The central limit theorem (CLT) claims that the standardized sum of a random sequence converges in distribution to a normal random variable as the length tends to infinity. We prove the existence of a family of counterexamples to the CLT for d-tuplewise independent sequences of length n for all d=2,...,n-1. The proof is based on [n, k, d+1] binary linear codes. Our result implies that d-tuplewise independence is too weak to justify the CLT, even if the size d grows linearly in length n.

The paper studies controllability of an aggregate demand response system, i.e., the amount of the change of the total electric consumption in response to the change of the electric price, for real-time pricing (RTP). In order to quantify the controllability, this paper defines the controllability index as the lowest occurrence probability of the total electric consumption when the best possible the electric price is chosen. Then the paper formulates the problem which finds the consumer group maximizing the controllability index. The controllability problem becomes hard to solve as the number of consumers increases. To give a solution of the controllability problem, the article approximates the controllability index by the generalized central limit theorem. Using the approximated controllability index, the controllability problem can be reduced to a problem for solving nonlinear equations. Since the number of variables of the equations is independent of the number of consumers, an approximate solution of the controllability problem is obtained by numerically solving the equations.

Prediction of cross-talk is an important facet of multicore fiber (MCF) design. Several approaches for estimating cross-talk in MCF have been proposed but none are faultless, especially when applied to MCF with heterogeneous cores. We propose a new calculation approach that attempts to solve this problem. In our approach, cross-talk in multicore fibers is estimated by coupled power theory. The coefficients in the coupled power equation are theoretically calculated by the central limit theorem and by quantum mechanical time-dependent perturbations. The results from our calculations agree with those of Monte Carlo simulations of heterogeneous MCFs.

We design M(≥3)-phase spreading sequences of Markov chains optimal in terms of bit error probabilities in asynchronous SSMA (spread spectrum multiple access) communication systems. To this end, we obtain the distributions of the normalized MAI (multiple access interference) for such systems and find a necessary and sufficient condition that the distributions become independent of the phase shifts.

We extend the sliding block code in symbolic dynamics to transform J (≥2) sequences of Markov chains with time delays. Under the assumption that the chains are irreducible and aperiodic, we prove the central limit theorem (CLT) for the normalized sums of extended sliding block codes from J sequences of Markov chains. We apply the theorem to the system analysis of asynchronous spread spectrum multiple access (SSMA) communication systems using spreading sequences of Markov chains. We find that the standard Gaussian approximation (SGA) for estimations of bit error probabilities in such systems is the 0-th order approximation of the evaluation based on the CLT. We also provide a simple theoretical evaluation of bit error probabilities in such systems, which agrees properly with the experimental results even for the systems with small number of users and low length of spreading sequences.

We study asynchronous SSMA communication systems using binary spreading sequences of Markov chains and prove the CLT (central limit theorem) for the empirical distribution of the normalized MAI (multiple-access interference). We also prove that the distribution of the normalized MAI for asynchronous systems can never be Gaussian if chains are irreducible and aperiodic. Based on these results, we propose novel theoretical evaluations of bit error probabilities in such systems based on the CLT and compare these and conventional theoretical estimations based on the SGA (standard Gaussian approximation) with experimental results. Consequently we confirm that the proposed theoretical evaluations based on the CLT agree with the experimental results better than the theoretical evaluations based on the SGA. Accordingly, using the theoretical evaluations based on the CLT, we give the optimum spreading sequences of Markov chains in terms of bit error probabilities.

In this paper, the problem in the distribution of the test statistic of the Discrete Fourier Transform (DFT) test included in SP800-22 released by the National Institute of Standards and Technology (NIST), which causes a very high rate of rejection compared with the significance level, is considered on the basis of the distribution of the spectrum. The statistic of the DFT test, which was supposed to follow the standard normal distribution N(0, 1) according to the central limit theorem, seems to follow the normal distribution N(0.691, 0.5) approximately. The author derived the distribution function of the spectrum, and changed the threshold value from the default value of to the value of 1.7308 , where n is the length of a random number sequence. By this modification, the test statistic becomes to follow the normal distribution N(0, 0.5) approximately. The disagreement between this variance (= 0.5) and that of the standard normal distribution (= 1) can be considered to originate in the dependence of the spectrum. The evidences of the dependence are shown.

Analytical derivation of bit error rates for multi-user coherent chaos-shift-keying (CSK) communication systems are presented in this paper. Nearly exact results are obtained by applying the central limit theorem of statistics to sums of independent variables. Based on χ2 distribution approximations, more viable but still very accurate results decrease complexity of the calculations. The χ2 approach is compared with the widely used Gaussian approximation approach to show its superiority in most cases. Bit error performance bounds for the multi-user CSK system from the approach are deduced as further contributions of this paper. The theoretical results obtained are entirely consistent with a range of simulations.

Noise generation systems are used to generate noise signals with specified characteristics. In recent study, noise generation system using DCT outperforms the conventional noise generation system when a noise model requires complicated PSD(Power Spectral Density) specifications. In this paper, low area and low power structures of non-DCT block in DCT-based noise generation system are proposed. Simulation results show that the low area structure results in area reduction by 61-64% and the low power structure achieves power reduction by 88-89% except DCT blocks.

A flexible noise generation algorithm using DCT is proposed. The proposed method outperforms the conventional methods when a noise model requires complicated PSD (Power Spectral Density) specifications. Also, it is shown that the proposed system can be used for the test of VDSL (Very high-speed Digital Subscriber Line).

We investigate the intrinsic current fluctuations in small Si-MOSFETs via the Monte Carlo device simulation. It is demonstrated that the temporal fluctuation of the drain current in Si-MOSFETs attains a significant fraction of the averaged drain current when the device width is scaled down to the deep sub-µm regime. This is caused by the drastic decrease in the number of channel electrons. This finding holds true whenever the device width is reduced to deep sub-µm, regardless of the channel length. Most importantly, current fluctuation is associated with the quasi-equilibrium thermal noise in the heavily-doped source and drain regions, whereas its magnitude with respect to the averaged drain current is directly related to the number of channel electrons underneath the gate.

We explain three random sampling techniques that are simple but widely applicable for various problems involving huge data sets. The first technique is an immediate application of large deviation bounds. The second and the third ones are sequential sampling or adaptive sampling techniques. We fix one simple problem and explain these techniques by demonstrating algorithms for this problem and discussing their correctness and efficiency.