Quantizer Design Research Articles

Coding–Decoding-Based Sliding Mode Control for Markovian Jump Systems Under Constrained Bit Rate: An Adaptive Quantizer Approach

This paper investigates the asynchronous sliding mode control (SMC) issue for uncertain hidden Markovian jump systems (MJSs) under constrained bit rate. An improved coding-decoding procedure with state-dependent adaptive quantization parameters is established to enable the controller to decode state and mode information from the system and the detector, respectively. Based on this procedure, a decoded-data-based asynchronous SMC strategy is provided and sufficient conditions are developed to ensure that the closed-loop dynamics are exponentially ultimately bounded and the system state is driven onto a sliding region simultaneously in the sense of mean square. The desired parameters of the quantizer and controller are obtained by solving an optimization problem, in which the objective function is constructed by using the trade-off between the ultimate state bound and the decay rate. Moreover, the integrative design of bit rate allocation protocol and quantizer as well as control parameters are converted into a nonlinear programming problem with integer constraint, which is solved by means of an improved sparrow search algorithm. Finally, a direct current motor system is employed to illustrate the effectiveness of the present approach under three different cases.

Enhancing Direct Position Determination in Distributed Base Station Systems Through Time-Varying Quantization Design

Enhancing Direct Position Determination in Distributed Base Station Systems Through Time-Varying Quantization Design

A Learning Framework for Bandwidth-Efficient Distributed Inference in Wireless IoT

The limited bandwidth and power resources of wireless sensors in distributed environments has resulted in new challenges in handling the ever-growing volume of transmissions generated by the Internet of Things (IoT) applications. To overcome these challenges, each sensor should compress and quantize its observations before sending them to a fusion center (FC) for global decision inference. Unfortunately, most of the conventional compression techniques and entropy quantizers only focus on reconstruction fidelity as a performance measure, neglecting the sensing goal. In this paper, we propose a joint design of compression mechanisms and entropy quantizers with the sensing goal for machine-to-machine (M2M) communications. We define a deep learning-based framework for compressing and quantizing observations from correlated sensors. Unlike traditional methods, our proposed method not only maximizes the reconstruction fidelity but also optimally compresses sensor observations in terms of the accuracy of the inferred decision (i.e., the sensing goal) at the FC. The proposed framework is widely applicable as it does not impose any assumptions on observation distribution. Furthermore, a novel loss function has been proposed to focus on learning complementary features at each sensor. Our experimental results demonstrate that the framework outperforms other benchmark models.

Channel Modeling and Quantization Design for 3D NAND Flash Memory.

As the technology scales down, two-dimensional (2D) NAND flash memory has reached its bottleneck. Three-dimensional (3D) NAND flash memory was proposed to further increase the storage capacity by vertically stacking multiple layers. However, the new architecture of 3D flash memory leads to new sources of errors, which severely affects the reliability of the system. In this paper, for the first time, we derive the channel probability density function of 3D NAND flash memory by taking major sources of errors. Based on the derived channel probability density function, the mutual information (MI) for 3D flash memory with multiple layers is derived and used as a metric to design the quantization. Specifically, we propose a dynamic programming algorithm to jointly optimize read-voltage thresholds for all layers by maximizing the MI (MMI). To further reduce the complexity, we develop an MI derivative (MID)-based method to obtain read-voltage thresholds for hard-decision decoding (HDD) of error correction codes (ECCs). Simulation results show that the performance with jointly optimized read-voltage thresholds can closely approach that with read-voltage thresholds optimized for each layer, with much less read latency. Moreover, the MID-based MMI quantizer almost achieves the optimal performance for HDD of ECCs.

Real-Time Monitoring Ornstein–Uhlenbeck Process: Improving Fidelity Under Freshness Guarantees

This work studies improving the data fidelity for real-time monitoring of an Ornstein-Uhlenbeck process in a sensor-monitor status update system under stringent information freshness provision. Violation probability of age of information (VPA), i.e., the long-term proportion the age of information exceeds a given threshold is adopted to strictly assess freshness. Based on the automatic repeat-request transmission protocol, the VPA at the monitor is derived in closed-form. To evaluate the fidelity, the time-average mean squared error (MSE) between the real-time process value and the estimation at the monitor is also obtained, where the coupling between the time-average MSE and the VPA is characterized in detail. By analyzing the monotonicity of the time-average MSE and the VPA, the optimal quantization precision that achieves the minimal time-average MSE under a given VPA constraint is proposed, where an algorithm for quickly addressing the optimum is also given. Numerical results validate the effectiveness of the proposed optimal quantization design.

Dynamic Quantizer Design for Target Tracking for Wireless Sensor Network With Imperfect Channels

Wireless sensor networks (WSNs) have been demonstrated to enhance parameter estimation performance for target tracking. In this paper, a prior information based quantizer design framework is proposed for target tracking for WSNs. In the proposed framework, the imperfect wireless channels between local sensors and the fusion center are considered. To make full use of the historical states and measurements embedded into the Bayesian tracking methodology, the quantizer design is suggested to be implemented with considering the prior state information. To this end, a channel-aware posterior Cramér-Rao lower bound (PCRLB) is derived based on the state prediction and further used as the performance indicator for quantizer design. Regarding target tracking, we model the quantizer design problem as a non-convex and highly nonlinear optimization problem that is intractable in general. We split the problem in terms of different scenarios, and for one-bit quantizer design based on a binary symmetric channel (BSC), we find that the optimal solution can be analytically computed. While for the general fading channel-based quantizer design problems, we propose two polynomial-time algorithms to find the solutions. Meanwhile, an approximation-based channel-aware particle filter (A-CAPF) is proposed to improve the implementation efficiency of state filtering. Simulation results demonstrate the enhanced performance and execution efficiency of the proposed algorithms in the context of the BSC and Rayleigh fading channel.

Quantization Design for Resistive Memories With Multiple Reads

Due to the crossbar array architecture, the sneakpath problem severely degrades the data integrity in the resistive random access memory (ReRAM). In this letter, we investigate the channel quantizer design for ReRAM arrays with multiple reads, which is a typical technique to improve the data recovery performance of data storage systems. Starting with a quantized channel model of ReRAM with multiple reads, we first derive a general approach for designing the channel quantizer, for both single-bit and multiple-bit quantizations. We then focus on the single-bit quantization, which is highly suitable for practical applications of ReRAM. In particular, we propose a semi-analytical approach to design the multiple-read single-bit quantizer with less complexity. We also derive the theoretical bit-error probability of the optimal single-bit detector/quantization as the benchmark. Results indicate that the multiple-read operation is effective in improving the error rate performance of ReRAM. Moreover, our proposed multiple-read detector outperforms the prior art detector and achieves the performance of the optimal detector.

Estimation Entropy, Lyapunov Exponents, and Quantizer Design for Switched Linear Systems

In this paper, we study connections between the estimation entropy of a switched linear system and its Lyapunov exponents. We prove lower and upper bounds for the estimation entropy in terms of the Lyapunov exponents and show that, under the so-called regularity assumption, those bounds coincide. To do that, we use a geometric object called Oseledets’ filtration of the system. Further, we show how to use the exponents and the Oseledets’ filtration to design a quantization scheme for state estimation of switched linear systems. Then, we prove that we can make this algorithm work at an average data-rate arbitrarily close to the upper bound we provided for the estimation entropy of the given system. Furthermore, we can choose the average data-rate to be arbitrarily close to the estimation entropy whenever the switched linear system is regular. We show that, under the regularity assumption, the quantization scheme is completely causal in the sense that it depends only on information that is available up to the current time instant. We show that regularity is a natural property of many practical systems, such as Markov jump linear systems, and give sufficient conditions for it.

Hardware Accelerated Design of a Dual-Mode Refocusing Algorithm for SAR Imaging Systems.

The use of satellite synthetic aperture radar (SAR) for moving target imaging has gained popularity recently. Researchers are focused on improving its imaging quality. To achieve high-quality and fast imaging, we have developed a dual-mode refocusing algorithm. We optimized the algorithm's target speed estimation and carried out data enhancement and quantization design for SAR image refocusing. The design is implemented on a Xilinx XC5VFX130T FPGA. The dual-mode image data are based on a slice size of 512 × 512 for slice mode and 256 × 256 for scan mode in a time-series function simulation. The serial-parallel conversion and pipeline design balances the operating speed and logic resources for optimal performance. Experiment results on slice data of real SAR images show that the system's processing speed can reach two frames per second, utilizing 69633 LUTs, 255 RAMs, and 296 DSPs.

Design and Analysis of Hardware-Limited Non-Uniform Task-Based Quantizers

Hardware-limited task-based quantization is a new design paradigm for data acquisition systems equipped with serial scalar analog-to-digital converters using a small number of bits. By taking into account the underlying system task, task-based quantizers can efficiently recover the desired parameters from the low-bit quantized observation. Current design and analysis frameworks for hardware-limited task-based quantization are only applicable to inputs with bounded support and uniform quantizers with non-subtractive dithering. Here, we propose a new framework based on generalized Bussgang decomposition that enables the design and analysis of hardware-limited task-based quantizers that are equipped with non-uniform scalar quantizers or that have inputs with unbounded support. We first consider the scenario in which the task is linear. Under this scenario, we derive new pre-quantization and post-quantization linear mappings for task-based quantizers with mean squared error (MSE) that closely matches the theoretical MSE. Next, we extend the proposed analysis framework to quadratic tasks. We demonstrate that our derived analytical expression for the MSE accurately predicts the performance of task-based quantizers with quadratic tasks.

Design of Switching-type Dynamic Quantizers for Continuous-Time Nonlinear Systems

This paper focuses on designing discrete-valued input systems using dynamic quantizers, which convert continuous-valued signals into discrete ones. Although the optimal design of dynamic quantizer is much studied, there are some unresolved problems. This study focuses on one of the unresolved problems: the design of a switching-type discrete-time dynamic quantizer for continuous-time nonlinear systems. In this paper, we first reduced the quantizer design problem to a selection problem of continuous-time linear models for a given nonlinear system. Then, we evaluated this approach via simulations of the swing-up problem for a cart-type inverted pendulum.

Quantized Synchronization Control of Networked Nonlinear Systems: Dynamic Quantizer Design With Event-Triggered Mechanism.

This article investigates the quantized control issue for synchronizing a networked nonlinear system. Due to limited energy and channel resources, the event-triggered control (ETC) method and input quantization are simultaneously taken into account in this article. First, a dynamic quantizer, which discretely adjusts its parameters online and possesses a finite quantization range, is introduced to achieve exact synchronization, rather than quasisynchronization. Next, a new distributed Zeno-free ETC strategy is proposed based on the dynamic quantizer. Then, two different situations, that is, the quantizer is designed with/without the network topology information, are, respectively, discussed. Synchronization criteria are, respectively, derived under such two circumstances by using the Lyapunov method. Finally, numerical examples are provided to show the effectiveness of the theoretical results.

A Distributed Computationally Aware Quantizer Design via Hyper Binning

We design a distributed function-aware quantization scheme for distributed functional compression. We consider 2 correlated sources <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and a destination that seeks an estimate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\hat{f}$</tex-math></inline-formula> for the outcome of a continuous function <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ). We develop a compression scheme called hyper binning in order to quantize f via minimizing the entropy of joint source partitioning. Hyper binning is a natural generalization of Cover's random code construction for the asymptotically optimal Slepian-Wolf encoding scheme that makes use of orthogonal binning. The key idea behind this approach is to use linear discriminant analysis in order to characterize different source feature combinations. This scheme captures the correlation between the sources and the function's structure as a means of dimensionality reduction. We investigate the performance of hyper binning for different source distributions and identify which classes of sources entail more partitioning to achieve better function approximation. Our approach brings an information theory perspective to the traditional vector quantization technique from signal processing.

Finite-Bit Quantization for Distributed Algorithms With Linear Convergence

This paper studies distributed algorithms for (strongly convex) composite optimization problems over mesh networks, subject to quantized communications. Instead of focusing on a specific algorithmic design, a black-box model is proposed, casting linearly convergent distributed algorithms in the form of fixed-point iterates. The algorithmic model is equipped with a novel random or deterministic Biased Compression (BC) rule on the quantizer design, and a new Adaptive encoding Non-uniform Quantizer (ANQ) coupled with a communication-efficient encoding scheme, which implements the BC-rule using a finite number of bits (below machine precision). This fills a gap existing in most state-of-the-art quantization schemes, such as those based on the popular compression rule, which rely on communication of some scalar signals with negligible quantization error (in practice quantized at the machine precision). A unified communication complexity analysis is developed for the black-box model, determining the average number of bits required to reach a solution of the optimization problem within a target accuracy. It is shown that the proposed BC-rule preserves linear convergence of the unquantized algorithms, and a trade-off between convergence rate and communication cost under ANQ-based quantization is characterized. Numerical results validate our theoretical findings and show that distributed algorithms equipped with the proposed ANQ have more favorable communication cost than algorithms using state-of-the-art quantization rules.

Sneak Path Interference-Aware Adaptive Detection and Decoding for Resistive Memory Arrays

Resistive random-access memory (ReRAM) is an emerging non-volatile memory technology for high-density and high-speed data storage. However, the sneak path interference (SPI) occurred in the ReRAM crossbar array seriously affects its data recovery performance. In this letter, we first propose a quantized channel model of ReRAM, based on which we design both the one-bit and multi-bit channel quantizers by maximizing the mutual information of the channel. A key channel parameter that affects the quantizer design is the sneak path occurrence probability (SPOP) of the memory cell. We first use the average SPOP calculated statistically to design the quantizer, which leads to the same channel detector for different memory arrays. We then adopt the SPOP estimated separately for each memory array for the quantizer design, which is generated by an effective channel estimator and through an iterative detection and decoding scheme for the ReRAM channel. This results in an array-level SPI-aware adaptive detection and decoding approach. Moreover, since there is a strong correlation of the SPI that affects memory cells in the same rows/columns than that affecting cells in different rows/columns, we further derive a column-level scheme which outperforms the array-level scheme. We also propose a channel decomposition method that enables effective ways for theoretically analyzing the ReRAM channel. Simulation results show that the proposed SPI-aware adaptive detection and decoding schemes can approach the ideal performance with three quantization bits, with only one decoding iteration.

Quantization and sparsity-aware processing for energy-efficient NVM-based convolutional neural networks

Nonvolatile memory (NVM)-based convolutional neural networks (NvCNNs) have received widespread attention as a promising solution for hardware edge intelligence. However, there still exist many challenges in the resource-constrained conditions, such as the limitations of the hardware precision and cost and, especially, the large overhead of the analog-to-digital converters (ADCs). In this study, we systematically analyze the performance of NvCNNs and the hardware restrictions with quantization in both weight and activation and propose the corresponding requirements of NVM devices and peripheral circuits for multiply–accumulate (MAC) units. In addition, we put forward an in situ sparsity-aware processing method that exploits the sparsity of the network and the device array characteristics to further improve the energy efficiency of quantized NvCNNs. Our results suggest that the 4-bit-weight and 3-bit-activation (W4A3) design demonstrates the optimal compromise between the network performance and hardware overhead, achieving 98.82% accuracy for the Modified National Institute of Standards and Technology database (MNIST) classification task. Moreover, higher-precision designs will claim more restrictive requirements for hardware nonidealities including the variations of NVM devices and the nonlinearities of the converters. Moreover, the sparsity-aware processing method can obtain 79%/53% ADC energy reduction and 2.98×/1.15× energy efficiency improvement based on the W8A8/W4A3 quantization design with an array size of 128 × 128.

All-Digital LoS MIMO With Low-Precision Analog-to-Digital Conversion

Line-of-sight (LoS) multi-input multi-output (MIMO) systems exhibit attractive scaling properties with increase in carrier frequency: for a fixed form factor and range, the spatial degrees of freedom increase quadratically for 2D arrays, in addition to the typically linear increase in available bandwidth. In this paper, we investigate whether modern all-digital baseband signal processing architectures can be devised for such regimes, given the difficulty of analog-to-digital conversion for large bandwidths. We propose low-precision quantizer designs and accompanying spatial demultiplexing algorithms, considering <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> LoS MIMO with QPSK for analytical insight, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> MIMO with QPSK and 16QAM for performance evaluation. Unlike prior work, channel state information is utilized only at the receiver (i.e., transmit precoding is not employed). We investigate quantizers with regular structure whose high-SNR mutual information approaches that of an unquantized system. We prove that amplitude-phase quantization is necessary to attain this benchmark; phase-only quantization falls short. We show that quantizers based on maximizing per-antenna output entropy perform better than standard Minimum Mean Squared Quantization Error (MMSQE) quantization. For spatial demultiplexing with severely quantized observations, we introduce the novel concept of virtual quantization which, combined with linear detection, provides reliable demodulation at significantly reduced complexity compared to maximum likelihood detection.

On Mutual Information-Based Optimal Quantizer Design

The problem of optimal quantizer design that maximizes the mutual information between the input and the quantized output of a communication channel is considered. It is shown that an optimal quantizer exists which employs convex polytopes as its decision regions in the Euclidean space of likelihood ratios. This complements the previous results in the literature by presenting a new and intuitive proof, establishing a unified treatment of the most general case, extending the solution to continuous-input channels, and providing a characterization for the form of optimal decision rule based on likelihood ratios, whereas the previous results are expressed in terms of the posterior probabilities and depend on the channel input distribution. The result is corroborated with an analytical example employing the transmission of a spherically symmetric random vector source over an additive white Gaussian noise channel.

Performance of Post-Training Two-Bits Uniform and Layer-Wise Uniform Quantization for MNIST Dataset from the Perspective of Support Region Choice

This paper contributes to the goal of finding an efficient compression solution for post-training quantization from the perspective of support region choice under the framework of low-bit uniform quantization. The decision to give preference to uniform quantization comes from the fact that support region choice is the most sensitive in the uniform quantization of nonuniform sources (e.g., Laplacian sources). Therefore, in this paper, we analyse in detail how the choice of the support region influences the performance of two-bits uniform quantization, measured with signal to quantization noise ratio (SQNR), and the accuracy of the compressed neural network (NN) model. We provide experimental and theoretical results for a few significant cases of two-bits uniform quantizer design, where we assume that Laplacian source models the distribution of weights in our fully connected NN. We opt for Laplacian distribution since it models well weights of NNs. Specifically, we analyse whether it is possible to apply the simplest uniform quantization in trained NN model weight representation with a bit rate of R = 2 bit/sample while preserving the accuracy of the model to a great extent. Also, our goal is to determine whether the choice of the key parameter of two-bits uniform quantizer (support region threshold) equally reflects on both, SQNR and accuracy. Moreover, we extend our analysis to the application of layer-wise two-bits uniform quantization in order to examine whether it is possible to achieve an additional improvement of the accuracy of our NN model for the MNIST dataset. We believe that the detailed analysis of post-training quantization described and conducted in this paper is very useful for all further research studies of this very current topic, especially due to the fact that the problem regarding post-training quantization is addressed from a particularly important perspective of choosing the support region.

A Physical-Layer Key Generation Approach Based on Received Signal Strength in Smart Homes

Due to the characteristics of wireless network transmission, smart home devices are vulnerable to malicious attacks. Malicious attackers can not only intercept the transmission data of smart home devices to grasp the user’s personal privacy information but also can eavesdrop the transmission between devices to forge the user’s legal information. These attacks have brought great security risks to people’s daily lives. In order to ensure the security of transmitted data, establishing keys for smart home devices is necessary. In this article, an adaptive physical-layer key generation scheme based on received signal strength (RSS) is proposed in Smart Homes. The scheme performs group quantization and adaptive quantization on the collected RSS measurements. The design of group quantization improves the randomness of the generated keys and makes 0 and 1 in generated keys more evenly distributed. The advantage of adaptive quantization is to design adaptive quantization intervals. The smart home devices can select the appropriate quantized reference levels according to the RSS measurements in different scenarios. In order to verify the practicability of the key generation scheme, we analyze the performance of the proposed scheme in static and dynamic scenarios. In addition, this scheme is compared with other key generation schemes from various performance indicators. The comparison results show that our scheme is better than other schemes in terms of randomness.