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Thinh Nguyen - One of the best experts on this subject based on the ideXlab platform.
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thresholding Quantizer design for mutual information maximization under output constraint
Vehicular Technology Conference, 2020Co-Authors: Thuan Nguyen, Thinh NguyenAbstract:We consider a channel with discrete input ${X}$, a continuous noise that corrupts the input ${X}$ to produce the continuous-valued output ${U}$. A thresholding Quantizer is then used to quantize the continuous-valued output ${U}$ to the final discrete output ${V}$. The goal is to jointly design a thresholding Quantizer that maximizes the mutual information between input and quantized output ${I}$(${X}$;${V}$) while minimizing a pre-specified function of the quantized output $F(p_{V})$. A general dynamic programming algorithm is proposed having the time complexity $O(KNM^{2})$ where N, M and ${K}$ are the sizes of input ${X}$, output ${U}$ and quantized output ${V}$, respectively. Moreover, we show that if $F(p_{V})=\displaystyle \sum _{i=1}^{K}g_{i}(p_{v_{i}})$ where $g_{i}(.)$ is a convex function, $p_{v_{i}} \in p_{V}=\{p_{v}1,\cdots ~p_{v_{K}}\}$ is the probability mass function of output $v_{i}\in V$ and the channel conditional density $p(u|x)$ satisfies the dominated condition (often true in practice), then the existing SMAWK algorithm can be applied to reduce the time complexity of the dynamic programming algorithm from $O(KNM^{2}$) to ${O}$(KNM). Both theoretical and numerical results are provided to verify our contributions.
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on thresholding Quantizer design for mutual information maximization optimal structures and algorithms
Vehicular Technology Conference, 2020Co-Authors: Thuan Nguyen, Thinh NguyenAbstract:Consider a channel having the discrete input X that is corrupted by a continuous noise to produce the continuous-valued output U. A thresholding Quantizer is then used to quantize the continuous-valued output U to the final discrete output V. One wants to design a thresholding Quantizer that maximizes the mutual information between the input and the final quantized output I(X;V). In this paper, the structure of optimal thresholding Quantizer is established that finally results in two efficient algorithms having the time complexities $O(NM+K\log^{2}(NM))$ for finding the local optimal Quantizer and $O(KM\log(NM))$ for finding the global optimal Quantizer where N, M, K are the size of input X, received output U and quantized output V, respectively. Both theoretical and numerical results are provided to verify our contributions.
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optimal Quantizer structure for binary discrete input continuous output channels under an arbitrary quantized output constraint
arXiv: Signal Processing, 2020Co-Authors: Thuan Nguyen, Thinh NguyenAbstract:Given a channel having binary input X = (x_1, x_2) having the probability distribution p_X = (p_{x_1}, p_{x_2}) that is corrupted by a continuous noise to produce a continuous output y \in Y = R. For a given conditional distribution p(y|x_1) = \phi_1(y) and p(y|x_2) = \phi_2(y), one wants to quantize the continuous output y back to the final discrete output Z = (z_1, z_2, ..., z_N) with N \leq 2 such that the mutual information between input and quantized-output I(X; Z) is maximized while the probability of the quantized-output p_Z = (p_{z_1}, p_{z_2}, ..., p_{z_N}) has to satisfy a certain constraint. Consider a new variable r_y=p_{x_1}\phi_1(y)/ (p_{x_1}\phi_1(y)+p_{x_2}\phi_2(y)), we show that the optimal Quantizer has a structure of convex cells in the new variable r_y. Based on the convex cells property of the optimal Quantizers, a fast algorithm is proposed to find the global optimal Quantizer in a polynomial time complexity.
David J. Love - One of the best experts on this subject based on the ideXlab platform.
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advanced Quantizer designs for fdd based fd mimo systems using uniform planar arrays
IEEE Transactions on Signal Processing, 2018Co-Authors: Jiho Song, Junil Choi, David J. LoveAbstract:Massive multiple-input multiple-output (MIMO) systems, which utilize a large number of antennas at the base station, are expected to enhance network throughput by enabling improved multiuser MIMO techniques. To deploy many antennas in reasonable form factors, base stations are expected to employ antenna arrays in both horizontal and vertical dimensions, which is known as full-dimensional (FD) MIMO. The most popular two-dimensional array is the uniform planar array (UPA), where antennas are placed in a grid pattern. To exploit the full benefit of massive MIMO in frequency division duplexing, the downlink channel state information (CSI) should be estimated, quantized, and fed back from the receiver to the transmitter. However, it is difficult to accurately quantize the channel in a computationally efficient manner due to the high dimensionality of the massive MIMO channel. In this paper, we develop both narrow-band and wideband CSI Quantizers for FD-MIMO taking the properties of realistic channels and the UPA into consideration. To improve quantization quality, we focus on not only quantizing dominant radio paths in the channel, but also combining the quantized beams. We also develop a hierarchical beam search approach, which scans both vertical and horizontal domains jointly with moderate computational complexity. Numerical simulations verify that the performance of the proposed Quantizers is better than that of previous CSI quantization techniques.
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advanced Quantizer designs for fd mimo systems using uniform planar arrays
Global Communications Conference, 2016Co-Authors: Jiho Song, Junil Choi, Ji-yun Seol, David J. LoveAbstract:Uniform planar antenna (UPA) structures are expected to become popular for massive multiple-input multiple- output (MIMO) systems because they enable deployment of a large number of antennas in limited space. In frequency division duplexing (FDD) systems, quantized channel state information (CSI) should be fed back from users to base stations to make adaptive transmission possible. However, it is difficult to accurately quantize massive MIMO channels due to their large dimensions. In this paper, we propose practical CSI Quantizers for full-dimension (FD) MIMO systems employing UPAs. We focus on quantizing and combining dominant beams in channels by keeping realistic channel properties and antenna structures into account. To scan a channel space, we also develop a multi-round beam search approach. Numerical results verify that the proposed Quantizers show better quantization performance than the previous channel quantization techniques.
Thuan Nguyen - One of the best experts on this subject based on the ideXlab platform.
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thresholding Quantizer design for mutual information maximization under output constraint
Vehicular Technology Conference, 2020Co-Authors: Thuan Nguyen, Thinh NguyenAbstract:We consider a channel with discrete input ${X}$, a continuous noise that corrupts the input ${X}$ to produce the continuous-valued output ${U}$. A thresholding Quantizer is then used to quantize the continuous-valued output ${U}$ to the final discrete output ${V}$. The goal is to jointly design a thresholding Quantizer that maximizes the mutual information between input and quantized output ${I}$(${X}$;${V}$) while minimizing a pre-specified function of the quantized output $F(p_{V})$. A general dynamic programming algorithm is proposed having the time complexity $O(KNM^{2})$ where N, M and ${K}$ are the sizes of input ${X}$, output ${U}$ and quantized output ${V}$, respectively. Moreover, we show that if $F(p_{V})=\displaystyle \sum _{i=1}^{K}g_{i}(p_{v_{i}})$ where $g_{i}(.)$ is a convex function, $p_{v_{i}} \in p_{V}=\{p_{v}1,\cdots ~p_{v_{K}}\}$ is the probability mass function of output $v_{i}\in V$ and the channel conditional density $p(u|x)$ satisfies the dominated condition (often true in practice), then the existing SMAWK algorithm can be applied to reduce the time complexity of the dynamic programming algorithm from $O(KNM^{2}$) to ${O}$(KNM). Both theoretical and numerical results are provided to verify our contributions.
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on thresholding Quantizer design for mutual information maximization optimal structures and algorithms
Vehicular Technology Conference, 2020Co-Authors: Thuan Nguyen, Thinh NguyenAbstract:Consider a channel having the discrete input X that is corrupted by a continuous noise to produce the continuous-valued output U. A thresholding Quantizer is then used to quantize the continuous-valued output U to the final discrete output V. One wants to design a thresholding Quantizer that maximizes the mutual information between the input and the final quantized output I(X;V). In this paper, the structure of optimal thresholding Quantizer is established that finally results in two efficient algorithms having the time complexities $O(NM+K\log^{2}(NM))$ for finding the local optimal Quantizer and $O(KM\log(NM))$ for finding the global optimal Quantizer where N, M, K are the size of input X, received output U and quantized output V, respectively. Both theoretical and numerical results are provided to verify our contributions.
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optimal Quantizer structure for binary discrete input continuous output channels under an arbitrary quantized output constraint
arXiv: Signal Processing, 2020Co-Authors: Thuan Nguyen, Thinh NguyenAbstract:Given a channel having binary input X = (x_1, x_2) having the probability distribution p_X = (p_{x_1}, p_{x_2}) that is corrupted by a continuous noise to produce a continuous output y \in Y = R. For a given conditional distribution p(y|x_1) = \phi_1(y) and p(y|x_2) = \phi_2(y), one wants to quantize the continuous output y back to the final discrete output Z = (z_1, z_2, ..., z_N) with N \leq 2 such that the mutual information between input and quantized-output I(X; Z) is maximized while the probability of the quantized-output p_Z = (p_{z_1}, p_{z_2}, ..., p_{z_N}) has to satisfy a certain constraint. Consider a new variable r_y=p_{x_1}\phi_1(y)/ (p_{x_1}\phi_1(y)+p_{x_2}\phi_2(y)), we show that the optimal Quantizer has a structure of convex cells in the new variable r_y. Based on the convex cells property of the optimal Quantizers, a fast algorithm is proposed to find the global optimal Quantizer in a polynomial time complexity.
B Atal - One of the best experts on this subject based on the ideXlab platform.
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efficient vector quantization of lpc parameters at 24 bits frame
IEEE Transactions on Speech and Audio Processing, 1993Co-Authors: Kuldip K Paliwal, B AtalAbstract:For low bit rate speech coding applications, it is important to quantize the LPC parameters accurately using as few bits as possible. Though vector Quantizers are more efficient than scalar Quantizers, their use for accurate quantization of linear predictive coding (LPC) information (using 24-26 bits/frame) is impeded by their prohibitively high complexity. A split vector quantization approach is used here to overcome the complexity problem. An LPC vector consisting of 10 line spectral frequencies (LSFs) is divided into two parts, and each part is quantized separately using vector quantization. Using the localized spectral sensitivity property of the LSF parameters, a weighted LSF distance measure is proposed. With this distance measure, it is shown that the split vector Quantizer can quantize LPC information in 24 bits/frame with an average spectral distortion of 1 dB and less than 2% of the frames having spectral distortion greater than 2 dB. The effect of channel errors on the performance of this Quantizer is also investigated and results are reported. >
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efficient vector quantization of lpc parameters at 24 bits frame
International Conference on Acoustics Speech and Signal Processing, 1991Co-Authors: Kuldip K Paliwal, B AtalAbstract:Though vector Quantizers are more efficient than scalar Quantizers, their use for fine quantization of linear predictive coding (LPC) information (using 24-26 b/frame) is impeded due to their prohibitively high complexity. In the present work, a split vector quantization approach is used to overcome the complexity problem. The LPC vector, consisting of ten line spectral frequencies (LSFs), is divided into two parts and each part is quantized separately using vector quantization. Using the localized spectral sensitivity property of the LSF parameters, a weighted LSF distance measure is proposed. Using this distance measure, it is shown that the split vector Quantizer can quantize LPC information in 24 b/frame with 1-dB average spectral distortion and >
Gerhard Kramer - One of the best experts on this subject based on the ideXlab platform.
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low precision a d conversion for maximum information rate in channels with memory
IEEE Transactions on Communications, 2012Co-Authors: Georg Zeitler, Andrew C Singer, Gerhard KramerAbstract:Analog-to-digital converters that maximize the information rate between the quantized channel output sequence and the channel input sequence are designed for discrete-time channels with intersymbol-interference, additive noise, and for independent and identically distributed signaling. Optimized scalar Quantizers with Λ regions achieve the full information rate of log2(Λ) bits per channel use with a transmit alphabet of size Λ at infinite signal-to-noise ratio; these Quantizers, however, are not necessarily uniform Quantizers. Low-precision scalar and two-dimensional analog-to-digital converters are designed at finite signal-to-noise ratio, and an upper bound on the information rate is derived. Simulation results demonstrate the effectiveness of the designed Quantizers over conventional Quantizers. The advantage of the new Quantizers is further emphasized by an example of a channel for which a slicer (with a single threshold at zero) and a carefully optimized channel input with memory fail to achieve a rate of one bit per channel use at high signal-to-noise ratio, in contrast to memoryless binary signaling and an optimized Quantizer.
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low precision a d conversion for maximum information rate in channels with memory
International Symposium on Information Theory, 2011Co-Authors: Georg Zeitler, Andrew C Singer, Gerhard KramerAbstract:We consider the discrete-time channel with intersymbol-interference and additive noise under output analog-to-digital conversion (quantization) at the receiver. The analog-to-digital converter is optimized so as to maximize the information rate between the quantized channel output sequence and the channel input sequence, where the input sequence has independent and identically distributed symbols. An upper bound on the information rate is derived. Simulation results demonstrate the effectiveness of the designed Quantizers over conventional Quantizers at 1-bit/sample precision. The advantage of those Quantizers is further emphasized by an example of a channel for which a simple slicer and a carefully optimized channel input with memory fail to achieve a rate of one bit per channel use at high signal-to-noise ratio, in contrast to memoryless binary signaling and an optimized Quantizer.
