This paper presents the miss-detection probability (MDP) of the Physical Random Access Channel (PRACH) with a short sequence for the 3GPP New Radio specifications in the presence of carrier frequency offset (CFO) in millimeter-wave bands. At a base-station receiver, the correlation of every repetition unit of the PRACH-preamble sequence between the received PRACH signal and the PRACH-preamble sequence candidates is computed using a matched filter in the frequency domain. This is followed by combining the correlations of the repeated PRACH-preamble sequences that correspond to the fast Fourier transform blocks in the time domain. The multiple correlations of the repeated PRACH sequences are combined by coherent combining with in-phase and quadrature components or by combining in squared form in the power domain, followed by the detection of the sequence and received timing of the desired PRACH. This paper first investigates the effect of the repetition of the PRACH-preamble sequence on reducing the MDP for various 3GPP Tapped Delay Line channel models in non-line-of-sight (NLOS) and LOS environments. Next, we establish the best combining method for the correlations of the repeated PRACH sequences from two candidates based on the PRACH MDP for various types of PRACH formats and for various subcarrier spacings (SCSs) from 120 kHz to 960 kHz in the presence of CFO based on extensive simulations. We also show that a wide SCS of up to 960 kHz is effective in reducing the PRACH MDP in the presence of CFO for the frequency stability of a set of user equipment of up to 3 ppm at the carrier frequency of 60 GHz.

Frequency hopping sequences (FHSs) play a significant role in modern frequency hopping spread spectrum communication and radar systems. In terms of application, the aperiodic Hamming correlation (HC) holds greater significance compared to the periodic HC as it directly impacts the communication performance. In addition, it is crucial for each user’s FHS to have a substantial wide-gap (WG) in order to prevent the received signals from interfering with each other. In this letter, we obtain a new bound by extending the aperiodic bound proposed by Peng-Fan and the WG FHS bound introduced by Li-Fan-Yang-Wang. The proposed bound is strict since they can be verified using specific parameters of aperiodic WG FHSs.

In 2004, Ryoh Fuji-Hara et al. (IEEE Trans. Inf. Theory. 50(10):2408-2420, 2004) proposed an open problem of finding a maximum multiplicative subgroup G in ℤn satisfying two conditions: (1) the sum of any two distinct elements in G is nonzero; (2) any difference from G is still a unit in ℤn. The subgroups satisfying Condition (2) is called difference unit group. Difference unit group is related to difference packing, zero-difference balanced function and partitioned difference family, and thus have many applications in coding and communication. Suppose the canonical factorization of n is ∏ki=1 peii. In this letter, we mainly answer the open problem with the result that the maximum cardinality of such a subgroup G is $\frac{d}{2^m}$, where d = gcd(p1 － 1, p2 － 1, ・・・, pk － 1) and m = ν2(d). Also an explicit construction of such a subgroup is introduced.

Recently, trace representation of a class of balanced quaternary sequences of period p from the classical cyclotomic classes was given by Yang et al. (Cryptogr. Commun.,15 (2023): 921-940). In this letter, based on the generalized cyclotomic classes, we define a class of balanced quaternary sequences of period pn, where p = ef + 1 is an odd prime number and satisfies e ≡ 0 (mod 4). Furthermore, we calculate the defining polynomial of these sequences and obtain the formula for determining their trace representations over ℤ4, by which the linear complexity of these sequences over ℤ4 can be determined.

The auto-correlation property of Huffman sequence makes it a good candidate for its application in radar and communication systems. However, high peak-to-average power ratio (PAPR) of Huffman sequence severely limits its application value. In this paper, we propose a novel algorithm to construct Huffman sequences with low PAPR. We have used the roots of the polynomials corresponding to Huffman sequences of length M + 1 to construct Huffman sequences of length 2M + 1, with low PAPR.

In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely LONGEST INCREASING SUBSEQUENCE RECONFIGURATION. We give a polynomial-time algorithm for deciding whether there is a reconfiguration sequence between two longest increasing subsequences in a sequence. This implies that INDEPENDENT SET RECONFIGURATION and TOKEN SLIDING are polynomial-time solvable on permutation graphs, provided that the input two independent sets are largest among all independent sets in the input graph. We also consider a special case, where the underlying permutation graph of an input sequence is bipartite. In this case, we give a polynomial-time algorithm for finding a shortest reconfiguration sequence (if it exists).

The influence of the gate voltage or base pair ratio modulation on the λ-DNA FET performance was examined. The result of the gate voltage modulation indicated that the captured electrons in the guanine base of the λ-DNA molecules greatly influenced the Id-Vd characteristics, and that of the base pair ratio modulation indicated that the tendency of the conductivity was partly clarified by considering the activation energy of holes and electrons and the length and numbers of the serial AT or GC sequences over which the holes or electrons jumped. In addition, the influence of the dimensionality of the DNA molecule on the conductivity was discussed theoretically.

This paper proposes three new information measures for individual sequences and clarifies their properties. Our new information measures are called as the non-overlapping max-entropy, the overlapping smooth max-entropy, and the non-overlapping smooth max-entropy, respectively. These measures are related to the fixed-length coding of individual sequences. We investigate these measures, and show the following three properties: (1) The non-overlapping max-entropy coincides with the topological entropy. (2) The overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the Ziv-entropy. (3) When an individual sequence is drawn from an ergodic source, the overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the entropy rate of the source. Further, we apply these information measures to the fixed-length coding of individual sequences, and propose some new universal coding schemes which are asymptotically optimum.

It is proven that many public-key cryptosystems would be broken by the quantum computer. The knapsack cryptosystem which is based on the subset sum problem has the potential to be a quantum-resistant cryptosystem. Murakami and Kasahara proposed a SOSI trapdoor sequence which is made by combining shifted-odd (SO) and super-increasing (SI) sequence in the modular knapsack cryptosystem. This paper firstly show that the key generation method could not achieve a secure density against the low-density attack. Second, we propose a high-density key generation method and confirmed that the proposed scheme is secure against the low-density attack.

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.

In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F4n to F4. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.

A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.

The frequency hopping sequence plays a crucial role in determining the system's anti-jamming performance, in frequency hopping communication systems. If the adjacent frequency points of FHS can ensure wide-gap, it will better improve the anti-interference capability of the FH communication system. Moreover, if the period of the sequence is expanded, and each frequency point does not repeat in the same sequence, the system's ability to resist electromagnetic interference will be enhanced. And a one-coincidence frequency-hopping sequence set consists of FHSs with maximum Hamming autocorrelation 0 and cross-correlation 1. In this paper, we present two constructions of wide-gap frequency-hopping sequence sets. One construction is a new class of wide-gap one-coincidence FHS set, and the other is a WGFHS set with long period. These two WGFHS sets are optimal with respect to WG-Peng-Fan bound. And each sequence of these WGFHS sets is optimal with respect to WG-Lempel-Greenberger bound.

This paper focuses on a pseudorandom number generator called an NTU sequence for use in cryptography. The generator is defined with an m-sequence and Legendre symbol over an odd characteristic field. Since the previous researches have shown that the generator has maximum complexity; however, its bit distribution property is not balanced. To address this drawback, the author introduces dynamic mapping for the generation process and evaluates the period and some distribution properties in this paper.

Even correlation and odd correlation of sequences are two kinds of measures for their similarities. Both kinds of correlation have important applications in communication and radar. Compared with vast knowledge on sequences with good even correlation, relatively little is known on sequences with preferable odd correlation. In this paper, a generic construction of sequences with low odd correlation is proposed via interleaving technique. Notably, it can generate new sets of binary sequences with optimal odd correlation asymptotically meeting the Sarwate bound.

The calculation of cross-correlation between a sequence with good autocorrelation and its decimated sequence is an interesting problem in the field of sequence design. In this letter, we consider a class of ternary sequences with perfect autocorrelation, proposed by Shedd and Sarwate (IEEE Trans. Inf. Theory, 1979, DOI: 10.1109/TIT.1979.1055998), which is generated based on the cross-correlation between m-sequence and its d-decimation sequence. We calculate the cross-correlation distribution between a certain pair of such ternary perfect sequences and show that the cross-correlation takes three different values.

The low-hit-zone (LHZ) frequency hopping sequence (FHS) sets are widely applicable in quasi-synchronous frequency hopping multiple-access (QS-FHMA) systems. In order to reduce mutual interference (MI) in the zone around the signal origin between different users, we recommend the LHZ FHS set instead of the conventional FHS set. In this letter, we propose a design of LHZ FHS sets via interleaving techniques. The obtained sequences can be confirmed that they are near-optimal in relation to the Peng-Fan-Lee bound.

Human motion prediction has always been an interesting research topic in computer vision and robotics. It means forecasting human movements in the future conditioning on historical 3-dimensional human skeleton sequences. Existing predicting algorithms usually rely on extensive annotated or non-annotated motion capture data and are non-adaptive. This paper addresses the problem of few-frame human motion prediction, in the spirit of the recent progress on manifold learning. More precisely, our approach is based on the insight that achieving an accurate prediction relies on a sufficiently linear expression in the latent space from a few training data in observation space. To accomplish this, we propose Regressive Gaussian Process Latent Variable Model (RGPLVM) that introduces a novel regressive kernel function for the model training. By doing so, our model produces a linear mapping from the training data space to the latent space, while effectively transforming the prediction of human motion in physical space to the linear regression analysis in the latent space equivalent. The comparison with two learning motion prediction approaches (the state-of-the-art meta learning and the classical LSTM-3LR) demonstrate that our GPLVM significantly improves the prediction performance on various of actions in the small-sample size regime.

For any m strings of total length n, we propose an O(mn log n)-time, O(n)-space algorithm that finds a maximal common subsequence of all the strings, in the sense that inserting any character in it no longer yields a common subsequence of them. Such a common subsequence could be treated as indicating a nontrivial common structure we could find in the strings since it is NP-hard to find any longest common subsequence of the strings.

In frequency hopping communication, time delay and Doppler shift incur interference. With the escalating upgrading of complicated interference, in this paper, the time-frequency two-dimensional (TFTD) partial Hamming correlation (PHC) properties of wide-gap frequency-hopping sequences (WGFHSs) with frequency shift are discussed. A bound on the maximum TFTD partial Hamming auto-correlation (PHAC) and two bounds on the maximum TFTD PHC of WGFHSs are got. Li-Fan-Yang bounds are the particular cases of new bounds for frequency shift is zero.