Quantizer Output Research Articles

Efficient Look-Up Table from Expanded Convolutional Network for Accelerating Image Super-resolution

The look-up table (LUT) has recently shown its practicability and effectiveness in super-resolution (SR) tasks due to its low computational cost and hardware independence. However, most existing methods focus on improving the performance of SR, neglecting the demand for high-speed SR on low-computational edge devices. In this paper, we propose an efficient expanded convolution (EC) layer, which expands the output size of regular convolution to enlarge the receptive field (RF) indirectly. It can increase the size of the LUT corresponding to the network linearly with the increase of RF. Additionally, after introducing the EC, multiple LUTs are merged into one LUT, achieving faster running speed while maintaining SR performance. More specifically, we expand the coverage of the convolutional output so that the output at the current position covers the target position and its surroundings, forming an overlapping sliding window at the output end. We sum up the overlapping parts of the sliding window as the output, thereby achieving the effect of enlarging the RF size. Moreover, by expanding the numerical range of the accumulated results and rescaling them to [0,255], the method can mitigate the error caused by quantization output. Experiments indicate that the proposed method performs better than the baseline method and is faster than other LUT-based SR methods.

Global Asymptotic Stabilization Control for Uncertain Nonlinear Systems With Input Quantization and Unknown Output Function

Global Asymptotic Stabilization Control for Uncertain Nonlinear Systems With Input Quantization and Unknown Output Function

Distributed soft video transmission based on hybrid digital and analog scheme

This study presents a novel distributed soft video delivery scheme using hybrid digital and analog framework, which realizes a relatively lightweight encoder as well as good robustness. Specifically, after applying scalar quantization to the interframes, the scaled analog information (quantization error) and the scaled digital information (quantized source) are superimposed and then transmitted. In this way, the proposed scheme directly delivers pseudo-analog symbols over the orthogonal frequency division multiplexing (OFDM) channels and involves no complicated digital codec. Moreover, we utilize cross-frame correlation to implement a distributed paradigm which further reduces the encoder complexity since the complex motion estimation and compensation algorithms are transferred to the decoder. Accordingly, the power distortion optimization scheme, which resolve the allocation of power and the parameters optimization to achieve minimum transmission distortion, is proposed. To solve it, first, we formulate the power distortion expressions regarding quantization parameters and power allocation coefficients. Subsequently, we divide the problem into two sub-problems based on the fast coordinate descent method and further propose a greedy iterative algorithm to optimize them. We also develop a data-driven optimization algorithm based on deep learning that reduces the additional delay brought by the iterative optimization method. At the receiver, we estimate the quantization output and quantization error by the modified linear least squares estimation with the virtual noise variance. Based on the simulation results, the proposed framework has a better performance in terms of peak signal-to-noise ratio and structural similarity than the relevant cutting-edge schemes while maintaining good robustness.

Load frequency composite control for multi-region interconnected power systems

This paper investigates a composite controller for load frequency control (LFC) in multi-region interconnected power systems via sliding mode observer design. State observers (SOs) and disturbance observers (DOs) are implied for the LFC based on the load variations with communication delays and quantization output measurements. A nonlinear integral sliding surface combined with a composite controller is developed to optimize control performance. Moreover, a three-area power system model is used to demonstrate the effectiveness of the proposed scheme in the illustrative example, confirming that frequency deviations can be rejected despite delays, uncertainties, and quantization during transmission.

Privacy-Preserving Distributed Economic Dispatch of Microgrids: A Dynamic Quantization-Based Consensus Scheme With Homomorphic Encryption

This paper is concerned with the privacy-preserving distributed economic dispatch problem (ED) of microgrids. A homomorphically encrypted consensus algorithm is developed in the absence of a third party to achieve optimal power distribution with the least cost while preventing sensitive information leakage during the entire communication process. For ease of data encryption, a novel estimator-like dynamic quantizer is first constructed, where the information to be transmitted is converted into a series of finite-level codewords. Then, a sufficient condition is derived, taking advantage of mathematical induction and the properties of matrix norms, to ensure that the quantization output is unsaturated and exact consensus is reached. Furthermore, by means of the additive homomorphic property of the Paillier algorithm to embed secrecy in pairwise interaction dynamics, the confidential communication strategy is adopted to ensure that the distributed algorithm converges to the optimal value without disclosing private or sensitive state information of agents. Finally, case studies are provided to illustrate the feasibility and validity of the adopted privacy-preserving ED scheme in IEEE 39-bus power systems.

Time-domain Continuous-time Delta-sigma Modulator using VCO-based Integrator and GRO-based Quantizer

This paper presents a 3SUPrd/SUP-order time-domain continuous-time delta-sigma modulator (CTDSM) using two voltage-controlled oscillator (VCO)-based integrators and a gated ring oscillator (GRO)-based quantizer. The GRO-based quantizer has 1SUPst/SUP-order noise-shaping characteristics without the increase of the signal transfer function (STF) order and has magnificent linearity. Also, the output of the GRO-based quantizer has an intrinsic data weighted averaging (DWA)-based dynamic element matching (DEM) pattern that is less susceptible to the DAC mismatch. The PWM signal, which is the input of the GRO-based quantizer, is generated by the VCO-based integrator without additional blocks. In the pre-layout simulation, the CTDSM consumes 3.84 mW and achieves an SNDR of 71.2 dB at a 400-MSs sampling frequency and a 10-MHz bandwidth.

Fully distributed quantized secure bipartite consensus control of nonlinear multiagent systems subject to denial-of-service attacks

This paper is intended to solve the fully distributed secure bipartite consensus problem of nonlinear multi-agent systems (MASs) with quantized information under Denial-of-Service (DoS) attacks. The attacks, which constrained on attack frequency and duration are studied. Firstly, we propose a novel secure output feedback control protocol integrated of the logarithmic quantizer and relative output measurements of neighboring agents, which can realize secure control under DoS attacks by choosing the design parameters correctly. Secondly, an adaptive control protocol that includes dynamic coupling strengths into the control law and the state observer function is developed. Contrast to the single adaptive control strategy, two adaptive couplings constructed in sensor-to-observer, and controller-to-actuator channels, respectively, which can alleviate the burden of the limited bandwidth and energy consumption more effectively. Furthermore, this control strategy with dynamic coupling gains is fully distributed, under which agents are not required to know a priori knowledge of any global information and the quantizer only needs to quantize the output state error information of agents. Then, theoretical guarantees on the effectiveness of the proposed controllers in steering the system to a secure bipartite (bounded) consensus under quantized output measurements and intermittent DoS attacks are derived. Finally, the numerical simulation inspired by a real-world physical network system is developed to verify the usefulness of the presented controllers.

Target Detection Using Quantized Cloud MIMO Radar Measurements

Target detection is studied for a cloud multiple-input multiple-output (MIMO) radar using quantized measurements. According to the local sensor quantization strategies and fusion strategies, this paper discusses three methods: quantize local test statistics which are linearly fused (QTLF), quantize local test statistics which are optimally fused (QTOF), and quantize local received signals which are optimally fused (QROF). We first directly analyze the detection performance of each method when the quantizer output is represented as a discrete random variable, where it is difficult to obtain a closed-form expression for the detection probability. Then, an approximate description for the quantization is analyzed for the case of a Gaussian signal and a closed-form expression for the detection probability is obtained. We prove that the QTOF method outperforms the QTLF method in general, and for small SCNR the QROF method has the best detection performance among the three methods, while for large SCNR the QROF method performs the worst. The correctness of theoretical analysis is verified by simulations.

Asymptotically Scale-Invariant Multi-Resolution Quantization

A multi-resolution quantizer is a sequence of quantizers where the output of a coarser quantizer can be deduced from the output of a finer quantizer. In this paper, we propose an asymptotically scale-invariant multi-resolution quantizer, which performs uniformly across any choice of average quantization step, when the length of the range of input numbers is large. Scale invariance is especially useful in worst case or adversarial settings, ensuring that the performance of the quantizer would not be affected greatly by small changes of storage or error requirements. We also show that the proposed quantizer achieves a tradeoff between rate and error that is arbitrarily close to the optimum.

Communication constrained robust guidance strategy using quantized artificial time delay based control with input saturation

This work proposes the use of a logarithmic quantizer to minimize the computational load on the onboard processor of missiles. The quantizer output discretizes the continuous guidance command to a finite set of predefined discrete levels. This in turn puts an end to the need for installing a powerful state of the art modern processor onboard a missile, while enabling designers to install a comparatively cost efficient and compact processor. To include robustness properties, the proposed guidance strategy adopts the artificial time-delayed control (TDC) philosophy. The use of TDC methodology eliminates the conservative assumptions of a priori knowledge about uncertainty bounds as required by most state-of-the-art robust control schemes. Thus, the proposed guidance law is able to achieve interception even in the presence of uncertainties while significantly reducing control updates due to the use of input quantizer. Input saturation is also considered for the proposed quantized time-delay control (QTDC) based guidance strategy. The Uniformly Ultimately Bounded (UUB) convergence of the closed-loop system states is demonstrated through the Lyapunov theory. Simulation studies involving various engagement scenarios and a comparative performance study of the QTDC guidance scheme with the conventional periodic time-triggered TDC technique are provided to highlight the efficacy of the proposed approach. In this work, a quantized input time delay based control is used to significantly reduce the control updates while designing an efficient robust control strategy. A sense of time-energy efficiency is introduced for the overall system and input saturation is also considered.

Dynamic Programming for Sequential Deterministic Quantization of Discrete Memoryless Channels

In this article, under a general cost function C, we present a dynamic programming (DP) method to obtain an optimal sequential deterministic quantizer (SDQ) for q-ary input discrete memoryless channel (DMC). The DP method has complexity O(q (N-M) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M), where N and M are the alphabet sizes of the DMC output and quantizer output, respectively. Then, starting from the quadrangle inequality, two techniques are applied to reduce the DP method's complexity. One technique makes use of the Shor-Moran-Aggarwal-Wilber-Klawe (SMAWK) algorithm and achieves complexity O(q (N-M) M). The other technique is much easier to be implemented and achieves complexity O(q (N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> - M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> )). We further derive a sufficient condition under which the optimal SDQ is optimal among all quantizers and the two techniques are applicable. This generalizes the results in the literature for binary-input DMC. Next, we show that the cost function of α-mutual information ( α-MI)-maximizing quantizer belongs to the category of C. We further prove that under a weaker condition than the sufficient condition we derived, the aforementioned two techniques are applicable to the design of α-MI-maximizing quantizer. Finally, we illustrate the particular application of our design method to practical pulse-amplitude modulation systems.

Compression-based Data Reduction Technique for IoT Sensor Networks

Energy savings are very common in IoT sensor networks because IoT sensor nodes operate with their own limited battery. The data transmission in the IoT sensor nodes is very costly and consume much of the energy while the energy usage for data processing is considerably lower. There are several energy-saving strategies and principles, mainly dedicated to reducing the transmission of data. Therefore, with minimizing data transfers in IoT sensor networks, can conserve a considerable amount of energy. In this research, a Compression-Based Data Reduction (CBDR) technique was suggested which works in the level of IoT sensor nodes. The CBDR includes two stages of compression, a lossy SAX Quantization stage which reduces the dynamic range of the sensor data readings, after which a lossless LZW compression to compress the loss quantization output. Quantizing the sensor node data readings down to the alphabet size of SAX results in lowering, to the advantage of the best compression sizes, which contributes to greater compression from the LZW end of things. Also, another improvement was suggested to the CBDR technique which is to add a Dynamic Transmission (DT-CBDR) to decrease both the total number of data sent to the gateway and the processing required. OMNeT++ simulator along with real sensory data gathered at Intel Lab is used to show the performance of the proposed technique. The simulation experiments illustrate that the proposed CBDR technique provides better performance than the other techniques in the literature.

Information-Distilling Quantizers

Let X and Y be dependent random variables. This paper considers the problem of designing a scalar quantizer for Y to maximize the mutual information between the quantizer's output and X, and develops fundamental properties and bounds for this form of quantization, which is connected to the log-loss distortion criterion. The main focus is the regime of low I(X;Y), where it is shown that, if X is binary, a constant fraction of the mutual information can always be preserved using <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (log(1/I(X;Y))) quantization levels, and there exist distributions for which this many quantization levels are necessary. Furthermore, for larger finite alphabets 2 <; | <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> | <; ∞, it is established that an η-fraction of the mutual information can be preserved using roughly (log(| <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> | /I(X;Y))) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η·(|<i>X</i>| - 1)</sup> quantization levels.

Multiple-Signal Single-Loop Filter (MSSF) sigma-delta modulators

This paper presents a new family of Sigma-Delta modulators, the so called Multiple-Signal Single-Loop Filter (MSSF) modulators, where several input signals are added at the modulator input, then passed through only one single loop filter, and converted to digital by means of a column of quantizers, equal in number to the number of input signals. As long as a suitable correction path is added to the input of every quantizer, the input signals are separated at the quantizers' outputs in such a way that they are converted to digital independently of each other. Each quantizer output has the digital version of only one of the input signal plus its corresponding quantization noise shaped by the order of the loop filter. The procedure to achieve the above is explained for a general Sigma-Delta modulator in the ideal case. This paper also studies the performance degradation produced by mismatch in the coefficients of the correction paths. High-level simulations show that the MSSF modulator, even under the effects of mismatch, is a power efficient approach to convert multiple input signals.

Distributed Decision Fusion with M-ary Signaling and k-bit Transmission on Sensor Observation in Wireless Sensor Networks

Multi-level decisions on sensor detection is able to improve the detection performance on the final decision made at the fusion center (FC) in wireless sensor networks (WSN). In this paper, the performance analysis of an M-ary signaling (MS) scheme using analog transmission and a k-bit transmission (KB) scheme is both examined for distributed binary detection. Under the multi-level decision algorithms, each sensor sends a signal carrying the information of a quantized version of a local decision statistic such as the conditional mean or the log-likelihood ratio. In MS, the output of the quantizer is transmitted directly without digitalizing and coding process, while in KB, each quantization output is coded with k bits and hereby a sensor sends a k-bit hard local decision to the FC. At the FC, the linear combiner detection rule on the transmission schemes is both adopted to make the final decision. The effects of the sensor decision and the transmission errors are incorporated in the analysis of the erroneous performance of the final decision. The goal of the proposed schemes is to minimize the final errors at the FC via optimizing the region allocation on the multi-level decision at the sensor. The numerical results illustrate that the proposed schemes achieve significant improvement in error performance over the conventional schemes under either additive white Gaussian noise (AWGN) channel or Rayleigh faded channel.

A Nonuniform-Quantized Successive Cancellation Decoding of Polar Codes Over AWGN Channels

Since polar codes are capacity-achieving codes, there have been various research works devoted to devising efficient implementation methods as well as improving error-correction performance. Since quantization is a critical implementation issue, in this paper, a nonuniform quantization method is proposed for the successive cancellation (SC) decoder of polar codes, which finds quantization boundary values based on the analysis of various quantization levels over the additive white Gaussian noise channel. Since low computational complexity, high reliability, and efficient memory management are required in the next-generation communication and memory systems, 2-4 bit precision levels are mainly considered in the proposed nonuniform quantization method. Depending on the presence of erasure, quantization levels are divided into three types, and the message alphabets and update rules are derived for each type. Also, a construction method of polar codes suitable for the proposed nonuniform-quantized SC decoder is proposed, which simultaneously determines the information set and the quantization boundary values based on the density evolution analysis and an upper bound of the block error probability. To determine quantization boundary values, a multivariate objective function is defined and an iterative coarse-to-fine search algorithm to minimize this objective function is proposed. In addition, a scaling method of quantizer output values is proposed when the number of quantization levels of quantizer is smaller than the number of quantization levels of decoder. Finally, simulation results confirm that the proposed nonuniform-quantized SC decoder shows better error-correction performance, lower decoding complexity, and higher memory efficiency compared to the best known uniform-quantized SC decoder.

Reducing Quantizer Distortion Due to Insufficient Resolution in Massive MIMO Receivers

Use of low-resolution (1-4 bits) Analog-to-Digital Converters (ADCs) can reduce power consumption in Massive Multiple-Input, Multiple-Output (MIMO) receivers. Ordinary linear beamforming may suffice for low-resolution ADCs under conditions on the Signal-to-Noise Ratio (SNR) and number of antennas that may be called low but sufficient resolution. However, if the SNR increases or number of antennas decreases, an error floor will typically occur. We introduce three low-complexity iterative algorithms to reduce quantization noise in such low but insufficient resolution cases. These algorithms process the raw quantizer outputs prior to detection, achieving up to two orders-of-magnitude reduction in Bit Error Rate (BER). Our algorithms are based on the new `equivalent model' for quantizers developed in our prior work. These algorithms can be applied to any number of bits and any modulation format. We focus on Orthogonal Frequency-Division Multiplexing (OFDM) to show that quantizer distortion can be corrected without going to the frequency domain.

Performance Model and Design Rules for Optical Systems Employing Low-Resolution DAC/ADC

We present an additive noise model for the signal-to-noise ratio prediction in optical systems employing low-resolution (4 bits and below) digital-to-analog and analog-to-digital converters. Firstly, the expected ASIC power consumption saving by employing low-resolution digital-to-analog and analog-to-digital converters rather than their high-resolution version (8 bits) is assessed and found to be up to 20% for a 4-bit physical resolution. Secondly, to assess the achievable data rate with low-resolution, we present a prediction model, which relies on two steps. First, the mean square error at the low-resolution quantizer output due to quantization and clipping is computed. Second, the mean square error is converted into a signal-to-noise ratio, carefully accounting for the operating parameters (sampling frequency, symbol rate, clipping factor). The domain of validity of this model is assessed for both quantization and clipping noises separately. The predictions are confronted with numerical simulations and a set of experiments in a back-to-back optical set-up. The results show that the signal-to-noise ratio can be predicted with an error of less than 0.5 dB within the domain of validity of the model. Finally, we use this model to establish the resolution requirements for the next generation of metropolitan optical systems (>400 Gbit/s) and compare them with most recent experiments using low-resolution digital-to-analog converters.

Quick Estimation of Periodic Signal Parameters From 1-Bit Measurements

Estimation of periodic signals, based on quantized data, is a topic of general interest in the area of instrumentation and measurement. Although several methods are available, new applications require low-power, low-complexity, and adequate estimation accuracy. In this paper, we consider the simplest possible quantization, that is, binary quantization, and describe a technique to estimate the parameters of a sampled periodic signal, using a fast algorithm. By neglecting the possibility that the sampling process is triggered by some signal-derived event, sampling is assumed to be asynchronous , that is, the ratio between the signal and the sampling periods is defined to be an irrational number. To preserve enough information at the quantizer output, additive Gaussian input noise is assumed as the information encoding mechanism. With respect to the published techniques addressing the same problem, the proposed approach does not rely on the numerical estimation of the maximum likelihood function but provides solutions that are very close to this estimate. At the same time, since the main estimator is based on matrix inversion, it proves to be less time-consuming than the numerical maximization of the likelihood function, especially when solving problems with a large number of parameters. The estimation procedure is described in detail and validated using both simulation and experimental results. The estimator performance limitations are also highlighted.

New Equivalent Model of a Quantizer With Noisy Input and Its Applications for MIMO System Analysis and Design

We propose a novel equivalent model for a quantizer with noisy input (the desired signal corrupted by measurement noise). It presents the quantizer output as a sum of the desired signal after it passes through a nonlinear element with a known equivalent transfer function and an equivalent additive white noise. The equivalent transfer function takes the form of a conditional expectation of the quantizer output given the desired signal portion of its input. The proposed model proves to be effective for the analysis and design of MIMO systems employing low-resolution quantizers (analog to digital and digital to analog converters, ADCs and DACs, respectively). We also demonstrate the efficacy of the model through several example applications for 1) the design of digital dither that mitigates the effect of DAC quantization error in a MIMO transmitter and significantly reduces the DAC resolution requirement; 2) the determination of the minimal ADC resolution required for operation of conventional MIMO receivers designed for infinite-resolution ADC arrays, without incurring significant performance degradation; and 3) the design of simple MIMO receivers (ML and MMSE) that mitigate the effect of insufficient ADC resolution, thereby extending the receiver SNR operating range without an undue complexity increase.