Binary Sequence Pairs Research Articles

Towards sustainability assessment through a flexibility index as the condition number

Green chemistry and green engineering, projected in the concept of sustainability, provide inherently safe processes. These safety aspects can be determined indirectly through process controllability and flexibility. Although several indexes have been proposed to measure these parameters, the flexibility index and controllability measured by the condition number are notable. However, these two indicators are usually measured individually, and information inherent to synergies is lost due to the link between profitability and process safety. In the present work we aim to evaluate a quantitative parameter (from the condition number), to simultaneously measure flexibility and controllability of processes to generate a simple measure of sustainability to processes. To demonstrate the relationship of controllability and flexibility, through the condition number, three sequences of solar grade silicon production were explored. In addition, the advantages of using the proposed indicator were demonstrated through a pair of binary and multicomponent reactive distillation sequences. The results clearly showed that the condition number measuring controllability at low frequencies can be related to flexibility. And that this is potentially an indicator that can simultaneously measure controllability and flexibility, and with its use in process design, sustainable processes will be ensured.

Balanced (Almost) Binary Sequence Pairs of Period Q ≡ 1(mod 4) with Optimal Autocorrelation and Cross-Correlation

Balanced (Almost) Binary Sequence Pairs of Period Q ≡ 1(mod 4) with Optimal Autocorrelation and Cross-Correlation

Constructions of Binary Sequence Pairs of Length 5<i>q</i> with Optimal Three-Level Correlation

Constructions of Binary Sequence Pairs of Length 5<i>q</i> with Optimal Three-Level Correlation

LOOK, KNAVE

AbstractWe examine a recursive sequence in which $s_n$ is a literal description of what the binary expansion of the previous term $s_{n-1}$ is not. By adapting a technique of Conway, we determine the limiting behaviour of $\{s_n\}$ and dynamics of a related self-map of $2^{\mathbb {N}}$ . Our main result is the existence and uniqueness of a pair of binary sequences, each the complement-description of the other. We also take every opportunity to make puns.

New Sets of Binary Cross Z-Complementary Sequence Pairs

Spatial modulation (SM) is a special kind of multiple-input multiple-output (MIMO) technique, in which one transmit antenna is activated during each symbol duration. Recently, cross Z-complementary sequence pairs (CZCPs) have been evolved as a new sequence pair to be used for pilot design in SM over frequency-selective channels. CZCPs are sequence pairs having zero autocorrelation sums and zero cross-correlation sums within specific time-shifts. In this letter, we propose systematic constructions of binary CZCPs with new lengths of the form $2^\alpha 10^\beta 26^\gamma ~(\alpha \geq 1)$ , $10^\beta $ , $26^\gamma $ and $10^\beta 26^\gamma $ . We have also proved that for a specific kind of binary CZCP, the magnitude of non-zero aperiodic cross-correlation sums at each time shift outside the zero cross-correlation zone is lower bounded by 4. Finally, we have compared our proposed constructions with the previous constructions.

Similarity analysis of stacking sequences in a SiC nanowire pair grown from the same catalyst nanoparticle using Levenshtein distance.

Stacking faults are easily formed in silicon carbide (SiC) crystals, and this is also the case for SiC nanowires. The stacking faults exercise influences on SiC's properties, therefore it is important to understand their formation mechanism and to control their formation for applications of SiC and its nanowires. In this study, we propose a method for investigating stacking faults' formation mechanism in nanowires and provide its proof of concept. Stacking sequences in a pair of SiC nanowires that were grown from the same metal catalyst nanoparticle were quantified as a pair of binary sequences, and Levenshtein distances between partial sequences extracted from the two sequences were measured to detect similarity between them, and the result was compared with that obtained using a surrogate data of one sequence. The similarity analysis using Levenshtein distances works as a probe for investigating possible influences of some phenomena in the catalyst nanoparticle on the formation of stacking faults. The analysis did not detect a correlation between the two sequences. Although a possibility that the formation of stacking faults in the nanowires were owing to some phenomena in the catalyst nanoparticle cannot be denied, the extrinsic cause in the catalyst nanoparticle was not detected through our analysis in this case.

Almost Difference Set Pairs and Ideal Three-Level Correlation Binary Sequence Pairs

Almost difference set pairs are used in cryptography and coding theory, and a majority of the acknowledged almost difference set pairs are constructed by Chinese remainder theorem, cyclotomy or interleaving. In this paper, through the addition or deletion of elements from difference sets and difference set pairs, we ourselves construct almost difference set pairs and sequences thereof. Further, we obtain the ideal three-level correlation binary sequence pairs with high energy efficiency by some renown difference sets or difference set pairs, e.g. Palay-Hardmard difference sets.

Sets of binary sequences with small total Hamming distances

The sum of the Hamming distances between pairs of binary sequences in a set is considered. It is shown that this sum is at least 8 and 48 for sets of four and eight sequences, respectively, and is at least (n−1)2 for sets of n sequences where n is not equal to 4 or 8. Sets meeting this minimum are explicitly specified.

Enhancing the performance of coherent OTDR systems with polarization diversity complementary codes.

Monitoring the optical phase change in a fiber enables a wide range of applications where fast phase variations are induced by acoustic signals or by vibrations in general. However, the quality of the estimated fiber response strongly depends on the method used to modulate the light sent to the fiber and capture the variations of the optical field. In this paper, we show that distributed optical fiber sensing systems can advantageously exploit techniques from the telecommunication domain, as those used in coherent optical transmission, to enhance their performance in detecting mechanical events, while jointly offering a simpler setup than widespread pulse-cloning or spectral-sweep based schemes with acousto-optic modulators. We periodically capture an overall fiber Jones matrix estimate thanks to a novel probing technique using two mutually orthogonal complementary (Golay) pairs of binary sequences applied simultaneously in phase and quadrature on two orthogonal polarization states. A perfect channel response estimation of the sensor array is achieved, subject to conditions detailed in the paper, thus enhancing the sensitivity and bandwidth of coherent ϕ-OTDR systems. High sensitivity, linear response, and bandwidth coverage up to 18 kHz are demonstrated with a sensor array composed of 10 fiber Bragg gratings (FBGs).

Constructions for almost perfect binary sequence pairs with even length

The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic correlation are required. Several types of almost perfect binary sequence pairs of length T = 2q are constructed, where q is an odd number. These almost perfect binary sequence pairs are based on binary ideal sequence or binary ideal two-level correlation sequence pairs by using Chinese remainder theorem. For these almost perfect binary sequence pairs with good balanced property, their corresponding divisible difference set pairs (DDSPs) are also derived.

Phased unitary Golay pairs, Butson Hadamard matrices and a conjecture of Ito’s

Pairs of complementary binary or quaternary sequences of length v such as Golay pairs, complex Golay pairs and periodic Golay pairs may be used to construct Hadamard matrices and complex Hadamard matrices of order 2v. We generalize these and define unitary Golay pairs and phased unitary Golay pairs of length v with entries in the kth roots of unity for any $$k \ge 2$$ . This leads to a construction of Butson Hadamard matrices of order 2v over the kth roots of unity for even k. Ito conjectured that a central relative (4v, 2, 4v, 2v)-difference set exists in a dicyclic group of order 8v for all $$v \ge 1$$ , and this is known to imply the Hadamard conjecture. With our construction we prove that Ito’s conjecture also implies the stronger complex Hadamard conjecture. As a consequence, with this method we construct a complex Hadamard matrix of order 2v for any v for which Ito’s conjecture is verified, in particular, any $$v \le 46$$ .

New Construction Methods for Binary Sequence Pairs of Period <i>pq</i> with Ideal Two-Level Correlation

New Construction Methods for Binary Sequence Pairs of Period <i>pq</i> with Ideal Two-Level Correlation

New quaternary sequences of even length with optimal auto-correlation

Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two binary sequences of the same length, which are called component sequences. In this paper, using interleaving method, we present several classes of component sequences from twin-prime sequences pairs or GMW sequences pairs given by Tang and Ding in 2010; or two, three or four binary sequences defined by cyclotomic classes of order $4$. Hence we can obtain new classes of quaternary sequences, which are different from known ones, since known component sequences are constructed from a pair of binary sequences with optimal auto-correlation or Sidelnikov sequences.

Constructions of Binary Sequence Pairs of Period $3p$ With Optimal Three-Level Correlation

In this letter, we present a new generalized cyclotomic method over $Z_{3p}$ based on the Chinese remainder theorem and the cyclotomic classes of order 2. Two new families of binary sequence pairs of period $N=3p$ with optimal three-level correlation values are constructed by utilizing these new generalized cyclotomic classes, where $p>3$ is an odd prime. All the constructed binary sequence pairs have optimal correlation values {−3, 1} or {−1, 3}.

Low Correlation Sequences From Linear Combinations of Characters

Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared with a random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation values (for each sequence in the pair) and significantly lower mean square crosscorrelation values. If we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation, and if we define demerit factor as the reciprocal of merit factor, then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of 1. Our constructions provide sequence pairs with a crosscorrelation demerit factor significantly less than 1, and at the same time, the autocorrelation demerit factors of the individual sequences can also be made significantly less than 1 (which also indicates better than average performance). The sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters, such as maximal linear recursive sequences (m-sequences) and Legendre sequences. In this paper, exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters. Data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length.

Binary Sequences With Three-Valued Cross Correlations of Different Lengths

In general, it is hard to find the cross correlation distribution between two sequences. In particular, there are only few cases that the cross correlation is three-valued. In this paper, new pairs of binary sequences with three cross correlation values are presented. These two sequences have different lengths: $2^{2k}-1$ and $3(2^{k}-1)$ , respectively. We determine the cross correlation distribution between these two sequences. We also give the possible correlation values for the shift decimated sequences. The magnitude of cross correlation values is shown to be low. The techniques presented in this paper may be useful to handle other similar cases.

New Families of Binary Sequence Pairs with Three-Level Correlation and Odd Composite Length

New Families of Binary Sequence Pairs with Three-Level Correlation and Odd Composite Length

New constructions of quaternary low correlation zone sequence sets

Sequence sets with low correlation have very important applications in modern communication systems. As in quasi-synchronous code-division multiple access (QS-CDMA) system, sequence sets with low correlation zone (LCZ) perform better than other well-known sequence sets. Furthermore, binary or quaternary sequence sets are preferred because of their easy implementation. In this paper, based on the inverse Gray mapping and special binary sequence pairs, new quaternary LCZ sequence sets were constructed. In the LCZ, the maximum of the nontrivial autocorrelation and crosscorrelation values is 1 which show that the QS-CDMA system used the new sequences sets can control the interference in a very low level.

The Autocorrelation Magnitude of Balanced Binary Sequence Pairs of Prime Period <inline-formula> <tex-math notation="TeX">$N\equiv 1(\bmod\ 4)$</tex-math></inline-formula> With Optimal Cross-Correlation

In this paper, for balanced binary sequence pairs (BBSPs for short) of period N ≡ 1(mod, 4), the optimality of their cross-correlation is determined. Next, a lower bound on the maximal out-of-phase autocorrelation magnitude is established for BBSPs of period N ≡ 1(mod, 4) with optimal cross-correlation. Furthermore, BBSPs with optimal cross-correlation whose maximal out-of-phase autocorrelation magnitude achieves the new lower bound are constructed based on the cyclotomy of order 4. These proposed sequences have a periodic total squared correlation value meeting the Ganapathy-Pados-Karystinos bound, and are therefore an option for use in asynchronous CDMA systems.

Two new classes of binary sequence pairs with three-level cross-correlation

A pair of binary sequences is generalized from the concept of a two-level autocorrelation function of single binary sequence. In this paper, we describe two classes of binary sequence pairs of period $N=2q$, where $q=4f+1$ is an odd prime and $f$ is an even integer. Those classes of binary sequence pairs are based on cyclic almost difference set pairs. They have optimal three-level cross-correlation, and either balanced or almost balanced.