Non-uniform Quantization Research Articles

Image Compression Using High Level Wavelet Transformer with Non-Uniform Quantizer and Different Levels Huffman Codes

Image compression solutions are a pivotal field that gain over a remarkable research interest and called upon to extend widely with respect to the increasing of its applications. The considerable challenge of this solution is related to the storage and bandwidth requirements. A highly compression rate with a high image resolution is considered to be the key factors for implementing a robust image compression technique. In this paper, the proposed method is deemed to be simple and effective due to using different levels of compression process which is starting from dividing the image into sub-images and using high level discrete wavelet transform (DWT). In addition, the Huffman code with non-uniform Quantizer has been used to minimize the compression data rate with high quality reconstructed image. The promising simulation results of the proposed method achieved the most two significant criteria which are denoted by high image quality and a high image compressed ratio. For instance, the proposed strategy simulation results of Lena image achieved PSNR equals to 42.4094 dB with a compression ratio (CR) equals to 47.5435. Moreover, the simulation results of Flower image accomplished PSNR equals to 42.8348 dB with a compression ratio equals to 55.3389 under the same simulation conditions.

Gaussian source coding based on variance‐mismatched three‐level scalar quantisation using Q ‐function approximations

This study deals with three-level scalar quantisation of a Gaussian source, followed by Huffman encoder, especially suitable for signal compression purposes. The variance-matched and variance-mismatched versions of quantiser are considered. Simple approximate closed-form expressions for performance evaluation in terms of signal-to-quantisation-noise ratio and bit rate are derived using the corresponding Q-function approximations. The accuracy of the derived formulas is tested using the relative error as a measure of performance. It is shown that the derived formulas for variance-matched (for a reference variance) and variance-mismatched (in a wide range of input signal variances) provide higher accuracy in comparison to baselines using other available Q-function approximations or available approximate formulas for non-uniform scalar quantisation of Gaussian source.

ICELIA: A Full-Stack Framework for STT-MRAM-Based Deep Learning Acceleration

A large variety of applications rely on deep learning to process big data, learn sophisticated features, and perform complicated tasks. Utilizing emerging non-volatile memory (NVM)'s unique characteristics, including the crossbar array structure and gray-scale cell resistances, to perform neural network (NN) computation is a well-studied approach in accelerating deep learning applications. Compared to other NVM technologies, STT-MRAM has its unique advantages in performing NN computation. However, the state-of-the-art research have not utilized STT-MRAM for deep learning acceleration due to its device- and architecture-level challenges. Consequently, this paper enables STT-MRAM, for the first time, as an effective and practical deep learning accelerator. In particular, it proposes a full-stack framework iCELIA spanning multiple design levels, including device-level fabrication, circuit-level enhancements, architecture-level synaptic weight quantization, and system-level accelerator design. The primary contributions of iCELIA over our prior work CELIA include a new non-uniform weight quantization scheme and much enhanced accelerator system design. The proposed framework significantly mitigates the model accuracy loss due to reduced data precision in a cohesive manner, constructing a comprehensive STT-MRAM accelerator system for fast NN computation with high energy efficiency and low cost.

역제곱 비균일 양자화 기법을 활용한 심층신경망의 에너지 효율성 개선

역제곱 비균일 양자화 기법을 활용한 심층신경망의 에너지 효율성 개선

Modeling and Optimization of Wireless Channel in High-Speed Railway Terrain

The high-speed railway (HSR) wireless channel models based on field measurements have poor universality and low modeling accuracy due to the limitations of the experimental methods and the terrain conditions. To overcome this problem, this paper considers the wireless channels in various HSR scenarios (such as tunnels, mountains, viaducts, cuttings and plains) as the research objects and establishes a novel finite-state Markov chain (FSMC) optimization simulation model based on the signal-to-noise ratio (SNR) threshold, the channel states and the state transition probability matrix, by using the nonuniform space division SNR quantization strategy (hereinafter referred to as Strategy 1) and the equal-area space division SNR quantization strategy (hereinafter referred to as Strategy 2). The SNR curves that are obtained via simulation closely fit the experimental results; therefore, the proposed simulation model can accurately characterize the channel state in a variety of HSR scenarios. Furthermore, the simulation results demonstrate that in the tunnel scenario, Strategy 1 realizes a smaller mean square error (MSE) and a higher modeling accuracy than Strategy 2. The MSE values of the two strategies are similar in the plain scenario. Strategy 2 realizes a smaller MSE and a higher modeling accuracy in the mountain, viaduct and cutting scenarios.

Learned Conjugate Gradient Descent Network for Massive MIMO Detection

In this work, we consider the use of model-driven deep learning techniques for massive multiple-input multiple-output (MIMO) detection. Compared with conventional MIMO systems, massive MIMO promises improved spectral efficiency, coverage and range. Unfortunately, these benefits are coming at the cost of significantly increased computational complexity. To reduce the complexity of signal detection and guarantee the performance, we present a learned conjugate gradient descent network (LcgNet), which is constructed by unfolding the iterative conjugate gradient descent (CG) detector. In the proposed network, instead of calculating the exact values of the scalar step-sizes, we explicitly learn their universal values. Also, we can enhance the proposed network by augmenting the dimensions of these step-sizes. Furthermore, in order to reduce the memory costs, a novel quantized LcgNet is proposed, where a low-resolution nonuniform quantizer is integrated into the LcgNet to smartly quantize the aforementioned step-sizes. The quantizer is based on a specially designed soft staircase function with learnable parameters to adjust its shape. Meanwhile, due to fact that the number of learnable parameters is limited, the proposed networks are easy and fast to train. Numerical results demonstrate that the proposed network can achieve promising performance with much lower complexity.

Learning a Single Tucker Decomposition Network for Lossy Image Compression with Multiple Bits-Per-Pixel Rates.

Lossy image compression (LIC), which aims to utilize inexact approximations to represent an image more compactly, is a classical problem in image processing. Recently, deep convolutional neural networks (CNNs) have achieved interesting results in LIC by learning an encoder-quantizer-decoder network from a large amount of data. However, existing CNN-based LIC methods generally train a network for a specific bits-perpixel (bpp). Such a "one-network-per-bpp" problem limits the generality and flexibility of CNNs to practical LIC applications. In this paper, we propose to learn a single CNN which can perform LIC at multiple bpp rates. A simple yet effective Tucker Decomposition Network (TDNet) is developed, where there is a novel tucker decomposition layer (TDL) to decompose a latent image representation into a set of projection matrices and a core tensor. By changing the rank of core tensor and its quantization, we can easily adjust the bpp rate of latent image representation within a single CNN. Furthermore, an iterative non-uniform quantization scheme is presented to optimize the quantizer, and a coarse-to-fine training strategy is introduced to reconstruct the decompressed images. Extensive experiments demonstrate the state-of-the-art compression performance of TDNet in terms of both PSNR and MS-SSIM indices.

A Super-Resolution Mixed-Signal Doherty Power Amplifier for Simultaneous Linearity and Efficiency Enhancement

This article presents a mixed-signal Doherty power amplifier (MSDPA) architecture for simultaneous linearity and efficiency enhancement. The MSDPA comprises one analog power amplifier (PA) as the main PA and one binary-weighted digital PA as the auxiliary PA. The MSDPA input is a generic envelope-varying complex-modulated signal. Based on the realtime amplitude-modulated (AM) envelope, auxiliary digital PA weightings are dynamically turned-on to perform optimum Doherty load modulation for superior linearity and back-off efficiency. Moreover, quantization noise is largely suppressed by the mixed-signal Doherty operation and nonuniform quantization (NUQ), while spectral images are substantially reduced by the quasi-first-order hold (quasi-FOH) operation, which together achieves super-resolution over conventional digital PAs; this makes the MSDPA conducive to millimeter-wave (mm-Wave) or compound PA designs by obviating the need for a large effective number of bits (ENOB) on AM digital controls. As a proof of concept, a 3-bit MSDPA is implemented at 27 GHz in a 45-nm silicon-on-insulator (SOI) CMOS process. The prototype PA achieves 40.1% peak power-added efficiency (PAE), 23.3-dBm saturated output power (Psat), and 39.4% PAE for 22.4-dBm P1dB at 27 GHz in continuous-wave (CW) measurements. The PAE at 6-dB power back-off (PBO) is 33.1%, which corresponds to a 1.68× improvement over a normalized Class-B PA. With only three control bits, the MSDPA PA supports a 12-Gb/s 64-QAM signal at -24.5-dB rms error vector magnitude (EVM) and average Pout/PAE of +15.6 dBm/27.8% without digital predistortion (DPD).

UNIQ

We present a novel method for neural network quantization. Our method, named UNIQ , emulates a non-uniform k -quantile quantizer and adapts the model to perform well with quantized weights by injecting noise to the weights at training time. As a by-product of injecting noise to weights, we find that activations can also be quantized to as low as 8-bit with only a minor accuracy degradation. Our non-uniform quantization approach provides a novel alternative to the existing uniform quantization techniques for neural networks. We further propose a novel complexity metric of number of bit operations performed (BOPs), and we show that this metric has a linear relation with logic utilization and power. We suggest evaluating the trade-off of accuracy vs. complexity (BOPs). The proposed method, when evaluated on ResNet18/34/50 and MobileNet on ImageNet, outperforms the prior state of the art both in the low-complexity regime and the high accuracy regime. We demonstrate the practical applicability of this approach, by implementing our non-uniformly quantized CNN on FPGA.

CQI-Based Interference-Aware Graph Resource-Sharing Scheme for Vehicular Networks

With the goal of maximizing the sum rate of vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) networks, a well-designed resource-sharing scheme tends to match the ones producing less amount of interference. The statistics also reveals that the interference incurred by a well-designed resource-sharing scheme concentrates at a certain level. This observation hints us that as the non-uniform quantization scheme is used, solely fewer quantization bits are required to capture the main characteristic of the resource-sharing interference. Thus, in this paper, we aim to reduce the overheads for reporting the channel state information (CSI) to avoid any intolerable amount of interference caused by improperly resource sharing between V2I and V2V connections. To achieve this, the non-uniform quantization method is developed to construct the channel-quality indicator (CQI) for capturing the most informative CSI using fewer bits. Taking the conventional interference-aware graph resource-sharing scheme with perfect CSI as the baseline, we find that with regular traffic density, one-bit CQI can achieve equivalent performance. That remarkably saves 95.5% of CSI overheads without sacrificing the sum rate.

Designing an Image Encryption Scheme Based on Compressive Sensing and Non-Uniform Quantization for Wireless Visual Sensor Networks

Wireless visual sensor networks (WVSN) have been widely used to capture images in the fields of monitoring, intelligent transportation, and reconnaissance in recent years. Because of the wireless transmission mode and the huge amount of image data, major challenges in this application are frequent information stealing, big data problems, and harsh communication circumstances. Some encryption schemes based on compressive sensing (CS) and chaotic systems have been proposed to cope with these threats, but most of them are vulnerable against the chosen-plaintext attack (CPA). To remedy these defects, this paper designs a novel method based on non-uniform quantization (NQ). Then, in order to evaluate the true compression ratio (CR), our work takes into account limited data precision in cipher images, while most papers ignored this fact and calculated CR with the assumption of infinite data precision. Besides, to eliminate the periodic windows in the bifurcation diagram of the logistic map (LM), an optimized logistic map (OLM) is designed. Furthermore, simulation results prove that the performance of anti-jamming in the proposed cryptosystem is better than that in existing schemes under the condition of strong noise interference or severe data loss. In conclusion, the proposed method could improve the performance of security and anti-jamming for WVSN.

Efficient Weights Quantization of Convolutional Neural Networks Using Kernel Density Estimation based Non-uniform Quantizer

Convolutional neural networks (CNN) have achieved excellent results in the field of image recognition that classifies objects in images. A typical CNN consists of a deep architecture that uses a large number of weights and layers to achieve high performance. CNN requires relatively large memory space and computational costs, which not only increase the time to train the model but also limit the real-time application of the trained model. For this reason, various neural network compression methodologies have been studied to efficiently use CNN in small embedded hardware such as mobile and edge devices. In this paper, we propose a kernel density estimation based non-uniform quantization methodology that can perform compression efficiently. The proposed method performs efficient weights quantization using a significantly smaller number of sampled weights than the number of original weights. Four-bit quantization experiments on the classification of the ImageNet dataset with various CNN architectures show that the proposed methodology can perform weights quantization efficiently in terms of computational costs without significant reduction in model performance.

A robust and secure image sharing scheme with personal identity information embedded

In a (t, n)-threshold secret image sharing (SIS) scheme, the secrecy of a secret image relies on check and balance among participants. Unfortunately, the decentralized management also brings an underlying security flaw, i.e., once an attacker impersonates an authorized participant to submit a fake shadow for reconstruction no information about the secret image can be revealed. In order to resist such an identity-based attack, a novel SIS scheme with identity-based authentication is proposed, where a natural image is encoded through compressive sensing and then the compressive image is divided into n shadows (i.e., shares) according to an innovate way in which the production of shadows is controlled by participants’ identification number. Only when any t or more authorized participants cooperate together can the original image be reconstructed. Besides, a simple but efficient non-uniform scalar quantization method and a group communication protocol are presented to perfect the proposed scheme. Performance and security analyses indicate that our scheme possesses many advantages, including no pixel expansion, flexible shadow size, progressive display capability, error-resilient capability, no necessity for secure channels, and high security against statistical attack, brute-force attack, and identity-based attack.

Multidimensional vector quantization-based fast statistical estimation in compressed digitalized radio-over-fiber systems.

A multidimensional vector quantization-based fast statistical-estimation (VQ-FSE) algorithm is proposed to enhance data compression performance in digitalized radio over fiber (D-RoF) systems. The original samples with Gaussian distribution are first transformed into these with uniform distribution via companding transformation. After the companding transformation operation, the signal vector is constructed by grouping multiple samples in a certain way so that there is little correlation among them. The constructed signal vector may follow approximately multidimensional uniform distribution, and then multidimensional uniform quantization can be easily carried out, where the complex optimized process in nonuniform quantization is not required. For the proposed two-dimensional (2D) VQ-FSE algorithm, the proposed scheme is numerically verified in a 20km D-RoF system with 2Gbit/s RF wireless signal. Compared with the scalar-quantization-based FSE algorithm, its compression ratio is significantly enhanced. In comparison to the 2D k-means-clustering-based VQ algorithm, the proposed scheme shares a similar compression ratio and offers lower computational complexity. Therefore, the proposed algorithm has the ability to provide better compression and lower complexity for the digitized D-RoF system when the original sample follows Gaussian distribution.

Self-coherent detection for optical OFDM via polarization diversity

An improved self-coherent digital-signal-processing-based optical receiver that utilizes polarization diversity is presented and analyzed. It demonstrates that coherent performance can be approached by employing field reconstruction on differential-phase detection and judicious digital signal processing. Performance is improved compared to known techniques by addressing two shortcomings that characterize self-coherent detection: 1. the phase drift caused during field reconstruction; and 2. the loss of synchronization induced by a zero-intensity sample with undefined phase. These will be met with phase estimation and periodic correction, and with polarization-diversity and a non-linear quantization scheme, respectively. It is demonstrated by means of simulations that the improved receiver allows achieving detection of an optical orthogonal frequency division multiplexing at uncoded bit-error-rate of 3*10-5, with 12 bit non-uniform quantization, over an 18 dB signal-to-noise ratio channel.

32-GS/s 6-bit DAC based on SiGe technology for IM-DD OFDM systems with non-uniform quantization.

In this paper, we design and fabricate a 32-GS/s 6-bit digital-to-analog convertor (DAC) based on SiGe technology. The DAC uses double sampling technique and segment current steering architecture to achieve high dynamic linearity. A corrector circuit is proposed to suppress the duty cycle error for linearity optimization. The spurious free dynamic range (SFDR) is above 31.5 dBc over the Nyquist bandwidth at the sampling rate of 32-GS/s. A full-rate input interface is integrated to realize data exchange with field-programmable gate array (FPGA). The experimental results show that the net data rate of 50-Gb/s orthogonal frequency division multiplexing (OFDM) signals with non-uniform quantization can be generated by the designed and fabricated DAC. The OFDM signal transmission over 10-km standard single mode fiber (SSMF) with 64-quadrature amplitude modulation (QAM) and 128-QAM formats have been successfully achieved.

BER performance analysis of coarsely quantized uplink massive MIMO

Abstract Having lower quantization resolution, has been introduced in the literature, to reduce the power consumption of massive MIMO and millimeter wave MIMO systems. Here, we analyze the bit error rate (BER) performance of quantized uplink massive MIMO employing few-bit resolution ADCs. Considering ZF detection, we derive a signal-to-interference, quantization and noise ratio (SIQNR) to achieve an analytical BER approximation for coarsely quantized M-QAM massive MIMO systems, by using a linear quantization model. The proposed expression is a function of the quantization resolution in bits. We further numerically investigate the effects of different quantization levels, from 1-bit to 4-bits, on the BER of three modulation types QPSK, 16-QAM, and 64-QAM. The uniform and non-uniform quantizers are employed in our simulation. Monte Carlo simulation results reveal that our approximate formula gives a tight upper bound on the BER performance of b-bit resolution quantized systems using non-uniform quantizers, whereas the use of uniform quantizers cause a lower performance. We also found a small BER performance degradation in coarsely quantized systems, for example 2–3 bits QPSK and 3–4 bits 16-QAM, compared to the full-precision (unquantized) case. However, this performance degradation can be compensated by increasing the number of antennas at the BS.

A 64-Gb/s 4-PAM Transceiver Utilizing an Adaptive Threshold ADC in 16-nm FinFET

A 64-Gb/s 4-pulse-amplitude modulation (PAM) transceiver fabricated with a 16-nm fin field effect transistor (FinFET) technology is presented with a power consumption that scales with link loss. The transmitter (TX) includes a three-tap feed-forward equalizer (FFE) (one pre and one post) achieving a level separation mismatch ratio (RLM) of 99% and a random jitter (RJ) of 162-fs rms. The maximum swing is 1.1 Vppd at a power consumption of 89.7 mW including clock distribution from a 1.2-V supply, corresponding to 1.39 pJ/bit. The receiver analog front end (RX-AFE) consists of a half-rate (HR) sampling continuous-time linear equalizer (CTLE) and 6-bit flash (1-bit folding) analog-to-digital converter (ADC) capable of non-uniform quantization. The non-uniform thresholds are selected based on a greedy search approach which allows the RX to reduce power at low channel loss in a highly granular manner and achieves better bit error rate (BER) than a uniform quantizer. For a channel with -8.6-dB loss at Nyquist, ADC can be configured in 2-bit mode, achieving BER <; 1e - 6 at an RX-AFE power consumption of 100 mW. For a -29.5-dB loss channel, the RX-AFE consumes 283.9 mW and achieves a BER <; 1e - 4 in conjunction with a software digital equalizer. For a -13.5-dB loss channel, a greedy search is used to optimize the quantization threshold levels, achieving an order of magnitude improvement in BER compared to uniform quantization.

A compact pitch and time representation for melodic contours in Indian art music.

Predominant melody offers a complete representation of melodic contours of heterophonic Indian Art Music (IAM). A compact representation of melodic contours while preserving raga characteristics is proposed. Such representations have applications in music transcription, analysis, and synthesis. Contours are quantized on a pitch-time grid after normalizing critical points with tonic and rhythmic pulse period estimates. Non-uniform quantization intervals are selected from pitch and time scales prevalent in IAM, while accommodating pitch and inter-note-interval variations on pitch-time grid. An evaluation of quantized-reconstructed contours through listening tests by trained musicians shows raga preserving capabilities of the proposed approach in spite of alterations in contour shapes.

Performance of the Gerschgorin Radii and Centers Ratio Detector for Cooperative Spectrum Sensing under Burst Control Channel Errors

In centralized cooperative spectrum sensing (CSS), cognitive radios (CRs) monitor the spectrum and send the related data to a fusion center (FC) via a control channel in order to more efficiently detect possible idle bands for opportunistic occupation. In centralized cooperative spectrum sensing (CSS), cognitive radios (CRs) monitor the spectrum and send the related data to a fusion center (FC) via a control channel in order to more efficiently detect possible idle bands for opportunistic occupation. In practice, such data must be quantized prior to transmission, which can lead to loss of the global spectrum sensing performance due to quantization errors. Additionally, wireless control channel impairments, such as the multipath fading, further contributes to performance degradation. In many researches, the control channel is considered error-free. Even when errors are considered, they usually affect the transmitted symbols independently, that is, the control channel is assumed to be memoryless. Error bursts come from the memory effect of the channel, and are typically found in wireless communications. In this paper we consider the effects of burst errors in the control channel as well as the problem of signal distortion caused by three methods of quantization in centralized CSS with sample fusion. The Gerschgorin Radii and Centers Ratio (GRCR) detector is used as the test statistic for spectrum sensing. Our findings show that: i) the GRCR is robust in the scenarios taken into consideration, ii) the uniform quantization may be preferred in some cases when the control channel is considered perfect, iii) the nonuniform quantization attains better performance under errors in the control channel, and iv) the effect of memory in the control channel may produce, in some situations, performance gains with respect to the memoryless channel, when both have the same average bit error rate.