data-sharing systems, such as epidemiological studies, where agencies are collecting far more personal data than they need, causing intrusions on patients' privacy. To study the capability of the data collection while protecting privacy from an information theory perspective, we formulate a new distributed multiparty computation problem called privacy-preserving epidemiological data collection. In our setting, a data collector requires a linear combination of K users' data through a storage system consisting of N servers. Privacy needs to be protected when the users, servers, and data collector do not trust each other. For the users, any data are required to be protected from up to E colluding servers; for the servers, any more information than the desired linear combination cannot be leaked to the data collector; and for the data collector, any single server can not know anything about the coefficients of the linear combination. Our goal is to find the optimal collection rate, which is defined as the ratio of the size of the user's message to the total size of downloads from N servers to the data collector. For achievability, we propose an asymptotic capacity-achieving scheme when E<N-1, by applying the cross-subspace alignment method to our construction; for the converse, we proved an upper bound of the asymptotic rate for all achievable schemes when E<N-1. Additionally, we show that a positive asymptotic capacity is not possible when E≥N-1. The results of the achievability and converse meet when the number of users goes to infinity, yielding the asymptotic capacity. Our work broadens current researches on data privacy in information theory and gives the best achievable asymptotic performance that any epidemiological data collector can obtain.

Robust Beamforming Design With Finite Blocklength for URLLC

Ultra-reliable and low-latency communications (URLLC) are essential for mission-critical applications, such as telemedicine, automatic drive, etc. In the design of URLLC, the robustness of multi-user beamforming transmission scheme is critical and challenging. To this end, we consider a robust beamforming design in the finite blocklength regime for a multi-user multi-antenna downlink system in the case of imperfect channel state information at the transmitter. A transmission power minimization problem is formulated to optimize the beamforming vectors under the premise of guaranteeing the requirements on transmission latency, reliability and the target user rates, which is non-convex. To solve it, we first reformulate the problem into a tractable form by using the convexity and concavity of asymptotic capacity in the finite blocklength regime, then adopt S-Procedure to convert the infinite constraints into finite ones. Finally, the Gaussian randomization method and the penalty function method are utilized to generate a feasible solution to the original optimization problem and to provide a good rank-one approximation, respectively. The simulation results confirm the robustness and effectiveness of the beamforming design.

Asymptotic Capacity Maximization for MISO Visible Light Communication Systems with a Liquid Crystal RIS-Based Receiver

Combined with reconfigurable intelligent surfaces (RISs), visible light communications (VLCs) can increase the communication performance to a great degree. However, the research into RIS-aided VLC systems has mainly focused on mirror array-based RISs deployed on the wall while neglecting liquid crystal (LC)-based RISs in VLC receivers. With the development of advanced materials, the LC RIS has been gradually attracting attention from researchers. Inspired by the current research into the LC RIS, the applications of the LC RIS in multiple-input single-output (MISO) VLC systems are investigated in this paper. We formulate an optimization problem with asymptotic capacity maximization as the objective function and the refractive index of the LC RIS as the independent variable. As for this nonconvex optimization problem, we propose the particle swarm optimization (PSO) algorithm to determine the configuration of parameters for the LC RIS. The simulation results indicate that the employment of the LC RIS in VLC receivers can raise the communication performance of the MISO-VLC systems; meanwhile, the proposed algorithm is an effective way to deal with the optimization problems for LC RIS-based MISO-VLC systems when compared with the exhaustive search method and a baseline scheme. The LC RIS is also expected to solve the dead zone problem in traditional VLC systems.

Configuring Reconfigurable Intelligent Surface for Parallel MIMO Visible Light Communications with Asymptotic Capacity Maximization

As an emerging technology, reconfigurable intelligent surface (RIS) has attracted increasing attention due to the ability to configure the wireless propagation environment. Parallel multiple-input multiple-output (MIMO) visible light communication (VLC) is suitable for some scenarios, e.g., multi-user time-division multiple access for indoor VLCs. The application of RIS in VLC is a promising trend in the future, and this paper investigates the employment of RIS in a parallel MIMO VLC system with asymptotic capacity maximization. To this end, the RIS-aided parallel MIMO VLC channel model is derived in this paper under the point source assumption, and then, as for the non-convex optimization problem, instead of searching exhaustively for the optimal solution, we propose a low-complexity near-optimal relaxing particle swarm optimization (RPSO) algorithm to optimize the RIS parameters. Meanwhile, we discover that the convex relaxation is an effective method for the optimization problems. Finally, numerical results indicate the effectiveness of the proposed design of RIS, and meanwhile, the asymptotic capacity can be improved to a great degree by adopting RIS in the parallel MIMO VLC system.

Asymptotic Capacity Loss Under Spectral Leakage Constraints for Weakly Nonlinear Transmitters

We investigate and elaborate upon a folklore in wireless communication systems that, when the nonlinearity at a transmitter is sufficiently weak so that the resulting spectral leakage is at a sufficiently low level, the capacity of the channel (including the transmitter) should be sufficiently close to the ideal channel capacity without transmitter nonlinearity. The context for this study is that effective predistortion techniques have been widely applied to linearize the transmitter nonlinearity in modern wireless communication systems, so as to render the electromagnetic radiation pattern to satisfy stringent spectral regrowth requirements. Based on the quasi-memoryless/memory polynomial model for the transmitter nonlinearity, via an information-theoretic approach, our study affirmatively validates the folklore, and more importantly, characterizes a quantitative relationship between the spectral leakage level and the capacity loss. Specifically, we prove that as the adjacent channel power ratio (ACPR) asymptotically vanishes, the capacity loss is upper bounded by a term that is proportional to the ACPR. We also establish a converse result, and further extend our results to spatial beamforming.

Capacity Maximization for Reconfigurable Intelligent Surface-Aided MISO Visible Light Communications

This paper investigates the employment of reconfigurable intelligent surfaces (RISs) to improve the asymptotic capacity of the multiple-input single-output (MISO) visible light communication (VLC) system in the case of high signal-to-noise (SNR). For the RIS-aided MISO-VLC system based on mirror array, we regard the high-SNR asymptotic capacity with the input subject to peak-intensity constraints as a goal and formulate an asymptotic capacity maximization problem to find the optimal orientations of mirrors. As for the non-convex optimization problem, we convert it into a quadratic programming (QP) problem with hemispherical constraints and prove that it can be solved by computing the maximum eigenvalue of an equivalent matrix. Simulation results indicate that the asymptotic capacity is able to be improved significantly by adopting RIS in MISO-VLC systems. Meanwhile, we observe that the proper deployment scheme of RIS is able to enhance the degree of improvement through several simulations.

On the Capacity of MISO Optical Intensity Channels With Per-Antenna Intensity Constraints

This paper investigates the capacity of general multiple-input single-output (MISO) optical intensity channels (OICs) under per-antenna peak- and average-intensity constraints. We first consider the MISO equal-cost constrained OIC (EC-OIC), where, apart from the peak-intensity constraint, average intensities of inputs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equal to</i> arbitrarily preassigned constants. The second model of our interest is the MISO bounded-cost constrained OIC (BC-OIC), where, as compared with the EC-OIC, average intensities of inputs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no larger than</i> arbitrarily preassigned constants. By leveraging tools from quantile functions, stop-loss transform and convex ordering of nonnegative random variables, we prove two decomposition theorems for bounded and nonnegative random variables, based on which we equivalently transform both the EC-OIC and the BC-OIC into respective single-input single-output channels under a peak-intensity and several stop-loss mean constraints. Capacity lower and upper bounds for both channels are established, based on which the asymptotic capacity at high and low signal-to-noise-ratio are determined.

HDMA: Holographic-Pattern Division Multiple Access

The next generation wireless communications aiming at enhancing capacity and massive connectivity significantly over high-frequency bands urge the development of novel multiple access technologies. In this paper, we propose a new type of space-division multiple access (SDMA), called holographic-pattern division multiple access (HDMA). We develop the principle for HDMA with the main idea of mapping the intended signals for receivers to a superposed holographic pattern. The multi-user holographic beamforming scheme for HDMA is then presented. Based on the theoretical analysis, we find that there exists an optimal holographic pattern such that the sum rate with simple zero-forcing precoding can achieve the asymptotic capacity of the HDMA system. Simulation results verify the theoretical analysis and show that the HDMA scheme outperforms the traditional SDMA scheme in terms of both the cost-efficiency and the sum rate.

On the Capacity of Intensity-Modulation Direct-Detection Gaussian Optical Wireless Communication Channels: A Tutorial

Optical wireless communication (OWC) using intensity-modulation and direct-detection (IM/DD) has a channel model which possesses unique features, due to the constraints imposed on the channel input. The aim of this tutorial is to overview results on the capacity of IM/DD channels with input-independent Gaussian noise as a model of OWC channels. It provides the reader with an entry point to the topic, and highlights some major contributions in this area. It begins with a discussion on channel models and how this IM/DD Gaussian channel model comes about, in addition to an explanation of input constraints. Then, it discusses the capacity of the single-input single-output channel, its computation, and capacity bounds and asymptotic capacity results. Then, it extends the discussion to the multiple-input multiple-output setup, and reviews capacity bounds for this channel model. Finally, it discusses multi-user channels modelled as a broadcast channel (downlink) or a multiple-access channel (uplink), with their associated capacity bounds.

On the Achievable Rate and Capacity for a Sample-Based Practical Photon-Counting Receiver

We investigate the achievable rate and capacity of a non-perfect photon-counting receiver. For the case of long symbol duration, the achievable rate under on-off keying modulation is investigated based on Kullback-Leibler (KL) divergence and Chernoff $\alpha$-divergence. We prove the tightness of the derived bounds for large peak power with zero background radiation with exponential convergence rate, and for low peak power of order two convergence rate. For large peak power with fixed background radiation and low background radiation with fixed peak power, the proposed bound gap is a small positive value for low background radiation and large peak power, respectively. Moreover, we propose an approximation on the achievable rate in the low background radiation and long symbol duration regime, which is more accurate compared with the derived upper and lower bounds in the medium signal to noise ratio (SNR) regime. For the symbol duration that can be sufficiently small, the capacity and the optimal duty cycle are is investigated. We show that the capacity approaches that of continuous Poisson capacity as $T_s=\tau\to0$. The asymptotic capacity is analyzed for low and large peak power. Compared with the continuous Poisson capacity, the capacity of a non-perfect receiver is almost lossless and loss with attenuation for low peak power given zero background radiation and nonzero background radiation, respectively. For large peak power, the capacity with a non-perfect receiver converges, while that of continuous Poisson capacity channel linearly increases. The above theoretical results are extensively validated by numerical results.

Reconfigurable Intelligent Surface Assisted Multi-User Communications: How Many Reflective Elements Do We Need?

Reconfigurable intelligent surfaces (RISs) consisting of multiple reflective elements are a promising technique to enhance communication quality as they can create favorable propagation conditions. In this letter, we characterize the fundamental relations between the number of reflective elements and the system sum-rate in RIS-assisted multi-user communications. It is known from previous works that the received signal-to-noise ratio (SNR) can linearly increase with the squared number of RIS reflective elements, but how many elements are sufficient to provide an acceptable system sum-rate still remains an open problem. To this end, we derive the asymptotic capacity with zero-forcing (ZF) precoding, and then analyze how many reflective elements are required so that the ratio of the system sum-rate to the capacity can exceed a predefined threshold. Numerical results verify our analysis.

GCSA Codes With Noise Alignment for Secure Coded Multi-Party Batch Matrix Multiplication

A secure multi-party batch matrix multiplication problem (SMBMM) is considered, where the goal is to allow a master to efficiently compute the pairwise products of two batches of massive matrices, by distributing the computation across S servers. Any X colluding servers gain no information about the input, and the master gains no additional information about the input beyond the product. A solution called Generalized Cross Subspace Alignment codes with Noise Alignment (GCSA- NA) is proposed in this work, based on cross-subspace alignment codes. The state of art solution to SMBMM is a coding scheme called polynomial sharing (PS) that was proposed by Nodehi and Maddah-Ali. GCSA-NA outperforms PS codes in several key aspects—more efficient and secure inter-server communication, lower latency, flexible inter-server network topology, efficient batch processing, and tolerance to stragglers. The idea of noise alignment can also be combined with N-source Cross Subspace Alignment (N-CSA) codes and fast matrix multiplication algorithms like Strassen’s construction. Moreover, noise alignment can be applied to symmetric secure private information retrieval to achieve the asymptotic capacity.

Low Complexity Optimization of the Asymptotic Spectral Efficiency in Massive MIMO NOMA

Massive multiple-input multiple-output (MIMO) technology facilitates huge increases in the capacity of wireless channels, while non-orthogonal multiple access (NOMA) addresses the problem of limited resources in traditional orthogonal multiple access (OMA) techniques, promising enhanced spectral efficiency. This work uses asymptotic capacity computation results to reduce the complexity of a power allocation algorithm for small-scale MIMO-NOMA, so that it may be applied for systems with massive MIMO arrays. The proposed method maximizes the sum-capacity of the considered system, subject to power and performance constraints, and demonstrates greater accuracy than alternative approaches despite remaining low-complexity for arbitrarily large antenna arrays.

On the Asymptotic Capacity of X-Secure T-Private Information Retrieval With Graph-Based Replicated Storage

The problem of private information retrieval with graph-based replicated storage was recently introduced by Raviv, Tamo and Yaakobi. Its capacity remains open in almost all cases. In this work the asymptotic (large number of messages) capacity of this problem is studied along with its generalizations to include arbitrary T -privacy and X-security constraints, where the privacy of the user must be protected against any set of up to T colluding servers and the security of the stored data must be protected against any set of up to X colluding servers. A general achievable scheme for arbitrary storage patterns is presented that achieves the rate (ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> -X -T )/N, where N is the total number of servers, and each message is replicated at least ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> times. Notably, the scheme makes use of a special structure inspired by dual Generalized Reed Solomon (GRS) codes. A general converse is also presented. The two bounds are shown to match for many settings, including symmetric storage patterns. Finally, the asymptotic capacity is fully characterized for the case without security constraints (X = 0) for arbitrary storage patterns provided that each message is replicated no more than T + 2 times. As an example of this result, consider PIR with arbitrary graph based storage (T = 1, X = 0) where every message is replicated at exactly 3 servers. For this 3-replicated storage setting, the asymptotic capacity is equal to 2/ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (G) where ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (G) is the maximum size of a 2-matching in a storage graph G[V, E]. In this undirected graph, the vertices V correspond to the set of servers, and there is an edge uv ∈ E between vertices u, v only if a subset of messages is replicated at both servers u and v.

The Asymptotic Capacity of Private Search

The private search problem is introduced, where a dataset comprised of $L$ i.i.d. records is replicated across $N$ non-colluding servers, each record takes values uniformly from an alphabet of size $K$, and a user wishes to search for all records that match a privately chosen value, without revealing any information about the chosen value to any individual server. The capacity of private search is the maximum number of bits of desired information that can be retrieved per bit of download. The asymptotic (large $K$) capacity of private search is shown to be $1-1/N$, even as the scope of private search is further generalized to allow approximate (OR) search over a number of realizations that grows with $K$. The results are based on the asymptotic behavior of a new converse bound for private information retrieval with arbitrarily dependent messages.

Asymptotic Capacity Results on the Discrete-Time Poisson Channel and the Noiseless Binary Channel with Detector Dead Time.

This paper studies the discrete-time Poisson channel and the noiseless binary channel where, after recording a 1, the channel output is stuck at 0 for a certain period; this period is called the “dead time.” The communication capacities of these channels are analyzed, with main focus on the regime where the allowed average input power is close to zero, either because the bandwidth is large, or because the available continuous-time input power is low.

Asymptotic Capacity for MIMO Communications With Insufficient Radio Frequency Chains

This paper presents an asymptotic capacity analysis for multiple-input multiple-output (MIMO) communications with insufficient transmit radio frequency (RF) chains and sufficient receive RF chains, which is named as iMIMO communications. We characterize the iMIMO channel capacity by the maximum mutual information given any vector inputs subject to not only an average power constraint but also a sparsity constraint. It is proven that an optimized Gaussian mixture input distribution is capacity-achieving in the high signal-to-noise-ratio (SNR) regime. The optimal mixture coefficients and the covariance matrices of the Gaussian mixtures are derived and also the corresponding asymptotic capacity. Furthermore, we discuss the impact of insufficient receive RF chains on the achievable spectral efficiency. We investigate the superiority of the capacity-achieving technique, which is an optimized non-uniform subspace modulation (NUSM), by comparing it with the best subspace selection (BSS) and the uniform subspace modulation (USM). The comparison results reveal that the optimized NUSM is optimal in the high SNR regime. Numerical results are presented to validate our analysis.

Capacity of optical wireless communication channels.

Optical wireless communications are realized by modulating the intensity of a light source and detecting intensity fluctuations at the receiver. This mode of operation, known as intensity modulation and direct detection (IM/DD), is simple to implement in practice. However, computing the channel capacity of the underlying channel is not straightforward because of the amplitude constraints that arise due to IM/DD operation. In particular, the transmit signal must be non-negative, while the peak and average amplitudes are constrained due to practical and safety considerations. Though a closed form for the capacity of IM/DD channels is not known, much work has been done to find capacity bounds and asymptotic capacity expressions. In this paper, a description of the IM/DD channel and its physical constraints is presented, followed by a review of recent progress pertaining to the capacity of IM/DD channels. Additionally, capacity-achieving distributions are discussed along with simple constructions that approach capacity. This article is part of the theme issue 'Optical wireless communication'.