Latin squares are a classical and well-studied topic of discrete mathematics, and recently Takeuti and Adachi (IACR ePrint, 2023) proposed (2, n)-threshold secret sharing based on mutually orthogonal Latin squares (MOLS). Hence efficient constructions of as large sets of MOLS as possible are also important from practical viewpoints. In this letter, we determine the maximum number of MOLS among a known class of Latin squares defined by weighted sums. We also mention some known property of Latin squares interpreted via the relation to secret sharing and a connection of Takeuti-Adachi’s scheme to Shamir’s secret sharing scheme.

Data resource sharing can guarantee the reliable and safe operation of distribution power grid. However, it faces the challenges of low security and high delay in the sharing process. Consortium blockchain can ensure the security and efficiency of data resource sharing, but it still faces problems such as arbitrary master node selection and high consensus delay. In this paper, we propose an improved practical Byzantine fault tolerance (PBFT) consensus algorithm based on intelligent consensus node selection to realize high-security and real-time data resource sharing for distribution power grid. Firstly, a blockchain-based data resource sharing model is constructed to realize secure data resource storage by combining the consortium blockchain and interplanetary file system (IPFS). Then, the improved PBFT consensus algorithm is proposed to optimize the consensus node selection based on the upper confidence bound of node performance. It prevents Byzantine nodes from participating in the consensus process, reduces the consensus delay, and improves the security of data resource sharing. The simulation results verify the effectiveness of the proposed algorithm.

We present a time-efficient lower bound κ on the number of gates in Toffoli-based reversible circuits that represent a given reversible logic function. For the characteristic vector s of a reversible logic function, κ(s) closely approximates σ-lb(s), which is known as a relatively efficient lower bound in respect of evaluation time and tightness. The primary contribution of this paper is that κ enables fast computation while maintaining a tightness of the lower bound, approximately equal to σ-lb. We prove that the discrepancy between κ(s) and σ-lb(s) is at most one only, by providing upper and lower bounds on σ-lb in terms of κ. Subsequently, we show that κ can be calculated more efficiently than σ-lb. An algorithm for κ(s) with a complexity of 𝓞(n) is presented, where n is the dimension of s. Experimental results comparing κ and σ-lb are also given. The results demonstrate that the two lower bounds are equal for most reversible functions, and that the calculation of κ is significantly faster than σ-lb by several orders of magnitude.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let C(t,e) denote the cyclic code with two nonzero αt and αe, where α is a generator of 𝔽*3m. In this letter, we investigate the ternary cyclic codes with parameters [3m - 1, 3m - 1 - 2m, 4] based on some results proposed by Ding and Helleseth in 2013. Two new classes of optimal ternary cyclic codes C(t,e) are presented by choosing the proper t and e and determining the solutions of certain equations over 𝔽3m.

In cyber-physical systems (CPSs) that interact between physical and information components, there are many sensors that are connected through a communication network. In such cases, the reduction of communication costs is important. Event-triggered control that the control input is updated only when the measured value is widely changed is well known as one of the control methods of CPSs. In this paper, we propose a design method of output feedback controllers with decentralized event-triggering mechanisms, where the notion of uniformly ultimate boundedness is utilized as a control specification. Using this notion, we can guarantee that the state stays within a certain set containing the origin after a certain time, which depends on the initial state. As a result, the number of times that the event occurs can be decreased. First, the design problem is formulated. Next, this problem is reduced to a BMI (bilinear matrix inequality) optimization problem, which can be solved by solving multiple LMI (linear matrix inequality) optimization problems. Finally, the effectiveness of the proposed method is presented by a numerical example.

In this study, we consider the data compression with side information available at both the encoder and the decoder. The information source is assigned to a variable-length code that does not have to satisfy the prefix-free constraints. We define several classes of codes whose codeword lengths and error probabilities satisfy worse-case criteria in terms of side-information. As a main result, we investigate the exact first-order asymptotics with second-order bounds scaled as Θ(√n) as blocklength n increases under the regime of nonvanishing error probabilities. To get this result, we also derive its one-shot bounds by employing the cutoff operation.

In this work we propose a Bayesian version of the Nagaoka-Hayashi bound when estimating a parametric family of quantum states. This lower bound is a generalization of a recently proposed bound for point estimation to Bayesian estimation. We then show that the proposed lower bound can be efficiently computed as a semidefinite programming problem. As a lower bound, we also derive a Bayesian version of the Holevo-type bound from the Bayesian Nagaoka-Hayashi bound. Lastly, we prove that the new lower bound is tighter than the Bayesian quantum logarithmic derivative bounds.

For an [n, k, d] (r, δ)-locally repairable codes ((r, δ)-LRCs), its minimum distance d satisfies the Singleton-like bound. The construction of optimal (r, δ)-LRC, attaining this Singleton-like bound, is an important research problem in recent years for thier applications in distributed storage systems. In this letter, we use Reed-Solomon codes to construct two classes of optimal (r, δ)-LRCs. The optimal LRCs are given by the evaluations of multiple polynomials of degree at most r - 1 at some points in Fq. The first class gives the [(r + δ - 1)t, rt - s, δ + s] optimal (r, δ)-LRC over Fq provided that r + δ + s - 1≤q, s≤δ, s

Orthogonal frequency division multiplexing (OFDM) is very sensitive to the carrier frequency offset (CFO). The CFO estimation precision heavily makes impacts on the OFDM performance. In this paper, a new Bayesian learning-assisted joint CFO tracking and channel impulse response estimation is proposed. The proposed algorithm is modified from a Bayesian learning-assisted estimation (BLAE) algorithm in the literature. The BLAE is expectation-maximization (EM)-based and displays the estimator mean square error (MSE) lower than the Cramer-Rao bound (CRB) when the CFO value is near zero. However, its MSE value may increase quickly as the CFO value goes away from zero. Hence, the CFO estimator of the BLAE is replaced to solve the problem. Originally, the design criterion of the single-time-sample (STS) CFO estimator in the literature is maximum likelihood (ML)-based. Its MSE performance can reach the CRB. Also, its CFO estimation range can reach the widest range required for a CFO tracking estimator. For a CFO normalized by the sub-carrier spacing, the widest tracking range required is from -0.5 to +0.5. Here, we apply the STS CFO estimator design method to the EM-based Bayesian learning framework. The resultant Bayesian learning-assisted STS algorithm displays the MSE performance lower than the CRB, and its CFO estimation range is between ±0.5. With such a Bayesian learning design criterion, the additional channel noise power and power delay profile must be estimated, as compared with the ML-based design criterion. With the additional channel statistical information, the derived algorithm presents the MSE performance better than the CRB. Two frequency-selective channels are adopted for computer simulations. One has fixed tap weights, and the other is Rayleigh fading. Comparisons with the most related algorithms are also been provided.

We show that every polynomial threshold function that sign-represents the ODD-MAXBITn function has total absolute weight 2Ω(n1/3). The bound is tight up to a logarithmic factor in the exponent.

Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.

In this letter, we consider the problem of joint selection of transmitters and receivers in a distributed multi-input multi-output radar network for localization. Different from previous works, we consider a more mathematically challenging but generalized situation that the transmitting signals are not perfectly orthogonal. Taking Cramér Rao lower bound as performance metric, we propose a scheme of joint selection of transmitters and receivers (JSTR) aiming at optimizing the localization performance under limited number of nodes. We propose a bi-convex relaxation to replace the resultant NP hard non-convex problem. Using the bi-convexity, the surrogate problem can be efficiently resolved by nonlinear alternating direction method of multipliers. Simulation results reveal that the proposed algorithm has very close performance compared with the computationally intensive but global optimal exhaustive search method.

In this paper, the spurious modes and quality-factor (Q) values of the one-port dual-mode AlN lamb-wave resonators at 500-1000 MHz were studied by theoretical analysis and experimental verification. Through finite element analysis, we found that optimizing the width of the lateral reflection boundary at both ends of the resonator to reach the quarter wavelength (λ/4), which can improve its spectral purity and shift its resonant frequency. The designed resonators were micro-fabricated by using lithography processes on a 6-inch wafer. The measured results show that the spurious mode can be converted and dissipated, splitting into several longitudinal modes by optimizing the width of the lateral reflection boundary, which are consistent well with the theoretical analysis. Similarly, optimizing the interdigital transducer (IDT) width and number of IDT fingers can also suppress the resonator's spurious modes. In addition, it is found that there is no significant difference in the Qs value for the two modes of the dual-mode resonator with the narrow anchor and full anchor. The acoustic wave leaked from the anchor into the substrate produces a small displacement, and the energy is limited in the resonator. Compared to the resonator with Au IDTs, the resonator with Al IDTs can achieve a higher Q value due to its lower thermo-elastic damping loss. The measured results show the optimized dual-mode lamb-wave resonator can obtain Qs value of 2946.3 and 2881.4 at 730.6 MHz and 859.5 MHz, Qp values of 632.5 and 1407.6, effective electromechanical coupling coefficient (k2eff) of 0.73% and 0.11% respectively, and has excellent spectral purity simultaneously.

This paper considers tracking of a non-cooperative emitter based on a single sensor. To this end, the direct target motion analysis (DTMA) approach, where the target state is straightforwardly achieved from the received signal, is exploited. In order to achieve observability, the sensor has to perform a maneuver relative to the emitter. By suitably building an approximated likelihood function, the unscented Kalman filter (UKF), which is able to work under high nonlinearity of the measurement model, is adopted to recursively estimate the target state. Besides, the posterior Cramér-Rao bound (PCRB) of DTMA, which can be used as performance benchmark, is also achieved. The effectiveness of proposed method is verified via simulation experiments.

Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q2+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.

A new approach for multi-target tracking in an occlusion environment is presented. In pedestrian tracking using a video camera, pedestrains must be tracked accurately and continuously in the images. However, in a crowded environment, the conventional tracking algorithm has a problem in that tracks do not continue when pedestrians are hidden behind the foreground object. In this study, we propose a robust tracking method for occlusion that introduces a degeneration hypothesis that relaxes the track hypothesis which has one measurement to one track constraint. The proposed method relaxes the hypothesis that one measurement and multiple trajectories are associated based on the endpoints of the bounding box when the predicted trajectory is approaching, therefore the continuation of the tracking is improved using the measurement in the foreground. A numerical evaluation using MOT (Multiple Object Tracking) image data sets is performed to demonstrate the effectiveness of the proposed algorithm.

In channel decoding, a decoder with suboptimal metrics may be used because of the uncertainty of the channel statistics or the limitations of the decoder. In this case, the decoding metric is different from the actual channel metric, and thus it is called mismatched decoding. In this paper, applying the technique of the DS2 bound, we derive an upper bound on the error probability of mismatched decoding over a regular channel for the ensemble of linear block codes, which was defined by Hof, Sason and Shamai. Assuming the ensemble of random linear block codes defined by Gallager, we show that the obtained bound is not looser than the conventional bound. We also give a numerical example for the ensemble of LDPC codes also introduced by Gallager, which shows that our proposed bound is tighter than the conventional bound. Furthermore, we obtain a single letter error exponent for linear block codes.

Weighted Round-Robin (WRR) is often used, due to its simplicity, for scheduling packets or tasks. With WRR, a number of packets equal to the weight allocated to a flow can be served consecutively, which leads to a bursty service. Interleaved Weighted Round-Robin (IWRR) is a variant that mitigates this effect. We are interested in finding bounds on worst-case delay obtained with IWRR. To this end, we use a network calculus approach and find a strict service curve for IWRR. The result is obtained using the pseudo-inverse of a function. We show that the strict service curve is the best obtainable one, and that delay bounds derived from it are tight (i.e., worst-case) for flows of packets of constant size. Furthermore, the IWRR strict service curve dominates the strict service curve for WRR that was previously published. We provide some numerical examples to illustrate the reduction in worst-case delays caused by IWRR compared to WRR.

One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.

Folding an m×n square grid pattern along the edges of a grid is called map folding. We consider a decision problem in terms of whether a partial overlapping order of the squares aligning on the boundary of an m×n map is valid in a particular fold model called simple fold. This is a variation of the decision problem of valid total orders of the map in a simple fold model. We provide a linear-time algorithm to solve this problem, by defining an equivalence relation and computing the folding sequence sequentially, either uniquely or representatively.