• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.9
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• pp.2029-2035
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• 2013

In this paper, we presented non-uniform quantization method for LDPC decoder specified in DVB-S2 standard. There are some problems in order to implement LDPC decoder in aspect to algorithm and implementation. In algorithm aspect, because of large number of iterations, LDPC decoding in general give rise to a large number of computation operations, mass power consumption, and decoding delay. Therefore, this paper studies Horizontal Shuffle Scheduling (HSS) algorithm which reduced iteration number without performance loss. In aspect of implementation, there are some solutions to improve the decoding speed, however this paper focused on non-uniform quantization which reduce the quantization bits of LDPC decoder. In simulation results, Decoding throughput of HSS LDPC decoder based on non-uniform quantization is 816Mbps and it improved 12% compared to conventional one.

• Journal of Broadcast Engineering
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• v.19 no.3
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• pp.329-341
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• 2014

Kernel-based mean-shift object tracking has gained more interests nowadays, with the aid of its feasibility of reliable real-time implementation of object tracking. This algorithm calculates the best mean-shift vector based on the color histogram similarity between target model and target candidate models, where the color histograms are usually produced after uniform color-space quantization for the implementation of real-time tracker. However, when the image of target model has a reduced contrast, such uniform quantization produces the histogram model having large values only for a few histogram bins, resulting in a reduced accuracy of similarity comparison. To solve this problem, a non-uniform quantization algorithm has been proposed, but it is hard to apply to real-time tracking applications due to its high complexity. Therefore, this paper proposes a fast non-uniform color-space quantization method using the histogram equalization, providing an adjusted histogram distribution such that the bins of target model histogram have as many meaningful values as possible. Using the proposed method, the number of bins involved in similarity comparison has been increased, resulting in an enhanced accuracy of the proposed mean-shift tracker. Simulations with various test videos demonstrate the proposed algorithm provides similar or better tracking results to the previous non-uniform quantization scheme with significantly reduced computation complexity.

• KIPS Transactions on Computer and Communication Systems
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• v.5 no.9
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• pp.237-246
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• 2016

DIBR (Depth Image Based Rendering) is a multimedia technology that generates the virtual multi-view images using a color image and a depth image, and it is used for creating glasses-less 3-dimensional display contents. This research describes the effect of depth accuracy about the objective quality of DIBR-based multi-view images. It first evaluated the minimum depth quantization bit that enables the minimum distortion so that people cannot recognize the quality degradation. It then presented the comparative analysis of non-uniform domain-division quantization versus regular linear quantization to find out how effectively express the accuracy of the depth information in same quantization levels according to scene properties.

• ETRI Journal
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• v.38 no.3
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• pp.463-468
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• 2016

With the constant increase in network traffic, wireless operators are finding it more challenging to keep network hardware costs to a minimum. At the same time, the energy cost associated with operating a network has increased proportionally. Therefore, the search for higher network capacity is simultaneously accompanied by the search for a cost-efficient network deployment. In this paper, we show that a saving in transmitted signal energy can be achieved at the signal design level by deploying very specific signal processing techniques. Using an orthogonal frequency-division multiplexing signal for Long-Term Evolution networks as an example, we utilize a novel non-uniform companding quantizer to save a transmitted signal energy. Our results show that by using non-uniform quantization it is possible to further optimize 4G wireless networks.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.10a
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• pp.635-636
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• 2013

In this research, a method that quantize the depth information to improve the quality of the intermediate view images when DIBR (Depth Image Based Rendering) is used. This paper specially describes the uniform quantization that divides the depth information equally and non-uniform quantization that allocates more depth information in certain areas to improve the quality of the area.

• ETRI Journal
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• v.32 no.6
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• pp.972-975
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• 2010

In this letter, we consider the lossy coding of a non-uniform binary source based on GF(q)-quantized low-density generator matrix (LDGM) codes with check degree $d_c$=2. By quantizing the GF(q) LDGM codeword, a non-uniform binary codeword can be obtained, which is suitable for direct quantization of the non-uniform binary source. Encoding is performed by reinforced belief propagation, a variant of belief propagation. Simulation results show that the performance of our method is quite close to the theoretic rate-distortion bounds. For example, when the GF(16)-LDGM code with a rate of 0.4 and block-length of 1,500 is used to compress the non-uniform binary source with probability of 1 being 0.23, the distortion is 0.091, which is very close to the optimal theoretical value of 0.074.

• Journal of information and communication convergence engineering
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• v.9 no.2
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• pp.193-196
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• 2011

Transmit antenna selection techniques are prominent since they exploit the spatial selectivity at the transmitter side. In the literature, antenna selection techniques assume full knowledge of the channel state information (CSI). In this paper, we consider that the CSI is not perfectly known at the transmitter; however, a quantized version of the channel coefficients is fed back by the users. We employ the non-uniform Lloyd-Max quantization algorithm which takes into consideration the distribution of the channel coefficients. Simulation results show that the degradation in the BER of the system with imperfect CSI at the transmitter is tolerable, especially when the transmit diversity order is high.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.5056-5078
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• 2018

In this work we propose a compression technique that makes use of linear and perceptually uniform CIE $La^*b^*$ color space in the JPEG image compression framework to improve its performance at lower bitrates. To generate quantization matrices suitable for the linear and perceptually uniform CIE $La^*b^*$ color space, a novel linear Contrast Sensitivity Function (CSF) is used. The compression performance in terms of Compression Ratio (CR) and Peak Signal to Noise Ratio (PSNR), is further improved by utilizing image dependent, variable and non-uniform image sub-blocks generated using a proposed histogram-based merging technique. Experimental results indicate that the proposed linear CSF based quantization technique yields, on an average, 8% increase in CR for the same reconstructed image quality in terms of PSNR as compared to the conventional YCbCr color space. The proposed scheme also outperforms JPEG in terms of CR by an average of 45.01% for the same reconstructed image quality.

• Journal of Broadcast Engineering
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• v.24 no.1
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• pp.164-181
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• 2019

This paper introduces the analysis and development of digital holographic data codec technology to effectively compress hologram data. First, the generation method and data characteristics of the hologram standard data set provided by JPEG Pleno are introduced. We analyze energy compaction according to hologram generation method using discrete wavelet transform and discrete cosine transform. The quantization efficiency according to the hologram generation method is analyzed by applying uniform quantization and non-uniform quantization. We propose a transformation method quantization method suitable for hologram generation method through transform and quantization experiments. Finally, holograms are compressed using standard compression codecs such as JPEG, JPEG2000, AVC/H.264 and HEVC/H.265 and the results are analyzed.