A complexity measure for families of binary sequences

We present an integrable solution for the detection of defective sensor elements using sigma-delta-(/spl Sigma//spl Delta/)-modulation and a matched filter. The sensor element is stimulated using a pseudo random binary sequence (PRBS). The sensor signal is read out and the analog output is digitized using a /spl Sigma//spl Delta/-modulator. The binary pulse density stream of the /spl Sigma//spl Delta/-modulator is the output of the sensor system and thus should ideally contain the PRBS. A matched filter has the task of detecting the pseudo random sequence in the pulse density stream and its sampled output is compared to a threshold thus making it possible to judge the functionality of the sensor element. By evaluating the magnitude of the matched filter output it is also possible to measure the sensor sensitivity. We present a discrete solution of this method, but an integrated chip using a standard 1.2 /spl mu/m CMOS process has been designed and is being fabricated.

Binary sequences with good autocorrelation have many applications in raging systems, spread spectrum communication systems, multi-terminal system identification, code division multiple access communications systems, and stream ciphers. Magma is a large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatory. We design the system to compare and analysis the binary pseudorandom sequences. It is easy to analysis the existing binary sequence and new construction. And it can compare the performance of different sequences and draw the figure. We implement it on the C# and SQL database system.

The purpose of this study was to compare the test-retest reliability of oxygen uptake (VO2) kinetics with carbon dioxide output (VCO2) kinetics using a pseudo random binary sequence (PRBS) exercise test. A reliable test of gas exchange kinetics would have the potential of being applied as a sports fitness test. Ten healthy male subjects agreed to participate in the study and all subjects completed two identical PRBS exercise tests (test 1 and test 2), separated by a 30 min period of inactivity. Three consecutive 300 s PRBS cycles were completed in each test with 20 s exercise intensity changes between 25 and 85 W using an electrically braked cycle ergometer. Fourier analysis was computed for frequencies 3.3, 6.7 and 10 mHz. Statistical analysis by two-way ANOVA with repeated measures did not reveal significant differences between test 1 and test 2 for either VO2 kinetics or VCO2 kinetics. Static gain of VO2 for test 1 [9.11 (SD 0.59) ml.min-1.W-1] and test 2 [9.23 (SD 0.64) ml.min-1.W-1] did not differ significantly between tests. The 95% limits of agreement for VCO2 kinetics displayed increased variability in comparison to VO2 kinetics at each frequency of amplitude ratio and phase shift. Systematic bias ranged between 0% and 4%, except at frequency 10 mHz of VCO2 kinetics phase shift which showed a 10% bias for slower VO2 kinetics in test 2. It is possible that the increased variability of VCO2 kinetics compared to VO2 kinetics might be attributable to a lower signal to noise ratio in VCO2 kinetics, variations in ventilation or the storage mechanisms of CO2. The lower variability of VO2 kinetics compared with VCO2 kinetics suggests that the PRBS test of VO2 kinetics has the greater potential for further development as an indicator of aerobic fitness.

In this paper we give a new family of elliptic curve pseudorandom binary sequences, and study the well-distribution, correlation, linear complexity, collision and avalanche effect of the family of sequences, by using the estimate of exponential sums over elliptic curves.

In this paper, a new family of binary sequences of period 2n-1 with low correlation is proposed for integer n = em and even m. The new family has family size 2n + 1 and maximum nontrivial correlation 2n+e/2 + 1 and 2n+e-1/2 + 1 for even and odd e respectively. Especially, for n = 2m and 3m, we obtain a new family of binary sequences with maximum nontrivial correlation 2n/2 + 1 + 1, and the obtained family is one of the binary families with best correlation among the known families with family size no less than their period 2n-1 for even n. Moreover, the correlation distribution of the new family is also determined.

The paper describes a class of nonlinear binary sequences which possess cyclic and multiple-state occurrence properties. Such sequences are null or cyclic, preceded by either a zero or finite transient phase.The sequences are realised by controlling the individual transfer between successive stages of a primaryregister by the states of a corrupting-register, which itself may be cyclic in behaviour.By considering a specific example the paper demonstrates that a pseudo-random binary sequence may be modified in this way. Two practical applications are discussed, namely the generation of vehicle travelling times used in traffic simulation studies of signalised intersections, and digital waveform synthesis

The investigation of patients who are unable to fixate the pattern visual stimulus generally requires the use of diffuse flash stimulation to elicit the visual evoked response. However, by comparison with pattern, flash stimulation has proved relatively insensitive in identifying lesions of the visual pathway. We investigated a more complex method of flash stimulation. A pseudorandom binary sequence has been used to generate the diffuse visual evoked response stimulus. The pseudorandom binary sequence, rather than producing a single flash, switches in a pseudorandom fashion between two levels of illumination. The result is a diffuse visual stimulus approximating band-limited white noise. The series is periodic, enabling signal averaging to be performed. By applying the methods of random signal analysis, the impulse or transient response of the visual pathway can be determined. Our normal pseudo-random binary sequence visual evoked response impulse function, derived from 29 normal subjects, had the morphologic characteristics of the conventional flash visual evoked response and a major positive component (P100), whose latency mean and standard deviation closely matched that of our normative pattern visual evoked response. However, the P100 amplitude standard deviation was significantly greater than that produced by conventional pattern and flash stimulation. We investigated 140 patients by means of pattern, flash and pseudorandom binary sequence stimulation. The pseudorandom binary sequence visual evoked response proved to be almost 12 times more effective than flash visual evoked response in detecting lesions of the visual system.

With the increasing reliance on technology, it has become crucial to secure every aspect of online information where pseudo random binary sequences (PRBS) can play an important role in today’s world of Internet. PRBS work in the fundamental mathematics behind the security of different protocols and cryptographic applications. This paper proposes a new PRBS namely MK (Mamun, Kumu) sequence for security applications. Proposed sequence is generated by primitive polynomial, cyclic difference set in elements of the field and binarized by quadratic residue (QR) and quadratic nonresidue (QNR). Introduction of cyclic difference set makes a special contribution to randomness of proposed sequence while QR/QNR-based binarization ensures uniformity of zeros and ones in sequence. Besides, proposed sequence has maximum cycle length and high linear complexity which are required properties for sequences to be used in security applications. Several experiments are conducted to verify randomness and results are presented in support of robustness of the proposed MK sequence. The randomness of proposed sequence is evaluated by popular statistical test suite, i.e., NIST STS 800-22 package. The test results confirmed that the proposed sequence is not affected by approximations of any kind and successfully passed all statistical tests defined in NIST STS 800-22 suite. Finally, the efficiency of proposed MK sequence is verified by comparing with some popular sequences in terms of uniformity in bit pattern distribution and linear complexity for sequences of different length. The experimental results validate that the proposed sequence has superior cryptographic properties than existing ones.

Applications like fuel cells, batteries or food analysis are typical fields of interest for electrical impedance spectroscopy (EIS).Another field with promising results are EIS measurements in semiconductor (sc) gas sensor applications [1].Due to their high sensitivity and low cost, sc gas sensors are ideally suited for different applications, especially in the field of safety and security.The major drawbacks of sc gas sensors, i.e. poor selectivity and sensor baseline drift, can be overcome by using temperature cycled operation (TCO) with DC measurement [2] or EIS, both in combination with intelligent signal processing.Currently, EIS for sc gas sensors is only possible in laboratory environments using commercial impedance analyzers, which are characterized by high cost, poor mobility and long acquisition time.However, for efficient development of application specific sc gas sensor systems and/or a self-monitoring strategy [3] extensive field tests are necessary.Therefore, a new hardware concept for EIS of sc gas sensors based on FPGA-technology was developed.This concept also allows a combination of EIS with TCO for the first time.Additionally, state-of-the-art feature extraction methods are applied to sc gas sensor data and new features were tested [4]. MotivationDue to their high sensitivity and low cost, semiconductor gas sensors are ideally suited for safety and security applications like fire and leakage detection [5,6].The major drawbacks of this type of sensor are the poor selectivity, the sensor baseline drift and sensor poisoning.Especially for safety and security applications these drawbacks must be overcome to allow a proper function of the system.Temperature cycled operation (TCO) and electrical impedance spectroscopy (EIS) -both in combination with intelligent signal processing -are the main approaches for improving both selectivity and stability.In TCO mode the sensor temperature is changed periodically [2] and the DC resistance of the sensor is read-out continually during this cycle.For EIS the sensor temperature is usually kept constant and the sensor impedance is measured over a wide frequency range, e.g. during a frequency sweep [1,7,8].To detect a sensor malfunction due to sensor poisoning a self-monitoring strategy can be realized by combining TCO und EIS (fig. 1) [3].This strategy is based on redundant information from both modes which are evaluated separately and comparing both results.Additional information can be used for selectivity enhancement.

Objective: Design of quadriphase codes with superior merit factor in basically a nonlinear multivariable optimization problem. Quadriphase transformation is applied to low side lobes in bi phase generation of binary sequence. In order to provide real time hardware for identification and generation of quadriphase pulse compression sequences. Methods/ Statistical Analysis: An efficient VLSI architecture has been proposed. The objectives to achieve high main lobe and low side lobes by poly phase codes. Findings: Initially pulse compression techniques are applied followed by binary quadriphase transformation. By applying a transformation to the biphase code using of sub pulses consequently results in the generation of codes. Near constant envelopes are created. Improvements/Applications: The systematic quadriphase sequences are useful for application to radar and continuation. There is scope for further development of merit factor. Keywords: Merit Factor (MF), Pseudo Random Binary Sequence (PRBS) Generator, Pulse Compression, Quadriphase Sequence

This paper presents a method for converting the full waveform electromagnetic response excited by the pseudo-random binary sequences (PRBS) into subsurface resistivity cross section, based on the recovery of the transient electromagnetic diffusion field. The impulse response of the earth is extracted from the full waveform data efficiently using the Wiener-Hopf equation. Then, the backward accumulation is used to obtain the step off response from the extracted earth impulse response. An OCCAM inversion routine, which incorporates the band limitation of the derived transient, is adopted to produce the geoelectric models. Finally, the method was applied to the experimental field data set, and the consistency between the recovered models and the geological condition verifies the validity of this method.

In this paper, for odd n and any k with gcd(n, k) = 1, new binary sequence families Sk of period 2n-1 are constructed. These families have maximum correlation $1+2^{n+3\\over 2}$, family size 22n+2n+1 and maximum linear span $n(n+1)\\over 2$. The correlation distribution of Sk is completely determined as well. Compared with the modified Gold codes with the same family size, the proposed families have the same period and correlation properties, but larger linear span. As good candidates with low correlation and large family size, the new families contain the Gold sequences and the Gold-like sequences. Furthermore, Sk includes a subfamily $\\mathcal{S}^k_1$ which has the same period, correlation distribution, family size and linear span as the family So(2) recently constructed by Yu and Gong. In particular, when k=1, $\\mathcal{S}^k_1$ is exactly So(2).

A new family of binary sequences with low 4-value autocorrelation of length 4p based on cyclotomic classes of order four is proposed, as well as the linear complexity and 2-adic complexity of these sequences are determined. The results show that the linear complexity of s is LC(s) = 4p−1, and the 2-adic complexity of s is Φ2s = log2 ((24p−1)/3), both of which are greater than half of the period. The sequences are safe enough to resist Berlekamp–Massey algorithm attacks and rational approximation algorithm attacks, which indicate that they are good sequences in communication.

The Gold sequence family [1] is one of the oldest and most well‐known families of binary sequences with optimal correlation properties. This chapter focuses on the binary Gold sequences and their relatives called Gold‐like sequences. Mathematical representations as well as the family sizes and maximum correlation magnitudes of these sequences are reviewed.

Based on the cyclotomy classes of extension fields, a family of binary cyclotomic sequences are constructed and their pseudorandom measures (i.e., the well-distribution measure and the correlation measure of order k) are estimated using certain exponential sums. A lower bound on the linear complexity profile is also presented in terms of the correlation measure.