Academic literature on the topic 'Non-Uniform Quantization'

In order to improve the accuracy of distributed consensus under digital communication, in the paper, assuming the initial states of nodes following uniform distribution, a non-uniform quantization scheme based on probabilistic quantization is proposed, and the entire data range is divided based on µ-law non-uniform quantization scheme. The quantization step-size near the average of initial states is smaller, and the corresponding quantization errors are smaller. Base on the proposed quantization scheme, a non-uniform probabilistically quantized distributed consensus algorithm is proposed. The performance and the mean square errors of the non-uniform probabilistically quantized distributed consensus algorithm is analyzed, by analyses and simulations, the results show the non-uniform probabilistically quantized distributed consensus can reach a consensus, and the mean square error is far smaller than that of probabilistically quantized distributed consensus.

This paper investigates the quantization methods of the reliability-based iterative decoding algorithm for LDPC codes. For the uniform quantization, we present a new design criterion to determine the quantization parameters with the clipping interval/probability. Compared to the original parameters setting, the presented design criterion can achieve higher resolution with the allowable quantization distortions. The presented parameter design criterion can be extended to the non-uniform quantization with a slight modification. Simulation results show that, the decoding algorithm can achieve better BER performances and faster convergence rate with smaller quantization bit when compared to the original parameters setting.

A novel unsupervised learning rule, called Boundary Adaptation Rule (BAR), is introduced for scalar quantization. It is shown that the rule maximizes information-theoretic entropy and thus yields equiprobable quantizations of univariate probability density functions. It is shown by simulations that BAR outperforms other unsupervised competitive learning rules in generating equiprobable quantizations. It is also shown that our rule can do better or worse than the Lloyd I algorithm in minimizing average mean square error, depending on the input distribution. Finally, an application to adaptive non-uniform analog to digital (A/D) conversion is considered.

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.

To reduce the detection failure of the exchanging signal power onto the OFDM subcarrier signal at uniform quantization, dynamic subcarrier mapping is applied. Moreover, to addressing low SNR’s wall-less than pre-determine threshold, non-uniform quantization or adaptive quantization for the signal quantization size parameter is proposed. μ-law is adopted for adaptive quantization subcarrier mapping which is deployed in mobility environment, such as Doppler Effect and Rayleigh Fading propagation. In this works, sensing node received signal power then sampled into a different polarity positive and negative in μ-law quantization and divided into several segmentation levels. Each segmentation levels are divided into several sub-segment has representing one tone signal subcarrier number OFDM which has the number of quantization level and the width power. The results show that by using both methods, a significant difference is obtained around 8 dB compared to those not using the adaptive method.

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.

An efficient non-uniform color quantization and similarity measurement methods are proposed to enhance the content-based image retrieval (CBIR) applications. The HSV color space is selected because it is close to human visual perception system, and a non-uniform color method is proposed to quantize an image into 37 colors. The marker histogram (MH) vector of size 296 values is generated by segmenting the quantized image into 8 regions (multiplication of 45°) and count the occurrences of the quantized colors in their particular angles. To cope with rotated images, an incremental displacement to the MH is applied 7 times. To find similar images, we proposed a new similarity measurement and other 4 existing metrics. A uniform color quantization of related work is implemented too and compared to our quantization method. One-hundred test images are selected from the Corel-1000 images database. Our experimental results conclude high retrieving precision ratios compared to other techniques.

The thesis demonstrates a low-cost, low-bandwidth and low-resolution Analog-to- Digital Converter(ADC) in 0.35 um CMOS Process. A second-order Sigma-Delta modulator is used as the basis of the A/D Converter. A Semi-Uniform quantizer is used with the modulator to take advantage of input distributions that are dominated by smaller-amplitude signals e.g. Audio, Voice and Image-sensor signals. A Single-bit feedback topology is used with a multi-bit quantizer in the modulator. This topology avoids the use of a multi-bit DAC in the feedback loop – hence the system does not need to use digital correction techniques to compensate for a multi-bit DAC nonlinearity.

High-Level Simulations of the second-order Sigma-Delta modulator single-bit feedback topology along with a Semi-Uniform quantizer are performed in Cadence. Results indicate that a 5-bit Semi-Uniform quantizer with a Over-Sampling Ratio of 32, can achieve a resolution of 10 bits, in addition, a semi-uniform quantizer exhibits a 5-6 dB gain in SNR over its uniform counterpart for input amplitudes smaller than –10 dB. Finally, this system is designed in 0.35um CMOS process.

Nowadays, the digital terrestrial television (DTT) market is characterized by the high capacity needed for high definition TV services. There is a need for an efficient use of the broadcast spectrum, which requires new technologies to guarantee increased capacities. Non-Uniform Constellations (NUC) arise as one of the most innovative techniques to approach those requirements. NUCs reduce the gap between uniform Gray-labelled Quadrature Amplitude Modulation (QAM) constellations and the theoretical unconstrained Shannon limit. With these constellations, symbols are optimized in both in-phase (I) and quadrature (Q) components by means of signal geometrical shaping, considering a certain signal-to-noise ratio (SNR) and channel model. There are two types of NUC, one-dimensional and two-dimensional NUCs (1D-NUC and 2D-NUC, respectively). 1D-NUCs maintain the squared shape from QAM, but relaxing the distribution between constellation symbols in a single component, with non-uniform distance between them. These constellations provide better SNR performance than QAM, without any demapping complexity increase. 2D-NUCs also relax the square shape constraint, allowing to optimize the symbol positions in both dimensions, thus achieving higher capacity gains and lower SNR requirements. However, the use of 2D-NUCs implies a higher demapping complexity, since a 2D-demapper is needed, i.e. I and Q components cannot be separated. In this dissertation, NUCs are analyzed from both transmit and receive point of views, using either single-input single-output (SISO) or multiple-input multiple-output (MIMO) antenna configurations. In SISO transmissions, 1D-NUCs and 2D-NUCs are optimized for a wide range of SNRs and different constellation orders. The optimization of rotated 2D-NUCs is also investigated. Even though the demapping complexity is not increased, the SNR gain of these constellations is not significant. The highest rotation gain is obtained for low-order constellations and high SNRs. However, with multi-RF techniques, the SNR gain is drastically increased, since I and Q components are transmitted in different RF channels. In this thesis, multi-RF gains of NUCs with and without rotation are provided for some representative scenarios. At the receiver, two different implementation bottlenecks are explored. First, the demapping complexity of all considered constellations is analyzed. Afterwards, two complexity reduction algorithms for 2D-NUCs are proposed. Both algorithms drastically reduce the number of distances to compute. Moreover, both are finally combined in a single demapper. Quantization of NUCs is also explored in this dissertation, since LLR values and I/Q components are modified when using these constellations, compared to traditional QAM constellations. A new algorithm that is based on the optimization of the quantizer levels for a particular constellation is proposed. The use of NUCs in multi-antenna communications is also investigated. It includes the optimization in one or two antennas, the use of power imbalance, the cross-polar discrimination (XPD) between receive antennas, or the use of different demappers. Assuming different values for the parameters evaluated, new Multi-Antenna Non-Uniform Constellations (MA-NUC) are obtained by means of a particularized re-optimization process, specific for MIMO. At the receiver, an extended demapping complexity analysis is performed, where it is shown that the use of 2D-NUCs in MIMO extremely increases the demapping complexity. As an alternative, an efficient solution for 2D-NUCs and MIMO systems based on Soft-Fixed Sphere Decoding (SFSD) is proposed. The main drawback is that SFSD demappers do not work with 2D-NUCs, since they perform a Successive Interference Cancellation (SIC) step that needs to be performed in separated I and Q components. The proposed method quantifies the closest symbol using Voronoi regions and allows SFSD demappers to work.
Hoy en día, el mercado de la televisión digital terrestre (TDT) está caracterizado por la alta capacidad requerida para transmitir servicios de televisión de alta definición y el espectro disponible. Es necesario por tanto un uso eficiente del espectro radioeléctrico, el cual requiere nuevas tecnologías para garantizar mayores capacidades. Las constelaciones no-uniformes (NUC) emergen como una de las técnicas más innovadoras para abordar tales requerimientos. Las NUC reducen el espacio existente entre las constelaciones uniformes QAM y el límite teórico de Shannon. Con estas constelaciones, los símbolos se optimizan en ambas componentes fase (I) y cuadratura (Q) mediante técnicas geométricas de modelado de la señal, considerando un nivel señal a ruido (SNR) concreto y un modelo de canal específico. Hay dos tipos de NUC, unidimensionales y bidimensionales (1D-NUC y 2D-NUC, respectivamente). Las 1D-NUC mantienen la forma cuadrada de las QAM, pero permiten cambiar la distribución entre los símbolos en una componente concreta, teniendo una distancia no uniforme entre ellos. Estas constelaciones proporcionan un mejor rendimiento SNR que QAM, sin ningún incremento en la complejidad en el demapper. Las 2D-NUC también permiten cambiar la forma cuadrada de la constelación, permitiendo optimizar los símbolos en ambas dimensiones y por tanto obteniendo mayores ganancias en capacidad y menores requerimientos en SNR. Sin embargo, el uso de 2D-NUCs implica una mayor complejidad en el receptor. En esta tesis se analizan las NUC desde el punto de vista tanto de transmisión como de recepción, utilizando bien configuraciones con una antena (SISO) o con múltiples antenas (MIMO). En transmisiones SISO, se han optimizado 1D-NUCs para un rango amplio de distintas SNR y varios órdenes de constelación. También se ha investigado la optimización de 2D-NUCs rotadas. Aunque la complejidad no aumenta, la ganancia SNR de estas constelaciones no es significativa. La mayor ganancia por rotación se obtiene para bajos órdenes de constelación y altas SNR. Sin embargo, utilizando técnicas multi-RF, la ganancia aumenta drásticamente puesto que las componentes I y Q se transmiten en distintos canales RF. En esta tesis, se han estudiado varias ganancias multi-RF representativas de las NUC, con o sin rotación. En el receptor, se han identificado dos cuellos de botella diferentes en la implementación. Primero, se ha analizado la complejidad en el receptor para todas las constelaciones consideradas y, posteriormente, se proponen dos algoritmos para reducir la complejidad con 2D-NUCs. Además, los dos pueden combinarse en un único demapper. También se ha explorado la cuantización de estas constelaciones, ya que tanto los valores LLR como las componentes I/Q se ven modificados, comparando con constelaciones QAM tradicionales. Además, se ha propuesto un algoritmo que se basa en la optimización para diferentes niveles de cuantización, para una NUC concreta. Igualmente, se ha investigado en detalle el uso de NUCs en MIMO. Se ha incluido la optimización en una sola o en dos antenas, el uso de un desbalance de potencia, factores de discriminación entre antenas receptoras (XPD), o el uso de distintos demappers. Asumiendo distintos valores, se han obtenido nuevas constelaciones multi-antena (MA-NUC) gracias a un nuevo proceso de re-optimización específico para MIMO. En el receptor, se ha extendido el análisis de complejidad en el demapper, la cual se incrementa enormemente con el uso de 2D-NUCs y sistemas MIMO. Como alternativa, se propone una solución basada en el algoritmo Soft-Fixed Sphere Decoding (SFSD). El principal problema es que estos demappers no funcionan con 2D-NUCs, puesto que necesitan de un paso adicional en el que las componentes I y Q necesitan separarse. El método propuesto cuantifica el símbolo más cercano utilizando las regiones de Voronoi, permitiendo el uso de este tipo de receptor.
Actualment, el mercat de la televisió digital terrestre (TDT) està caracteritzat per l'alta capacitat requerida per a transmetre servicis de televisió d'alta definició i l'espectre disponible. És necessari per tant un ús eficient de l'espectre radioelèctric, el qual requereix noves tecnologies per a garantir majors capacitats i millors servicis. Les constel·lacions no-uniformes (NUC) emergeixen com una de les tècniques més innovadores en els sistemes de televisió de següent generació per a abordar tals requeriments. Les NUC redueixen l'espai existent entre les constel·lacions uniformes QAM i el límit teòric de Shannon. Amb estes constel·lacions, els símbols s'optimitzen en ambdós components fase (I) i quadratura (Q) per mitjà de tècniques geomètriques de modelatge del senyal, considerant un nivell senyal a soroll (SNR) concret i un model de canal específic. Hi ha dos tipus de NUC, unidimensionals i bidimensionals (1D-NUC i 2D-NUC, respectivament). 1D-NUCs mantenen la forma quadrada de les QAM, però permet canviar la distribució entre els símbols en una component concreta, tenint una distància no uniforme entre ells. Estes constel·lacions proporcionen un millor rendiment SNR que QAM, sense cap increment en la complexitat al demapper. 2D-NUC també canvien la forma quadrada de la constel·lació, permetent optimitzar els símbols en ambdós dimensions i per tant obtenint majors guanys en capacitat i menors requeriments en SNR. No obstant això, l'ús de 2D-NUCs implica una major complexitat en el receptor, ja que es necessita un demapper 2D, on les components I i Q no poden ser separades. En esta tesi s'analitzen les NUC des del punt de vista tant de transmissió com de recepció, utilitzant bé configuracions amb una antena (SISO) o amb múltiples antenes (MIMO). En transmissions SISO, s'han optimitzat 1D-NUCs, per a un rang ampli de distintes SNR i diferents ordes de constel·lació. També s'ha investigat l'optimització de 2D-NUCs rotades. Encara que la complexitat no augmenta, el guany SNR d'estes constel·lacions no és significativa. El major guany per rotació s'obté per a baixos ordes de constel·lació i altes SNR. No obstant això, utilitzant tècniques multi-RF, el guany augmenta dràsticament ja que les components I i Q es transmeten en distints canals RF. En esta tesi, s'ha estudiat el guany multi-RF de les NUC, amb o sense rotació. En el receptor, s'han identificat dos colls de botella diferents en la implementació. Primer, s'ha analitzat la complexitat en el receptor per a totes les constel·lacions considerades i, posteriorment, es proposen dos algoritmes per a reduir la complexitat amb 2D-NUCs. Ambdós algoritmes redueixen dràsticament el nombre de distàncies. A més, els dos poden combinar-se en un únic demapper. També s'ha explorat la quantització d'estes constel·lacions, ja que tant els valors LLR com les components I/Q es veuen modificats, comparant amb constel·lacions QAM tradicionals. A més, s'ha proposat un algoritme que es basa en l'optimització per a diferents nivells de quantització, per a una NUC concreta. Igualment, s'ha investigat en detall l'ús de NUCs en MIMO. S'ha inclòs l'optimització en una sola o en dos antenes, l'ús d'un desbalanç de potència, factors de discriminació entre antenes receptores (XPD), o l'ús de distints demappers. Assumint distints valors, s'han obtingut noves constel·lacions multi-antena (MA-NUC) gràcies a un nou procés de re-optimització específic per a MIMO. En el receptor, s'ha modificat l'anàlisi de complexitat al demapper, la qual s'incrementa enormement amb l'ús de 2D-NUCs i sistemes MIMO. Com a alternativa, es proposa una solució basada en l'algoritme Soft-Fixed Sphere Decoding (SFSD) . El principal problema és que estos demappers no funcionen amb 2D-NUCs, ja que necessiten d'un pas addicional en què les components I i Q necessiten separar-se. El mètode proposat quantifica el símbol més pròxim utilitzan
Fuentes Muela, M. (2017). Non-Uniform Constellations for Next-Generation Digital Terrestrial Broadcast Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/84743
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we analyse different architectures of analog-to-digital converters (ADC) and propose an architecture based on sampling by crossing levels and adaptive quantization step, aiming at reducing the energy required to convert and process specific signals. The proposed architecture has parameters which can be dynamically configured by the user, as to adapt the conversion process to the signal being sampled and to the requirements of power consumption of the target application. The architecture was modeled and simulated using Matlab, and used to convert several test signals, of which an ECG signal. The use of the proposed architecture resulted in SNR improvements of up to 10dB if compared against uniform (periodic) sampling. The digital logic was implemented in FPGA from a SystemVerilog description functionally compatible with the Matlab model, and the analog part was implemented with discrete components.
Neste trabalho, faz-se uma análise de diferentes arquiteturas de conversores analógico-digitais, e propõe-se uma arquitetura de conversor analógico-digital baseado em amostragem por cruzamento de níveis (não-uniforme) com adaptação do passo de quantização, com o objetivo de reduzir o consumo de energia requerido pela conversão analógica-digital e processamento de sinais com características específicas. A arquitetura proposta possui parâmetros que podem ser configurados dinamicamente pelo usuário, a fim de que o processo de conversão se adeque às características do sinal a ser amostrado e aos requerimentos de consumo de energia da aplicação. A arquitetura foi modelada e simulada em MatLab, tendo sido utilizada na conversão de diversos sinais de teste, dentre os quais um sinal típico de eletrocardiograma. Verificou-se que a amostragem não-uniforme com adaptação do passo de quantização proposta resultou em um aumento da relação sinal-ruído do sinal amostrado de até 10dB quando comparado com a amostragem uniforme. A implementação da parte digital foi feita em FPGA a partir de uma descrição em SystemVerilog funcionalmente compatível com o modelo em Matlab, e a parte analógica foi implementada com componentes discretos.

It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin parallel or antiparallel to the magnetic field direction.

碩士
國立成功大學
電腦與通信工程研究所
102
In recent years, the coordinated beamforming (CBF) has attracted many attentions because of its effectiveness in the inter-cell interference (ICI) mitigation. In order to facilitate the operations of CBF, efficient channel state information (CSI) exchanges through backhaul links are necessary. From the literature, we find that uniform quantization of CSI was generally assumed in the feedback schemes. Statistically, however, uniform quantization may not be optimal from the viewpoint of the ICI in CBF, which is mainly caused by the quantization error (QE). In this paper, with a limited number of feedback bits, a non-uniform quantization method is proposed to apply more quantization levels to represent the feedback CSI with higher probability. This is because more accurate representation of frequent CSI can lead to lower QE so as to reduce the ICI level in most cases. To prove the effectiveness of the proposed scheme, the ICI in the considered two-cell CBF scenario is analyzed with various numbers of feedback bits. Also, higher transmission rate, especially in the cases with fewer feedback bits, is also proved by simulation results.