Revisiting Central Limit Theorem: Accurate Gaussian Random Number Generation in VLSI

Malik, Jamshaid Sarwar; Hemani, Ahmed; Malik, Jameel Nawaz; Silmane, Ben; Gohar, N. D.

doi:10.1109/tvlsi.2014.2322573

Cited by 10 publications

(5 citation statements)

References 24 publications

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“…The point of the theorem is that no matter the original distribution, the mean of a large enough sample will have a nearly normal distribution [ 13 ]. Many areas include CLT in its applications, such as computer science, psychology, political science, actuarial science [ 14 ], and engineering, economy, law, and probabilistic reasoning [ 15 , 16 , 17 ].…”

Section: Introductionmentioning

confidence: 99%

Accuracy and Precision Improvement of Temperature Measurement Using Statistical Analysis/Central Limit Theorem

Belo

Soares

Filho

et al. 2023

Sensors

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This paper describes a method for increasing the accuracy and precision of temperature measurements of a liquid based on the central limit theorem. A thermometer immersed in a liquid exhibits a response with determined accuracy and precision. This measurement is integrated with an instrumentation and control system that imposes the behavioral conditions of the central limit theorem (CLT). The oversampling method exhibited an increasing measurement resolution. Through periodic sampling of large groups, an increase in the accuracy and formula of the increase in precision is developed. A measurement group sequencing algorithm and experimental system were developed to obtain the results of this system. Hundreds of thousands of experimental results are obtained and seem to demonstrate the proposed idea’s validity.

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Section: Introductionmentioning

confidence: 99%

Accuracy and Precision Improvement of Temperature Measurement Using Statistical Analysis/Central Limit Theorem

Belo

Soares

Filho

et al. 2023

Sensors

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“…Therefore, area-efficient GNG architecture that generates accurate noise samples fast is required in developing such an emulation system. Conventional algorithms used in hardware GNGs are the Box-Muller (BM) [5]- [10], inversion [11], [12], Wallace [13] and central limit theorem (CLT) [14]- [16] methods. The BM method generates a pair of Gaussian random numbers independently by transforming a uniformly distributed random number [5]- [10].…”

Section: Introductionmentioning

confidence: 99%

“…As the accuracy of Gaussian random samples is heavily affected by the functions, the hardware GNG has utilized many block RAMs and multipliers to increase the accuracy. The CLT states that the sum of a sufficiently large number of independent uniform random numbers follows Gaussian distribution [14]- [16], meaning that a large number of samples should be added to generate a Gaussian random number. A finite number of additions result in errors compared to ideal Gaussian noise, and thus compensation is needed as presented in [16].…”

Section: Introductionmentioning

confidence: 99%

“…The CLT states that the sum of a sufficiently large number of independent uniform random numbers follows Gaussian distribution [14]- [16], meaning that a large number of samples should be added to generate a Gaussian random number. A finite number of additions result in errors compared to ideal Gaussian noise, and thus compensation is needed as presented in [16]. To increase the accuracy of noise, furthermore, the CLT is combined with the BM method [5].…”

Section: Introductionmentioning

confidence: 99%

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Area-Efficient Approach for Generating Quantized Gaussian Noise

Choi

Jung

Park

2016

IEEE Trans. Circuits Syst. I

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This paper presents an efficient method to generate quantized Gaussian noise. The proposed method is derived based on the fact that any signal received at a digital system should be quantized to several bits. On the contrary to the previous works that have focused on the precision of noise, the quantization process is taken into account in generating noise samples. As a result, the resultant bit-width of noise is significantly reduced and the computation complexity of generating Gaussian noise is also reduced by simplifying the interpolation process. The proposed architecture based on the inversion method is implemented on field-programmable gate array (FPGA) devices. Compared to the previous architecture based on the conventional inversion method, the proposed approach improves the throughput per slice by 460% while maintaining the statistical properties of Gaussian noise. Index Terms-Additive white Gaussian noise (AWGN), Gaussian noise, Gaussian noise generator (GNG), inversion method, quantized Gaussian noise.1549-8328

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“…If N is small, an approximation error is caused by the CLT[32]. However, the approximation error is negligible because the second term is relatively small for a large G value.…”

mentioning

confidence: 99%

Novel Packet Arrival Rate Estimator for LTE-Based Random Access

Jang

Moon

2022

IEEE Access

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Owing to the increasing demand for machine-to-machine (M2M) communications, random access is being intensively researched. With M2M communications, numerous devices can transmit random access packets simultaneously. This results in congestion in random access and degrades its performance. To control congestion scenarios, the packet arrival rate of random access must be obtained with a short delay and high accuracy. In this paper, a new estimator is proposed to obtain the packet arrival rate in a longterm evolution system. The packet arrival rate of random access is computed using the estimated number of random access packets in each slot. Using the proposed estimator, the number of random access packets is estimated based on the received energy vector for sequences and the number of detected sequences. Analysis and simulations show that the proposed estimator presents better performance for determining the number of random access packets than conventional approaches.INDEX TERMS M2M communications, random access, arrival rate, estimation, congestion.

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Revisiting Central Limit Theorem: Accurate Gaussian Random Number Generation in VLSI

Cited by 10 publications

References 24 publications

Accuracy and Precision Improvement of Temperature Measurement Using Statistical Analysis/Central Limit Theorem

Accuracy and Precision Improvement of Temperature Measurement Using Statistical Analysis/Central Limit Theorem

Area-Efficient Approach for Generating Quantized Gaussian Noise

Novel Packet Arrival Rate Estimator for LTE-Based Random Access

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