Random Noise Sequence Research Articles

TWO LEVEL IMAGE CRYPTOSYSTEM USING HYBRID-CHAOTIC KEY AND PRNG KEY FOR MULTI-MODALITY DIGITAL IMAGES WITH DISCRETE WAVELET TRANSFORM

In this information age, the need of secure picture transmission is critical. Medical data is hacked in the form of photographs, which costs more in terms of insurance claims. It is vital to safeguard photographs so that unauthorised individuals cannot view them. Chaos-based picture crypto systems are the most well-known of the several types of image crypto systems because their keys are invulnerable to assault or hacking. The chaotic features play a significant role in the development of keys for secure transmission and reception. The discrete wavelet transform (DWT) is a more basic transform that compresses the input image by combining approximation and detailed coefficients. The incorporation of the key in the approximate coefficients of the input image provides an efficient encryption when compared to other image crypto schemes. A two level image encryption is adopted in this work, where one level is achieved using the hybrid-chaotic sequences and the next level is utilizing the pseudo random noise sequence (PRNG) as the keys. A smaller value of variance value is achieved which shows the higher uniformity of pixel values in encrypted images of our proposed two level image cryptography. Also the better performance metrics in terms of entropy, NPCR, and UACI are achieved compared to a single level image encryption. The developed image crypto system is designed and simulated using MATLAB software package. KEYWORDS: two level chaos image cryptosystems, DWT, encryption, hybrid-chaotic maps, and PRNG key generation.

Finite-Time Error Bounds of Biased Stochastic Approximation With Application to TD-Learning

Motivated by the recent success of reinforcement learning algorithms, this paper studies a class of biased stochastic approximation (SA) procedures under a mild “ergodicity-like” assumption on the random noise sequence. Building on a multistep Lyapunov function that looks ahead to several future updates to accommodate the stochastic perturbations (thus gaining control over the bias), we prove a general result on the convergence of the SA iterates, and use it to derive non-asymptotic bounds on the mean-square error in the case of constant stepsizes. This novel viewpoint renders finite-time analysis of biased SA algorithms under a family of stochastic perturbations possible. For direct comparison with prior work, we demonstrate these bounds by applying them to TD-learning with linear function approximation, under the Markov chain observation model. The resultant finite-time error bound for TD-learning is the first of its kind, in the sense that it holds i) for the unmodified versions (i.e., without any modification to the updates) using even nonlinear approximators; as well as for Markov chains ii) under sublinear mixing conditions and iii) starting from any initial distribution, at least one of which has to be violated for existing results to be applicable.

A Modified PRBS: Vertical Stacked LFSR Primitive Polynomial for Secure Data Communication

Linear Feedback Shift Register (LFSR) generates the fault coverage test patterns to compute the target fault of data compression methods. Future Generation wireless communication covers irrespective of complex situation and dense environments marginable throughput to everyone. LFSR widely applied to generate Pseudo Random Noise Sequence, Digital Random Number Generator commonly employed in Cryptography, encoding techniques, Built in Self-Test (BIST) etc. Sequence generated by the LFSR are easily predictable as periodic nature of the sequence. A Modified Pseudo Random Sequence Generator (PRBS) with vertical stacked LFSR (VS-LFSR) is proposed to improve security against predictability nature of PRBS. The primitive polynomial of the nbit LFSR is vertically stacked with top most polynomial and ends with the least polynomial with this flexible of the primitive polynomial are processed and Random sequences are generated. The proposed method generates the random numbers of flexible ranges by appropriately selecting necessity primitive polynomial code in the vertical stack. Compare to conventional LFSR, all zero (0) states also generated in the VS-LFSR, enables the test pattern to have all 2npossible states of n-bit LFSR. With little hardware complexity, periodic pattern of LFSR is further improved with the maximum number of states and result attained maximum number of random outputs as Πn-202n-m - 1.

Implementation of Digital Communication System using Weil Sequence for Efficient Information Transmission

This paper deals with the implementation of a digital communication system using the software LabVIEW, wherein Weil sequences are used for encrypting the information signal and then BPSK (Binary phase shift keying) modulation technique is applied. A real time implementation is also developed using Universal Software Radio Peripheral (USRP 2930). The two Pseudo Random noise sequences namely Legendre and Weil sequences are discussed in this paper. These PN sequences find applications in satellite route frameworks, for example, Indian Regional Navigation Satellite System (IRNSS) and Global Positioning System (GPS). When the PRN sequences are utilized for transmission in GPS satellites, they assist in recognizing various satellites which operate at equivalent frequencies.

Detection of Low‐Frequency Earthquakes in Broadband Random Time Sequences: Are They Independent Events?

AbstractLow‐frequency earthquakes (LFEs) are detected primarily from continuous seismograms using a matched‐filter technique with an impulsive template waveform in a relatively narrow frequency band. However, this method can also detect events from some kinds of random time sequences without clearly isolated events. Here this fact is demonstrated via simple numerical simulations using the synthetic moment accelerations from a model of broadband slow earthquake, the Brownian slow earthquake (BSE) model, and a totally random noise sequence. The matched‐filter technique identifies time sections including relatively isolated pulse‐like fluctuations, as signals in both time sequences, depending on the threshold. These waveforms, stacked relative to the signal timing, show a clear impulse similar to the assumed template in both time sequences, which highlights that we might potentially misinterpret an original time sequence as containing many isolated pulse‐like events. An important difference exists between the BSE model and random noise at frequencies much lower than the analyzed frequency band, with the stacked BSE sequence containing coherent signals at very low frequencies, which are not visible in the noise. Real observations in the Cascadia subduction zone also contain similar coherent signals at low frequencies, suggesting that these LFE signals are coincident with some slow slip. Therefore, so‐called LFEs might potentially be a misinterpretation due to signal processing, or at least they are the tip of the iceberg, with these signals forming a component of a very broadband slow‐earthquake‐like slip process that possibly occurs over sub‐second to multi‐year timescales.

Bitstream radar waveforms for generic single-chip radar

Bitstreams, square wave digital signals, enable flexible radar implementations in modern digital technology. By using bitstreams in place of analog sinusoidal waveforms, we can realize continuous-wave (CW), stepped-frequency CW, frequency-modulated CW, or even pseudo random noise-sequence and pulsed radars, all with a single bit of amplitude resolution. The building blocks are a programable waveform generator, a sweep threshold quantizer, digital delay, and a digital XOR gate as a mixer. This gives us a novel, almost fully digital (requiring only a comparator) system, as previously proposed and which is extended here. The flexibility of the transmitter allows for easy switching between waveforms and the bitstream signal can be processed with single-bit digital gates. Single-bit signals allows for exploration of novel continuous time non-clocked digital implementations to maximize speed and energy efficiency. Mixing frequencies with a digital XOR gate creates harmonics, which are explored for multiple solutions utilizing digital delay. Analytical as well as simulation results are presented. Initial measurements from a 90 nm CMOS chip is provided for the transmitter and the full system, proving the feasibility of a digital future in radar.

A multimodal biometric watermarking system for digital images in redundant discrete wavelet transform

The traditional watermarking algorithms prove the rightful ownership via embedding of independent watermarks like copyright logos, random noise sequences, text etc into the cover images. Coupling biometrics with watermarking evolved as new and secure approach as it embeds user specific biometric traits and thus, narrows down the vulnerability to impostor attacks. A multimodal biometric watermarking system has been proposed in this paper in the redundant discrete wavelet transform(RDWT). Two biometric traits of the user i.e. the iris and facial features are embedded independently into the sub-bands of the RDWT of cover image taking advantage of its translation invariant property and sufficient embedding capacity. The ownership verification accuracy of the proposed system is tested based on the individual biometric traits as well as the fused trait. The accuracy was enhanced while using the fused score for evaluation. The security of the scheme is strengthened with usage of non-linear chaotic maps, randomization via Hessenberg decomposition, Arnold scrambling and multiple secret keys. The robustness of the scheme has been tested against various attacks and the verification accuracy evaluated based on false acceptance rate, false rejection rate, area under curve and equal error rate to validate the efficacy of the proposed scheme.

Influence of the colored noise on determining the period of a torsion pendulum**Project supported by the National Natural Science Foundation of China (Grant Nos. 11175160, 11275075, and 11575160).

Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio Δt/(1/λ) where Δt is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time Δt gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio Δt/(1/λ) is less than 1, the uncertainty remains substantially unchanged.

Probabilistic Estimates for Mixed Model Validation Problems With ${\cal H}_{\infty}$ Type Uncertainties

A mixed deterministic/probabilistic model validation problem is investigated in this technical note, which consists in an additive uncertain model with model uncertainty characterized by the H∞ norm. The data available for validation are time-domain experimental data corrupted by a random noise sequence. Our aim is to compute the probability for such an uncertain model to be validated by the data, and our main results are bounds on this probability that are computable based on the distribution of Chi-square random variables when the noise is a Gaussian variable, and solvable as an LMI problem when only statistical information such as the expectation and covariance of the noise are known.

A new spread spectrum watermarking method using two levels DCT

In this paper, a discrete cosine transform (DCT) based blind watermarking scheme based on spread spectrum communications is proposed. We perform block-based DCT (BDCT) on the host image; then using the DC coefficients of each block, we construct a low-resolution approximation image. We apply BDCT on this approximation image, then watermark is embedded by adding a pseudo random noise sequence into its high frequencies. In detection stage, we extract the approximation image from the watermarked image, then the same pseudo random noise sequence is generated, and its correlation is computed with high frequencies of the watermarked approximation image. In our method, higher robustness is obtained because of embedding the watermark in low frequencies. In addition, higher imperceptibility is gained by scattering the watermark's bit in different blocks. Compared with related works, our method proved to be highly resistant in cases of many common attacks, while preserving high peak signal to noise ratio for the watermarked images.

A robust spread spectrum watermarking method using two levels DCT

In this paper, a discrete cosine transform (DCT) based blind watermarking scheme based on spread spectrum communications is proposed. We perform block-based DCT (BDCT) on the host image; then using the DC coefficients of each block, we construct a low-resolution approximation image. We apply BDCT on this approximation image, then watermark is embedded by adding a pseudo random noise sequence into its high frequencies. In detection stage, we extract the approximation image from the watermarked image, then the same pseudo random noise sequence is generated, and its correlation is computed with high frequencies of the watermarked approximation image. In our method, higher robustness is obtained because of embedding the watermark in low frequencies. In addition, higher imperceptibility is gained by scattering the watermark's bit in different blocks. Compared with related works, our method proved to be highly resistant in cases of many common attacks, while preserving high peak signal to noise ratio for the watermarked images.

Quantification of noisy MRS signals with the Pseudo-Wigner Distribution.

This paper investigates the estimation errors induced by noise in the quantification of damped sinusoids with the Pseudo-Wigner Distribution (PWD). A constant amplitude single frequency noise is first considered. This simple model shows how underestimation or overestimation errors depend on the relative phase between signal and noise for a fixed signal-to-noise ratio (SNR). In a second step, cross-terms and noise amplitude fluctuations are identified as the main sources of discrepancy between the theoretical model and a practical situation where wideband noise is linearly added to a synthetic free induction decay (FID) signal. Cross-terms can be attenuated by band-pass filtering noise or by using a weighting (or smoothing) window in the PWD. An original procedure is then derived to make an on-line and noise-specific estimation of the statistical error in the quantification step. This property of the Wigner distribution is a unique feature in quantitative MRS. Confidence intervals are evaluated for a single damped sinusoid corrupted by eight random noise sequences with three different SNR's, 20, 10 and 5 dB, respectively. They are shown to match the statistical ranges of quantification results obtained with linear regression, until the SNR drops below 10 dB. Estimation accuracy of amplitude and damping constant is finally evaluated from the comparison of the Cramér-Rao (CR) lower bounds with the variance of estimation errors. CR-bounds are shown to be nearly achieved at each SNR.

On Adaptive Stabilization of Time-Varying Stochastic Systems

The basic stability issue of time-varying stochastic systems under adaptive control is studied. A difficulty arising from treating the stochastic case as compared to the deterministic case is the lack of an a priori upper bound on the sample paths of the random noise sequence. A projected gradient algorithm with small stepsize is used, avoiding possible large deviations of the estimates. It is shown that if the unknown parameters vary slowly in some sense, then an adaptive control law can be designed so that the closed-loop system is stable. Issues of performance and robustness are also discussed.

On the Rapid Initial Convergence of Least-Squares Equalizer Adjustment Algorithms

Adjustment algorithms for transversal equalizers derived from least-squares cost functions are known to converge extremely fast. While various simulation results confirming this fact abound in the literature, a theory explaining the fast convergence has been lacking. This paper reports on steps toward such a theory. For some commonly used start-up data sequences it was found that algebraic properties of the sampled signal vectors play a critical role in the transient behavior of these algorithms; namely, successive signal vectors are linearly independent for a large class of transmission channels in the absence of noise. After N iterations (N being the number of taps), the resulting coefficient vector is found to be related to well-known equalizer coefficient vectors. If a single pulse is used as a training signal, the zero forcing equalizer is obtained; if a pseudo random noise sequence, with a period in symbols equal to the number of coefficients is used, the steady-state solution of the cyclic equalization is obtained. Thus, after only N iterations, the least-squares algorithms yield a coefficient vector which is only asymptotically obtainable by gradient techniques.

Statistical design of nonrecursive digital filters

The problem of designing a finite duration impulse response (FIR) digital filter to approximate a desired spectral response is treated in this paper. The philosophy adopted is that for a given FIR filter structure, the filter coefficients can be designed to provide a minimum mean-squared error (MMSE) estimate of a random signal sequence (the design-signal) imbedded in a random noise sequence. By treating the signal and noise covariance functions as design parameters, one can design FIR filters with spectral responses that approximate the power spectral density of the design-signal. For signal processing applications that require some attention to signal fidelity, as well as noise rejection, the MMSE philosophy seems appropriate (as opposed to a maximum signal-to-noise ratio philosophy, for example). Several practical designs are presented that emphasize the simplicity of the design technique and illustrate the selection of design parameters. The designs show quite dramatically that the MMSE design technique can be competitive with existing low-pass and bandpass design techniques. Finally, considerable attention is given to an efficient Toeplitz matrix inversion algorithm that permits rapid inversion of the covariance matrices that arise in the MMSE design. The resulting computation times for the design of high-order filters (N = 128, e.g.) appear to be shorter than computation times for competing algorithms.