Bitstream Research Articles

An Efficient Algorithm for Designing Long Aperiodic Binary Sequences With Low Auto-Correlation Sidelobes

An Efficient Algorithm for Designing Long Aperiodic Binary Sequences With Low Auto-Correlation Sidelobes

High-Frequency Discrete-Interval Binary Sequence in Asynchronous C-VEP-Based BCI for Visual Fatigue Reduction.

In code-modulated visual evoked potential (c-VEP) based BCI systems, flickering visual stimuli may result in visual fatigue. Thus, we introduced a discrete-interval binary sequence (DIBS) as visual stimulus modulation, with its power spectrum optimized to emphasize high-frequency components (40 Hz-60 Hz). 8 and 17 subjects participated, respectively, in offline and online experiments on a 4-target asynchronous c-VEP-based BCI system designed to realize a high positive predictive value (PPV), a low false positive rate (FPR) during idle states, and a high true positive rate (TPR) in control states, while minimizing visual fatigue level. Two visual stimuli modulations were introduced and compared: a maximum length sequence (m-sequence) and the high-frequency discrete-interval binary sequence (DIBS). The decoding algorithm was compared among the canonical correlation analysis (CCA), the task-related component analysis (TRCA), and two approaches of sub-band component weight calculation (the traditional method and the proportional method) for FBCCA and FBTRCA. In the online experiments, the average PPV, FPR and TPR achieved, respectively [Formula: see text], [Formula: see text], [Formula: see text] with m-sequence, while [Formula: see text], [Formula: see text] and [Formula: see text] with DIBS. Estimated by objective eye-related metrics and a subjective questionnaire, the visual fatigue in DIBS cases is significantly smaller than that in m-sequence cases. In this study, the feasibility of a novel modulation approach for visual fatigue reduction was proved in an asynchronous c-VEP system, while maintaining comparable performance to existing methods, which provides further insights towards enhancing this field's long-term viability and user-friendliness.

A 1-16-Gb/s All-Digital Clock and Data Recovery With a Wideband, High-Linearity Phase Interpolator

An all-digital phase interpolator (PI)-based clock and data recovery (CDR) is proposed in this paper to accommodate any data rate continuously from 1 to 16 Gb/s with quadrature sampling clocks from 4 to 8 GHz. A new low-power two-step PI (TSPI) with high linearity over 4–8 GHz range is presented. The all-digital CDR control loop adopts a multimode phase detection scheme enabling continuous data rate support. The digital architecture not only eliminates the large filtering capacitor but also makes the design more tolerant to process, voltage, and temperature variations. The CDR core occupies 0.088 mm2 in a commercial 65-nm CMOS technology and consumes 73.1 mA at 16 Gb/s from a 1.2 V power supply. The differential nonlinearity of the PI is measured to be within 0.48 LSB. The measurement results show that this CDR can function at the proposed phase detection modes and is able to exceed the synchronous optical networking (SONET) OC-192 jitter tolerance mask at least by 0.2 unit interval at high frequencies (4–100 MHz) with a $2^{31}-1$ pseudorandom binary sequence data pattern at 10 Gb/s and a target bit error rate of $10^{-12}$ .

Interleaved Binary Demodulation Technique for Low-Cost and Fast-Response Visible Light Positioning Using Palindromic Sequences

Recent advancements in visible light positioning (VLP) systems have continuously improved positioning accuracy, extending the application fields in Internet-of-things and factory automation technologies. However, their multiplexing and modulation methods still limit the applicability of VLP systems. Multi-level driving and sensing techniques that use orthogonal frequencies increase the design complexity and are strictly constrained by the bandwidths of the illuminators and sensor devices. Existing binary modulations require additional amendments to the code synchronization. In addition, real-time VLP is fundamentally affected by the distorted signal after orthogonal demultiplexing. Herein, we present a low-cost expansion of VLP that employs binary demodulation in code-division multiplexing. The proposed method utilizes DC-biased binary sequences using the palindromic variant of the Hadamard matrix, which provides perfectly orthogonal sequences while maintaining robustness to signal changes. The proposed demodulation regroups the signal collections of orthogonal sequences in an interleaved manner and determines the source signals via re-modulation. Compared with existing methods, it does not require extra-synchronizing structures and naturally compensates for dynamic sensor signals solely via binary operations. Following its implementation in an FPGA using commercial LEDs and a PIN-PD, we validated that the method achieved 48 dB SNR at a source-to-sensor distance of 10 m. The experiments showed that the proposed method eliminates 45–66% of signal errors and 33–43% of positional displacement during the sensor movements at 800 mm/s. Combined with trilateration, the static positioning error is 0.0158 m on average in 1.31, 0.91, 2.36 m, whereas the standard deviation of the raw position is limited to 0.0016 m.

Constructions of mismatched binary periodic complementary pairs

Two mismatched binary sequences are called a mismatched binary periodic complementary pair (MB-PCP) if the sum of their periodic cross-correlation functions is a delta function. Such a pair is a generalization of the well-known Golay sequence pair, and has applications in the scenario where the mismatched filter is used. Up to now, there are only MB-PCPs of length $ 3q $ with peak value 4 or $ 2q-6 $, where $ q \equiv 3\; (\bmod \,4 ) $ is a prime. The objective of this paper is to construct four families of MB-PCPs of length $ pq $ via the generalized cyclotomy and the Chinese Remainder Theorem, where $ p $ and $ q $ are two different odd primes.

Method for the Simultaneous Generation of Two Nonlinear Pseudo Random Sequences: 5-ary and Binary

Multi-level signals and sequences have become a significant aspect of modern high-speed communication systems. Hence, to ensure the confidentiality and integrity of the transmitted information, advanced methods and devices are necessary to produce strong cryptographic properties for not only binary but also for nonbinary keystreams, which can be used in resource-constrained microcontrollers. The proposed method and apparatus generate both a balanced nonlinear 5-ary pseudo-random sequence and a binary keystream sequence. The nonlinearity is determined by applying shrinking and multiplexing techniques to the generated linear 5-ary pseudo-random sequence and the running zero in its conversion to a binary balanced sequence.

Періодичність цифрової реалізації логістичного рівняння. Частина І

In the paper, the periodicity of pseudo-chaotic implementations in fixed-point calculations is studied using the example of a logistic equation. It was established that with 32-bit represented numbers (three bits - the whole part, 29 bits - the fractional part), the maximum length of the observed cycle is L_(max )< 2^14 iterations, and the space of possible states of the chaotic system after the completion of the transition process is limited S≈2^14 different numbers. Histograms of the duration of transient processes preceding the exit of the trajectory into a cyclic orbit are constructed. It was found that the maximum durations of the transition process do not exceed (2Lmax, 4Lmax). The paper also demonstrates and substantiates the expediency of using a dynamic threshold when forming binary sequences based on chaotic numbers using the threshold method. It is shown that the criterion for the balance of the binary representation of chaotic sequences enables the optimal choice of the number of high-order bits that must be discarded in order to obtain a uniform distribution. Approaches to increase the cyclicity of period of digital implementations of chaotic systems are analyzed. It is shown that the period of the external disturbance must be coordinated with the durations of the cycles observed in the chaotic system. The results of the work show the limitations of chaotic systems, which must be correctly taken into account when using them in cryptography.

DNA Secret Writing With Laplace Transform of Mittag-Leffler Function

In this study, we present a new cryptosystem named Deoxyribose Nucleic Acid (DNA) secret writing with the Laplace transform of the Mittag-Leffler function. The method is proper for encrypting large files. In this technique, we consider the original message as binary sequence. These binary streams corresponding to the plain text is transformed to DNA bases by utilizing DNA encoding, then the DNA codes are transformed to positive integers. We apply the Laplace transform to these numbers which are coefficients of the expansion of the Mittag-Leffler function. To provide multi-stage protection, the outcome coefficients are transformed to binary sequences and other level of encryption with cumulative XOR is applied and equivalent MSBs obtained at every iteration are utilized for building cipher text. Decryption is implemented in the opposite way. We employ monobit test, correlation analysis for measuring the reliability of encryption, and Python programming language to obtain secret message, the plain text, and computations of statistical tests.

An innovative orthogonal matrix based on nonlinear chaotic system for compressive sensing

Compressed sensing exploits the signal’s sparsity by non-uniform sampling to achieve high-quality signal reconstruction at low sampling rates. This work aims to show the efficient performance of chaotic binary orthogonal matrices (CBOM) in compressed sensing. The nonlinear, high dimensional, irregular, and high complexity properties of chaotic systems can provide more diverse and efficient ways of sampling and reconstructing signals. The CBOM construction method proposed in this paper is divided into two steps, in the first step, the real-valued sequence of a one-dimensional chaotic map is binarised using the proposed Threshold-Matching Symbol Algorithm (TMSA) to obtain a chaotic binary sequence (CBS). The i.i.d properties of the CBS were proved using the Perron–Frobenius operator and the properties of the joint probability. The binarized CBS conditionally preserves the pseudo-random of chaotic sequences, as evidenced by the derivation of the well-distribution measure and the k-order correlation measure. In the second step, the binarised sequence CBS was split and orthogonalized to construct CBOM, which satisfies low storage and correlation. We prove that CBOM obeys the Restricted Isometric Condition (RIP). The orthogonalization of the matrix will further reduce matrix column correlation and improve the quality of the reconstruction. Numerical simulation results show that the proposed matrix has considerable sampling efficiency, comparable to Gaussian and partial Hadamard matrices, close to the theoretical limit. Meanwhile, the generation and reconstruction time of the proposed matrix is smaller than other matrices. Our framework covers partial one-dimensional chaotic maps, including Chebyshev, Tent, Logistic, and so on. We can easily apply this paradigm to various fields.

Filtered rays over iterated absolute differences on layers of integers

The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally characterized at the boundary by the notable Proth–Gilbreath Conjecture for prime numbers.We introduce a natural extension of the original triangular arrangement, obtaining a growing hexagonal covering of the plane. This is just the base level of what further becomes an endless discrete helicoidal surface. Although the repeated calculation of higher-order gaps causes the numbers that generate the helicoidal surface to decrease, there is no guarantee, and most often it does not even happen, that the levels of the helicoid have any regularity, at least at the bottom levels.However, we prove that there exists a large and nontrivial class of sequences with the property that their helicoids have all levels coinciding with their base levels. This class includes in particular many ultimately binary sequences with a special header For almost all of these sequences, we additionally show that although the patterns generated by them seem to fall somewhere between ordered and disordered, exhibiting fractal-like and random qualities at the same time, the distribution of zero and non-zero numbers at the base level has uniformity characteristics.Thus, we prove that a multitude of straight lines that traverse the patterns encounter zero and non-zero numbers in almost equal proportions.

Copyright protection of deep image classification models

With the growing number of tasks solved using deep learning methods, the need for protection against unauthorized distribution of the intellectual property such as pre-trained models of deep neural networks is growing. To date, one of the most common ways to protect copyright in the digital space is through embedding digital watermarks. When solving the problem of watermark embedding, an important criterion is the preservation of the model prediction accuracy after introducing the protective information. In this paper, we propose a method for embedding digital watermarks into image classification models based on adding images obtained by superimposing pseudo-holograms on images of the original dataset to the training set. A pseudo-hologram is an image synthesized on the basis of a given binary sequence by arranging pulses for bit encoding in the spectral region. Results of the experimental study show that the proposed method allows one to maintain the classification quality, while also retaining its performance regardless of the architecture of the protected neural network. The conducted series of attacks on protected models show that attempts of an attacker to completely remove the watermark will almost inevitably lead to a significant loss in the model prediction quality. The results of the experiments also include recommendations on the choice of method parameters, such as the size of the trigger and training sets, as well as the length of sequences encoded by pseudo-holograms.

Binary Sequences With Length n and Nonlinear Complexity Not Less Than n/2

Binary Sequences With Length <i>n</i> and Nonlinear Complexity Not Less Than <i>n</i>/2

New Binary Sequences with Low Odd Correlation via Interleaving Technique

New Binary Sequences with Low Odd Correlation via Interleaving Technique

Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions

In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity, correlation measure of order k, expansion complexity and 2-adic complexity. The number-theoretic sequences are the Legendre sequence and the two-prime generator, the Thue-Morse sequence and its sub-sequence along squares, and the prime omega sequences for integers and polynomials.

Improved and Secure LSB2 of Message Steganography

Data steganography is widely used in message protection from being read, and mostly used methods based on LSB and LSB2 methods are not enough secure. In this research paper a modified LSB2 method will be introduced. This method will use a complex complicated key to enhance the data protection degree. The key will be used to rearrange the message stream of bits before data hiding and before data extraction. The key will be sensitive to any minor changes giving a corrupted unreadable message when any change was done in the data extraction phase o data steganography phases. It will be shown that the proposed method very efficient comparing with other methods base on LSB or LSB2 methods. The proposed method will add an improvements to the process of steganography by reducing both the hiding and extracting times. It will be shown that the proposed modified LSB2 method will be used to treat any message short or long using any color image, the size of the used covering image will not affect the method efficiency, so we can use bigger covering images to enhance the quality of the stego image by optimizing the value of MSE and PSNR. The proposed method will be implemented and various analysis will be introduced to prove the improvements achieved by the proposed method.

Markov chain composite likelihood and its application in genetic recombination model

Phylogenetic Trees are critical in human genome research for investigating human evolution and identifying disease-associated genetic markers. New high-throughput genome sequencing technologies raise an urgent need to develop statistical methods that can construct phylogenetic trees from long genome sequences with quick computation speeds, while considering various biological complexities. Though an ancestral mixture model has been proposed [Chen SC, Lindsay BG. Building mixture trees from binary sequence data. Biometrika. 2006;93(4):843–860. doi: 10.1093/biomet/93.4.843] to this end by allowing genetic mutations over generations, another essential evolution factor, genetic recombination, is missed. Therefore, in this paper, we develop a novel genetic recombination model for tree construction and propose to use Markov chain composite likelihood (MCCL) to make model estimation computationally feasible. To further reduce computation complexity, a hierarchical estimator is constructed to estimate unknown ancestral distributions through MCCL. Simulation studies and real data example show that our proposed methods perform well and fast, so have the potential for implementation in long sequence genome data.

Substitution box generator with enhanced cryptographic properties and minimal computation time

With the widespread use of digital devices and the internet, implementing advanced security systems is essential to protect confidential information from cyberattacks and unauthorized access. The substitution box (S-box) is an integral part of security systems that confuses confidential data. Randomized or optimized S-box generators are commonly used in these systems. The former aims to generate highly key-dependent dynamical S-boxes, while the latter generates static S-boxes with optimal cryptographic properties. However, the process of generating S-boxes is computationally expensive, which limits the attainable encryption throughput. This highlights the need to develop new S-box generators that can offer optimal security with minimal computational overhead. We utilized the high resistance of elliptic curves against modern cryptanalysis to propose a novel S-box generator capable of generating both randomized and optimized S-boxes in minimal computation time. The proposed generator has three phases. In the first phase, it generates points on an elliptic curve, converts their coordinates into binary form, and merges them. The second phase diffuses the binary sequences to calculate indices for swapping operations. In the final phase, swapping operations are applied to the initial S-box, resulting in a randomized S-box. For optimizing the S-box, a simplified version of the generator is introduced by omitting swapping operations that reduce nonlinearity in the resulting S-box. The dynamic behavior of the proposed generator is analyzed by proving necessary conditions for outputting distinct S-boxes and ensuring that the resultant S-boxes have a uniform probability distribution. Rigorous security analysis reveals that our generator can output S-boxes with strong cryptographic properties. A detailed comparison indicates that our method is at least 10 times faster than the fastest available randomized generator, while maintaining comparable cryptographic properties. Furthermore, the proposed generator achieves higher nonlinearity of 108 compared to the best available optimized S-box generator with minimal computation time. Our theoretical and computational analyses suggest that our S-box generator is a promising candidate for practical applications that can effectively address the modern security threats and computational time demands. Specifically, we demonstrate the application of our S-box generator by integrating it into an image encryption scheme.

Beat processing in newborn infants cannot be explained by statistical learning based on transition probabilities

Newborn infants have been shown to extract temporal regularities from sound sequences, both in the form of learning regular sequential properties, and extracting periodicity in the input, commonly referred to as a regular pulse or the ‘beat’. However, these two types of regularities are often indistinguishable in isochronous sequences, as both statistical learning and beat perception can be elicited by the regular alternation of accented and unaccented sounds. Here, we manipulated the isochrony of sound sequences in order to disentangle statistical learning from beat perception in sleeping newborn infants in an EEG experiment, as previously done in adults and macaque monkeys. We used a binary accented sequence that induces a beat when presented with isochronous timing, but not when presented with randomly jittered timing. We compared mismatch responses to infrequent deviants falling on either accented or unaccented (i.e., odd and even) positions. Results showed a clear difference between metrical positions in the isochronous sequence, but not in the equivalent jittered sequence. This suggests that beat processing is present in newborns. Despite previous evidence for statistical learning in newborns the effects of this ability were not detected in the jittered condition. These results show that statistical learning by itself does not fully explain beat processing in newborn infants.

Distribution of Patterns of Constrained Length in Binary Sequences

On a finite sequence of binary (0-1) trials we define a random variable enumerating patterns of length subject to certain constraints. For sequences of independent and identically distributed binary trials exact probability mass functions are established in closed forms by means of combinatorial analysis. An explicit expression of the mean value of this random variable is obtained. The results associated with the probability mass functions are extended on sequences of exchangeable binary trials. An application in Information theory concerning counting of a class of run-length-limited binary sequences is provided as a direct byproduct of our study. Illustrative numerical examples exemplify further the results.

The Solution of Fermat’s Two Squares Equation and Its Generalization In Lucas Sequences

As it is well known, there are an infinite number of primes in special forms such as Fermat's two squares form, p=x^2+y^2 or its generalization, p=x^2+y^4, where the unknowns x, y, and p represent integers. The main goal of this paper is to see if these forms still have an infinite number of solutions when the unknowns are derived from sequences with an infinite number of prime numbers in their terms. This paper focuses on the solutions to these forms where the unknowns represent terms in certain binary linear recurrence sequences known as the Lucas sequences of the first and second types.