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Fault‐tolerant quantum computation requires error‐correcting codes that enable reliable universal quantum operations. This study introduces a novel approach that executes the logical Hadamard with low‐space requirements while preserving the original definition of logical operators within the framework of the rotated surface codes. Our method leverages a boundary deformation method to rotate the logical qubit transformed by transversal Hadamard. Following this, the original encoding of the logical qubit is reinstated through logical flip‐and‐shift operations. The estimated space–time cost for a logical Hadamard operation with a code distance d is 5d2 + 3d2. The efficiency enhancement of the proposed method is approximately four times greater than those of previous approaches, regardless of the code distance. Unlike the traditional method, implementing a logical Hadamard requires only two patches instead of seven. Furthermore, the proposed method ensures the parallelism of quantum circuits by preventing interferences between adjacent logical data qubits. [ABSTRACT FROM AUTHOR]

Perceptual loss functions are central to an ever-increasing number of tasks across computer vision. Their strength lies in their ability to translate perceptual nuances into numerical high-level features. A cornerstone of these functions are the high-dimensional, real-valued deep feature vectors. However, their memory-intensive nature often hinders deployment on devices with constrained resources. We introduce a concise perceptual loss function underpinned by Hadamard codes. For the ImageNet collection, our method delivers a lean representation of a mere 128 bytes. Impressively, this representation is not tied to any specific architecture, paving the way for the integration of industry-standard models. Utilizing our proposed binary codes in conjunction with kNN and Half-Space Proximal (HSP) classifiers (with HSP being a noteworthy alternative to kNN), we have secured commendable accuracy. This novel approach sets new benchmarks, enhancing state-of-the-art performance in knowledge transfer across a variety of image datasets. [ABSTRACT FROM AUTHOR]

Quantum error correction lies at the heart of building reliable quantum information processing systems. Stabilizer codes, a fundamental class of quantum errorcorrecting codes, play a pivotal role in mitigating the adverse effects of noise and decoherence in quantum systems. This paper introduces a novel construction of quantum stabilizer codes using Hadamard difference sets, an elegant mathematical concept derived from combinatorial design theory. In this paper, the construction of the quantum stabilizer codes over non- cyclic Hadamard difference sets with parameters (4m²,2m²-m, m²-m), where m is a positive integer is discussed. Firstly, the parity check matrices are constructed from the Circulant permutation matrices with the help of Hadamard difference sets and then, the Symplectic inner product condition for Hadamard difference sets over binary operation for parity check matrices are obtained to affirm the commutative condition for Stabilizer operators which is vital for the error detection. For application, we constructed a Hadamard difference sets with parameters (16,6,2) for m = 2 of ordered pair of the group Z2 Z8 × (non-cyclic group) and quantum stabilizer codes are obtained by parity-check matrix. [ABSTRACT FROM AUTHOR]

Wireless body area networks (WBANs), featuring wearable and implantable devices for collecting physiological data are increasingly critical in healthcare for enabling continuous remote monitoring, diagnostic improvements, and treatment optimization. Secure communication within WBANs is essential to protect sensitive health data from unauthorized access and manipulation. This paper introduces a novel secure digital (SD)- human body communication (HBC) transceiver (TR) system, tailored for WBAN applications, that prioritizes security and offers significant enhancements in size, power efficiency, speed, and data transmission efficiency over current solutions. Leveraging a combination of frequencyselective (FS) digital transmission with walsh codes (WCs) or quadrature amplitude modulation (QAM), and incorporating one-round encryption and decryption modules, the system complies with the IEEE 802.15.6 standard, ensuring broad compatibility. Specifically, the QAM-based SD-HBC TR system exhibits a 4% reduction in chip area, a 7.6% increase in operating frequency, a 3.4% decrease in power consumption, a 27.5% reduction in latency, and improvements of 33% in throughput and 35.5% in efficiency. Importantly, it achieves a bit error rate (BER) of up to 10-8, demonstrating high reliability across communication methods. This research significantly advances secure communication in WBANs, offering a promising approach for enhancing the reliability, efficiency, and security of healthcare monitoring technologies. [ABSTRACT FROM AUTHOR]

Summary: In the case of future access networks, such as 6G‐based applications, the free‐space optical communication (FSO) technology is an efficient solution. FSO in 6G is extremely popular because of its unique properties, which include ease of installation, high bandwidth, high security, license‐free long range, and interference resistance. However, environmental disturbances have a negative impact on the FSO system's functioning. Because of these atmospheric turbulences, the optical information gets restricted, which in turn reduces the link reliability, power density, and distance. This paper proposes a hybrid FSO strategy for improving system efficiency to address these problems. Signal creation is fundamental to every successful communication system. The FSO system consists of three components: the transmitter, the channel medium, and the receiver. The transmitter section includes a continuous wave laser, a Mach–Zehnder modulator, a nonreturn to zero transpose Walsh code generator, and a nonreturn to zero pulse generator. Wavelength division multiplexing‐optical code division multiple access‐spectrum slicing (WDM‐OCDMA‐SS) is used to facilitate efficient data transfer after signals have been generated by alternate mark inversion (AMI). In order to boost a weak signal, fused Raman erbium amplifiers (Fuse‐RE) are used. Q factor and log bit error rate (BER) are used to assess the performance of the suggested approach. The proposed model has obtained a log BER of −15.3291 for clear air and a Q factor of 8.2922, whereas the performances are implemented using Python. The proposed approach achieves better performance when compared to the existing methodologies. [ABSTRACT FROM AUTHOR]

In communication technologies such as digital watermarking, wireless sensor networks (WSNs), and visual light communication (VLC), error-correcting codes are crucial. The Enhanced Hadamard Error-Correcting Code (EHC), which is based on 2D Hadamard Basis Images, is a novel error correction technique that is presented in this study. This technique is used to evaluate the effectiveness of the video watermarking scheme. Even with highly sophisticated embedding techniques, watermarks usually fail to resist such comprehensive attacks because of the extraordinarily high compression rate of approximately 1:200 that is frequently employed in video dissemination. It can only be used in conjunction with a sufficient error-correcting coding method. This study compares the efficacy of the well-known Reed–Solomon Code with this novel technique, the Enhanced Hadamard Error-Correcting Code (EHC), in maintaining watermarks in embedded videos. The main idea behind this newly created multidimensional Enhanced Hadamard Error-Correcting Code is to use a 1D Hadamard decoding approach on the 2D base pictures after they have been transformed into a collection of one-dimensional rows. Following that, the image is rebuilt, allowing for a more effective 2D decoding procedure. Using this technique, it is possible to exceed the theoretical error-correcting capacity threshold of ⌊ d m i n − 1 2 ⌋ bits, where d m i n is the Hamming distance. It may be possible to achieve better results by converting the 2D EHC into a 3D format. The new Enhanced Hadamard Code is used in a video watermarking coding scheme to show its viability and efficacy. The original video is broken down using a multi-level interframe wavelet transform during the video watermarking embedding process. Low-pass filtering is applied to the video stream in order to extract a certain frequency range. The watermark is subsequently incorporated using this filtered section. Either the Reed–Solomon Correcting Code or the Enhanced Hadamard Code is used to protect the watermarks. The experimental results show that EHC far outperforms the RS Code and is very resilient against severe MPEG compression. [ABSTRACT FROM AUTHOR]

Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory. [ABSTRACT FROM AUTHOR]

Linear codes of length n over Z p s , p prime, called Z p s -additive codes, can be seen as subgroups of Z p s n . A Z p s -linear generalized Hadamard (GH) code is a GH code over Z p which is the image of a Z p s -additive code under a generalized Gray map. It is known that the dimension of the kernel allows to classify these codes partially and to establish some lower and upper bounds on the number of such codes. Indeed, in this paper, for p ≥ 3 prime, we establish that some Z p s -linear GH codes of length p t having the same dimension of the kernel are equivalent to each other, once t is fixed. This allows us to improve the known upper bounds. Moreover, up to t = 10 if p = 3 or t = 8 if p = 5 , this new upper bound coincides with a known lower bound based on the rank and dimension of the kernel. [ABSTRACT FROM AUTHOR]

Raman microscopes are widely used in various fields and their spectral resolutions differ greatly depending on the system and optical components. Thus, the microscopes must be calibrated before measurement to obtain reliable results. Although the first-order phonon peak of Si wafers at ⁓520 cm-1 is generally used as a calibrant of Raman microscopes, not only is it unclear how the positions of the first-order phonon peaks are comparable over Si wafers of different manufacturers, dopant types and crystal orientations, but they also shift with the temperature and residual stress. We examined the changes in the position of the first-order phonon peak at different temperatures using a HeNe laser at 633 nm and its plasma lines. Because a comparable linear relationship between the temperature and the wavenumber was obtained regardless of the Si wafer examined, most commercially available Si wafers can be used for the calibration of Raman microscopes. Although shifting of the peak was introduced by the laser power due to an increase in temperature at the laser spot, it was less sensitive than broadening of the peak width. A peak shift was observed with a 532-nm laser at 2.1 mW using a 100 air objective lens (numerical aperture: 0.9), but this did not occur with a 633- or 785-nm laser even at more than 10 mW. Thus, less laser power should be used to calibrate Raman microscopes using the first-order phonon peak of Si wafers under high-resolution conditions, especially for a 532-nm laser. [ABSTRACT FROM AUTHOR]

Spectral Amplitude Coding-Optical Codes Division Multiple Access (SAC-OCDMA) is a future multiplexing technique that witnessed a dramatic attraction for eliminating the problems of the internet in optical network field such as multiple-user access and speed's growth of the files or data traffic. In this research article, the performance of SAC-OCDMA system based on two encoding–decoding multidiagonal (MD) and Walsh Hadamard (WH) codes is enhanced utilizing three different schemes of dispersion compensating fiber (DCF): pre-, post- and symmetrical compensation. The system is simulated using Optisystem version 7.0 and Optigrating version 4.2. The performance of the proposed system is specified in terms of bit error rate (BER), Q-factor and eye diagram. It has been observed that the compensated system based on MD code is performs much better compared to the system based on WH code. On the other hand, the compensated SAC-OCDMA system with symmetrical DCF has the lowest values of BER and largest values of Q-factor, so it is considered the best simulated scheme contrasted with pre- and post-DCF. [ABSTRACT FROM AUTHOR]

DNA code design is a challenging problem, and it has received great attention in the literature due to its applications in DNA data storage, DNA origami, and DNA computing. The primary focus of this paper is in constructing new DNA codes using the cosets of linear codes over the ring Z 4 . The Hamming distance constraint, GC-content constraint, and homopolymers constraint are all considered. In this study, we consider the cosets of Simplex alpha code, Kerdock code, Preparata code, and Hadamard code. New DNA codes of lengths four, eight, sixteen, and thirty-two are constructed using a combination of an algebraic coding approach and a variable neighborhood search approach. In addition, good lower bounds for DNA codes that satisfy important constraints have been successfully established using Magma software V2.24-4 and Python 3.10 programming in our comprehensive methodology. [ABSTRACT FROM AUTHOR]

Metamaterial-based quarter-wave plates (QWPs) have emerged as promising candidates for advanced polarization control in a variety of optical applications, owing to their unique properties, such as ultra-thin profiles and tailored spectral responses. We design an ultra-thin, high-efficiency, and broadband QWP in transmission mode based on a TiO 2 /Au grating structure. We show that multiple reflections and the near-field effects associated with the integration of these devices pose challenges that must be considered when combining multiple metamaterials. We present insights that facilitate improved design methodology and the optimization of integrated metamaterial QWPs and other metadevices. Our results contribute to the development of miniaturized and high-density advanced lightwave and polarization control devices in optical systems. [ABSTRACT FROM AUTHOR]

The q k (full) factorial design with replication λ is the multi-set consisting of λ occurrences of each element of each q -ary vector of length k ; we denote this by λ × [ q ] k. An m × n row-column factorial design q k of strength t is an arrangement of the elements of λ × [ q ] k into an m × n array (which we say is of type I k (m , n , q , t)) such that for each row (column), the set of vectors therein are the rows of an orthogonal array of degree k , size n (respectively, m), q levels and strength t. Such arrays are used in experimental design. In this context, for a row-column factorial design of strength t , all subsets of interactions of size at most t can be estimated without confounding by the row and column blocking factors. In this manuscript we study row-column factorial designs with strength t ≥ 2. Our results for strength t = 2 are as follows. For any prime power q and assuming 2 ≤ M ≤ N , we show that there exists an array of type I k (q M , q N , q , 2) if and only if k ≤ M + N , k ≤ (q M − 1) / (q − 1) and (k , M , q) ≠ (3 , 2 , 2). We find necessary and sufficient conditions for the existence of I k (4 m , n , 2 , 2) for small parameters. We also show that I k + α (2 α b , 2 k , 2 , 2) exists whenever α ≥ 2 and 2 α + α + 1 ≤ k < 2 α b − α , assuming there exists a Hadamard matrix of order 4 b. For t = 3 we focus on the binary case. Assuming M ≤ N , there exists an array of type I k (2 M , 2 N , 2 , 3) if and only if M ≥ 5 , k ≤ M + N and k ≤ 2 M − 1. Most of our constructions use linear algebra, often in application to existing orthogonal arrays and Hadamard matrices. [ABSTRACT FROM AUTHOR]

Optical orthogonal codes (OOCs) are used in optical code division multiple access systems to allow a large number of users to communicate simultaneously with a low error probability. The number of simultaneous users is at most as big as the number of codewords of such a code. We consider (v , k , 2 , 1) -OOCs, namely OOCs with length v, weight k, auto-correlation 2, and cross-correlation 1. An upper bound B 0 (v , k , 2 , 1) on the maximal number of codewords of such an OOC was derived in 1995. The number of codes that meet this bound, however, is very small. For k ≤ 5 , the (v , k , 2 , 1) -OOCs have already been thoroughly studied by many authors, and new upper bounds were derived for (v , 4 , 2 , 1) in 2011, and for (v , 5 , 2 , 1) in 2012. In the present paper, we determine constructively the maximal size of (v , 6 , 2 , 1) - and (v , 7 , 2 , 1) -OOCs for v ≤ 165 and v ≤ 153 , respectively. Using the types of the possible codewords, we calculate an upper bound B 1 (v , k , 2 , 1) ≤ B 0 (v , k , 2 , 1) on the code size of (v , 6 , 2 , 1) - and (v , 7 , 2 , 1) -OOCs for each length v ≤ 720 and v ≤ 340 , respectively. [ABSTRACT FROM AUTHOR]

Belligerent sides of current military conflicts are first and foremost counting on intelligence, air supremacy, and electromagnetic spectrum dominance. Actual concepts of conducting military operations can be characterised by the massive employment of air defence systems, radars, and electronic warfare systems. An approach is aimed to strengthen air‐defence potential by improving the resilience of pulse radar against electronic warfare threats, such as an electronic attack. To cope with the above‐mentioned situation, a radar intrapulse modulation was designed, where a combination of Costas codes and Walsh‐Hadamard codes is applied. Using a particular waveform together with the proposed model for radar signal processing results in increased resilience against an electronic attack, especially against repeater jamming methods. Furthermore, it is also possible to process radar echoes at low levels of Signal‐to‐Noise Ratio (SNR), which enhances radar electronic counter–countermeasure capability. The main scientific contribution of the paper is in the unique design of the Pulse Compression Filter for Combined Intrapulse Modulation (PCF‐CIM) and in its modelling. Based on the statistical evaluation of results, using the proposed radar waveform together with PCF‐CIM, it is possible to detect radar signals with combined intrapulse modulation in the case of SNR ≥ −14 dB with TPR ≥0.9999 and FPR ≤10−6, where SNR stands for Signal‐to‐Noise Ratio, TPR stands for True Positive Rate, and FPR stands for False Positive Rate. [ABSTRACT FROM AUTHOR]

In this paper, a novel coupled code shifted M-ary differential chaos shift keying modulation scheme is proposed as a simple and low-cost solution to reference removal. In this scheme, only two information-bearing signals are transmitted. Both signals are modulated by selected Walsh code sequences with specific indices determined by the index bits, and one of them also carries an additional M-ary information symbol. Since these two information-bearing signals are coupled by the same chaotic message bearer, data bits can be easily recovered according to the correlation between these two signals so that the transmission of reference signals can be completely avoided. Theoretical Bit Error Rate (BER) expressions are derived over the additive white Gaussian noise and multipath Rayleigh fading channels. Furthermore, simulations and comparisons indicate that the proposed system can achieve better BER performance with lower complexity. [ABSTRACT FROM AUTHOR]

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OCDMA is an optical access technology that has a lot of potential because it can be asynchronously accessed and provides a higher level of security. The authors presented a new DW family code, a flexible double weight (FDW) code, and a novel polarization encoding approach in this paper. The new code is applicable to both odd- and even-weighted codes. The novel polarization encoding approach may be used for numerous wavelengths that overlap. Based on analytic principles, a comparison of two widely used spectrum amplitude-coding SAC-based OCDMA codes, notably modified frequency hopping (MFH), Hadamard, and the double weight (DW) code family. The comparison was based on observing the bit error rate (BER) in each situation. The DW code has a fixed weight of two. The FDW code was introduced to reduce phase-induced intensity noise and multiple access interference (MAI) in transmission networks. FDW codes are versions of the DW code family with weights larger than two. The FDW code outperforms the Hadamard, MFH, DW, modified double weight (MDW), and enhanced double weight (EDW) algorithms. FDW has the capacity to support up to 220 concurrent users. With the new polarization encoding technology, the FDW code can travel up to 60 km at a bit rate of 2.5 Gb/s and 40 km for a 10 Gb/s bit rate. [ABSTRACT FROM AUTHOR]

Fibre optic sensors using tilted fibre Bragg grating (TFBG) have high sensitivity for refractive index measurements. In order to achieve good metrological parameters of the measurement, an appropriate method of spectrum demodulation must be used. The method proposed in the article is an improvement of the spectral length algorithm. The spectral length parameter is treated as the sum of the derivative filter responses. In the original version, the first difference of spectrum elements was used, while this article proposes to use the wavelet transform to calculate the numerical derivative approximation. The advantage of this solution is an easy way to select the level of smoothing filtration by changing the scale parameter. The derivation is appropriate even for a relatively low signal-to-noise level. The approximation of the spectral length by the derivative calculated using the wavelet transform eliminates the high-frequency noise of the optical signal. The absolute value of determined spectral derivatives after significant smoothing can be used to estimate the wavelength of the decay of modes. After analyzing experimental data and performing calculations, it turns out that this is a linear method with better resolution than the contour length algorithm. [ABSTRACT FROM AUTHOR]

Most of the existing estimation methods of spreading code sequence are not suitable for the QPSK-DSSS. We propose a spreading code sequence estimation method based on fast independent component analysis (Fast-ICA). It mainly includes signal preprocessing, calculations of separation matrix, and spreading code sequence. Firstly, the received signal is segmented according to the period of the spreading code sequence, and the covariance matrix can be calculated. Then, the signal subspace and corresponding eigenvalues are obtained by eigenvalue decomposition of the covariance matrix. Subsequently, the received signal matrix needs to be whitened. Finally, the Fast-ICA algorithm is used to find the separation matrix to estimate the in-phase and orthogonal spreading code sequence. The experiment result shows that the estimation of the spreading code sequence can be carried out based on Fast-ICA under a low SNR of −12 dB. Compared with the constant modulus algorithm (CMA) and the decomposition method for the real part of the self-covariance matrix (EVD-R), this method has a better performance. [ABSTRACT FROM AUTHOR]

In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of Ó Catháin and Swartz. That is, we show how, if given a Butson Hadamard matrix over the k th roots of unity, we can construct a larger Butson matrix over the ℓ th roots of unity for any ℓ dividing k, provided that any prime p dividing k also divides ℓ . We prove that a Z p s -additive code with p a prime number is isomorphic as a group to a BH-code over Z p s and the image of this BH-code under the Gray map is a BH-code over Z p (binary Hadamard code for p = 2 ). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. Some structural properties of these codes are studied and examples are provided. [ABSTRACT FROM AUTHOR]

This paper presents a novel localization method based on the implementation of passive repeaters in multiple-input multiple-output (MIMO) systems. Passive repeaters can help in localizing users by taking advantage of their spreading in the communication environments. In the proposed method, the target area is divided into a grid. Each location in this grid has a unique field interference created by repeaters. Because of the unique field interference, each location causes a unique field signature at the base station when a user in that location transmits signals. The field signature corresponding to the center of each grid cell is used as a fingerprint for localizing users in that cell, and for all cells, a bank of matched filters corresponding to all stored fingerprints is constructed. When a signal arrives at the base station, the generated field signature is correlated with the bank of matched filters, and the location is determined based on the maximum correlation value. The numerical analysis is performed to verify the validity of the proposed method, and it is found that by means of passive repeaters, the user location can be determined with no need of calculating additional parameters. [ABSTRACT FROM AUTHOR]

In recent years, the Internet of Things (IoT) industry has become a research hotspot. With the advancement of satellite technology, the satellite Internet of Things is further developed along with a new generation of information technology and commercial markets. However, existing random access protocols cannot cope with the access of a large number of sensors and short burst transmissions. The current satellite Internet of Things application scenarios are divided into two categories, one has only sensor nodes and no sink nodes, and the other has sink nodes. A time-slot random access protocol based on Walsh code is proposed for the satellite Internet-of-Things scenario with sink nodes. In this paper, the load estimation algorithm is used to reduce the resource occupancy rate in the case of medium and low load, and a dynamic Walsh code slot random access protocol is proposed to select the appropriate Walsh code length and frame length h. The simulation results show that the slotted random access protocol based on Walsh code can effectively improve the throughput of the system under high load. The introduction of load estimation in the case of medium and low load can effectively reduce the resource utilization of the system, and ensure that the performance of the access protocol based on Walsh codes does not deteriorate. However, in the case of high load, a large resource overhead is still required to ensure the access performance of the system. [ABSTRACT FROM AUTHOR]

Multiple Frequency-Shift Keying (MFSK) has been used widely for underwater acoustic communications due to its low complexity and channel robustness. However, the traditional MFSK has the limitation of a low bit rate compared with coherent acoustic communication. To increase the bit rate, this study designs a new MFSK with the concept of orthogonal frequency division multiplexing (OFDM). We also adopt a channel-concatenated coding to resist the multipath interference and design the iterative joint decoding. The channel-concatenated coding consists of a Hadamard code and a convolutional code. Correspondingly, the iterative joint decoding uses the Hadamard–Viterbi joint soft decoding framework with a newly designed branch metric, which uses the Hadamard structure. As an important preprocessing link for a received signal, frame synchronization and Doppler compensation are also described in detail in this study. Simulations and experiments are conducted to show the effectiveness of the proposed MFSK underwater acoustic communications. [ABSTRACT FROM AUTHOR]

Regard T = { (g , ... , g) ∈ F q n : g ∈ F q } as an additive subgroup of the vector space F q n over a finite field F q . A code C ⊂ F q n is T-invariant if T acts on C induced by the addition of F q n . Using linear algebra and finite fields results, we investigate which important families of codes are T-invariant, including perfect codes, first-order Reed–Muller codes, and some Reed–Solomon codes. In particular, we characterize which perfect linear codes are T-invariant. A version of the Gilbert–Varshamov theorem for T-invariant codes is presented. We characterize which Hadamard codes are T-invariant for nonlinear codes. As an application, constructions of difference schemes are obtained using our results. Finally, difference schemes of strength 2 over a finite field are characterized using quasigroups endowed with a distributive law. [ABSTRACT FROM AUTHOR]

A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform (FHT-FSCL) is presented. The proposed decoder initializes $L$ $(L\geq 1)$ active decoding paths with $L$ random codeword permutations sampled from the full symmetry group of the codes. The path extension in the permutation domain is carried out until the first constituent RM code of order 1 is visited. Conventional path extension of the successive-cancellation list decoder is then utilized in the information bit domain. The simulation results show that for a RM code of length 512 with 46 information bits, by running 20 parallel permuted FHT-FSCL decoders with $L=4$ , we reduce 72% of the computational complexity, 22% of the decoding latency, and 84% of the memory consumption of the state-of-the-art simplified successive-cancellation decoder that uses 512 permutations sampled from the full symmetry group of the code, with similar error-correction performance at the target frame error rate of $10^{-4}$. [ABSTRACT FROM AUTHOR]

$\mathbb {Z}_{2^{s}}$ -additive codes are subgroups of $\mathbb {Z}^{n}_{2^{s}}$ , and can be seen as a generalization of linear codes over $\mathbb {Z}_{2}$ and $\mathbb {Z}_{4}$. A $\mathbb {Z}_{2^{s}}$ -linear code is a binary code (not necessarily linear) which is the Gray map image of a $\mathbb {Z}_{2^{s}}$ -additive code. We consider $\mathbb {Z}_{2^{s}}$ -additive simplex codes of type $\alpha $ and $\beta $ , which are a generalization over $\mathbb {Z}_{2^{s}}$ of the binary simplex codes. These codes are related to the $\mathbb {Z}_{2^{s}}$ -additive Hadamard codes. In this paper, we use this relationship to find a linear subcode of the corresponding $\mathbb {Z}_{2^{s}}$ -linear codes, called kernel, and a representation of these codes as cosets of this kernel. In particular, this also gives the linearity of these codes. Similarly, $\mathbb {Z}_{2^{s}}$ -additive MacDonald codes are defined for $s>2$ , and equivalent results are obtained. [ABSTRACT FROM AUTHOR]

Using a concatenated construction for -ary codes, we construct codes over in the Lee metrics which after a proper mapping to the binary alphabet (which in the case of is the well-known Gray map) become binary Hadamard codes (in particular, Hadamard matrices). Our construction allows to increase the rank and the kernel dimension of the resulting Hadamard code. Using computer search, we construct new nonequivalent Hadamard matrices of orders , , and with various fixed values of the rank and the kernel dimension in the range of possible values. It was found that in a special case, our construction coincides with the Kronecker (or Sylvester) construction and can be regarded as a version of a presently known [1] modified Sylvester construction which uses one Hadamard matrix of order and (not necessarily distinct) Hadamard matrices of order . We generalize this modified construction by proposing a more general Sylvester-type construction based on two families of (not necessarily distinct) Hadamard matrices, namely, on matrices of order and matrices of order . The resulting matrix is of order , as in the construction from [1]. [ABSTRACT FROM AUTHOR]

In this paper, a novel multi-user carrier index differential chaos shift keying (MU CI-DCSK) modulation scheme is proposed. For a better utilization of spectrum resources, each user is allocated a private subcarrier for reference signal transmission, while the remaining subcarriers are public and shared by all users to transmit their own data-bearing signals. To avoid user interferences in this design, users are distinguished in a code division multiple access (CDMA) way based on Walsh codes. By exploiting the redundancies in the transmitted signals, repeated segments of received signals are averaged, leading to greatly reduced noises and a noticeable improvement in bit error rate (BER) performance. BER expressions of this new system are derived over the additive white Gaussian noise (AWGN) and multi-path Rayleigh fading channels. Simulation results and comparisons are performed to verify the feasibility and advantages of this new scheme. [ABSTRACT FROM AUTHOR]

In this paper, we examine the performance of a spectral amplitude coding-optical code division multiple access (SAC-OCDMA) system using two different codes: m-sequence and Hadamard. Fiber Bragg grating (FBG) filters and balanced detection technique are employed for performance enhancement. The system performance is evaluated in terms of quality factor (Q), bit error rate (BER) and signal-to-noise ratio (SNR) as a function of number of users and fiber distance. The achieved results using a co-simulation Matlab-Optisystem version 17 are considered as improvements over previous works found in the literature. The results corresponding to a first comparative study of the system performance using the both code sequences show that using Hadamard code yields a better BER performance than using m-sequence code. This led us to study the performance of the proposed system for a larger number of users using the Hadamard code of length L = 32 (m = 5). The simulation results reveal that at a data rate of 100 Mbits/s and a FBG bandwidth of 0.4 nm, the suggested SAC-OCDMA system may support up to 13 users with a transmission distance of 5 Km. The obtained results also show that a distance of 45 Km can be used for a number of users up to 8 with BER = 9.8E − 09, Q = 5.82 and SNR = 20.71 dBm. [ABSTRACT FROM AUTHOR]

The differential chaos shift keying with code index modulation (CIM-DCSK) using Walsh codes can increase the data rate, but error rate performance degrades over practical multipath channel with high delay spread. To tackle this drawback, this paper proposes a parallel CIM-DCSK (PT-CIM-DCSK), where the first time slot is used to transmit the chaotic reference sequence, and the second slot is used to transmit the multiple sequences carrying data bits. In particular, multiple $q$ chaotic sequences are added for data transmission in parallel, and each sequence is modulated by CIM-DCSK with $m_{c}$ bits. By exploiting the quasi-orthogonal characteristics of permuted chaotic signals, the interference between $q$ sequences can be remarkably suppressed. In this way, given the data rate, PT-CIM-DCSK can achieve a larger length of Walsh segment than the CIM-DCSK, since its parallel transmission compensates the rate. In addition, the error performance of the proposed scheme over the multipath Rayleigh fading channel is theoretically analyzed. The theoretical and consistent simulation results demonstrate that the PT-CIM-DCSK can obtain significant performance gains over the conventional CIM-DCSK, and the gain can be up to 5 dB in multipath fading channel with high delay. This is because the larger Walsh segment of PT-CIM-DCSK provides the enhanced robustness against multipath effect. The performance superiority of the proposed scheme is further verified in practical ultra-wideband (UWB) wireless industrial scenarios, which suggests promising for low-cost and low-complexity wireless communication applications. [ABSTRACT FROM AUTHOR]

Visible light communication (VLC) is a technology that is currently being employed to achieve high data rates. Orthogonal frequency division multiplexing (OFDM) is a powerful scheme for intensity modulation and direct detection (IM-DD) that is becoming increasingly important. OFDM systems based on VLC are accomplished through the implementation of IM-DD constraints, including direct current biased optical OFDM (DCO-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM), and asymmetrically clipped DC-biased (ADO-OFDM), among others. The OFDM technique based on VLC is inefficient in terms of spectral efficiency and has a high peak to average power ratio (PAPR). In this article, the symbol time compression-image adjust (STC-IMADJS) technique will be proposed for throughput maximization and PAPR reduction in the DCO-OFDM, ACO-OFDM, and ADO-OFDM systems. Furthermore, the STC technique enables the simultaneous transmission of two sub-carriers through Walsh spreading codes without inference between them. As a result, the OFDM symbol has been reduced by 50%. The IMADJS strategy reduces the high PAPR of transmitted signals by compressing large signals and expanding small signals, as long as the average power level remains constant after compression. Therefore, the proposed STC-IMADJS technique doubles the throughput as well as significantly reduces the PAPR for OFDM systems based on VLC. The simulation results are performed using Matlab-2021a for 1024 sub-carriers. As a result, the simulation results show that the proposed technique reduces the PAPR by 3.7 dB ( 86 % ), 8.16 dB ( 93 % ), and 1.81 dB ( 20 % ) for DCO-OFDM, ACO-OFDM, and ADO-OFDM systems respectively. Furthermore, the technique has a significantly lower computational complexity than conventional OFDM systems based on VLC. Finally, the measures of performance through this article are bit error rate and complementary cumulative distribution function. [ABSTRACT FROM AUTHOR]

Deep representation learning is a subfield of machine learning that focuses on learning meaningful and useful representations of data through deep neural networks. However, existing methods for semantic classification typically employ pre-defined target codes such as the one-hot and the Hadamard codes, which can either fail or be less flexible to model inter-class correlation. In light of this, this paper introduces a novel learnable target coding as an auxiliary regularization of deep representation learning, which can not only incorporate latent dependency across classes but also impose geometric properties of target codes into representation space. Specifically, a margin-based triplet loss and a correlation consistency loss on the proposed target codes are designed to encourage more discriminative representations owing to enlarging between-class margins in representation space and favoring equal semantic correlation of learnable target codes respectively. Experimental results on several popular visual classification and retrieval benchmarks can demonstrate the effectiveness of our method on improving representation learning, especially for imbalanced data. • We propose an auxiliary feature regularization for deep representation learning. • We propose a learnable target coding scheme for capturing target correlations. • Our method consistently outperforms state-of-the-art on popular benchmarks. [ABSTRACT FROM AUTHOR]

Ideal imaging, which is constantly pursued, requires the collection of all kinds of optical information of the objects in view, such as three-dimensional spatial information (3D) including the planar distribution and depth, and the colors, i.e., spectral information (1D). Although three-dimensional spatial imaging and spectral imaging have individually evolved rapidly, their straightforward combination is a cumbersome system, severely hindering the practical applications of four-dimensional (4D) imaging. Here, we demonstrate the ultra-compact spectral light-field imaging (SLIM) by using a transversely dispersive metalens array and a monochrome imaging sensor. With only one snapshot, the SLIM presents advanced imaging with a 4 nm spectral resolution and near-diffraction-limit spatial resolution. Consequently, visually indistinguishable objects and materials can be discriminated through SLIM, which promotes significant progress towards ideal plenoptic imaging. The authors demonstrate compact spectral light-field imaging by using a transversely dispersive metalens array and a monochrome imaging sensor. They show that 4D images can be obtained in a single shot, and demonstrate discrimination of visually indistinguishable objects. [ABSTRACT FROM AUTHOR]

The Code‐division multiple access (CDMA) method is commonly used as the network infrastructure in multi‐core chips. One of its advantages is the simultaneous connection of all network components. Another advantage is the constant delay of this method. On the other hand, one drawback is that the number of transmitters is limited to the number of encoding bits. In this study, the authors used the combination of Walsh codes and their inverses, as well as the simultaneous application of the time‐division multiple access (TDMA) method, to increase the transmission capacity of this protocol more than four times the standard mode. In the proposed design, although the circuit area does not increase significantly, a fourfold increase in the throughput of the CDMA network is seen. Using the method proposed in this study, it will be possible to increase the capacity further. [ABSTRACT FROM AUTHOR]

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Z p s -additive codes of length n are subgroups of Z p s n , and can be seen as a generalization of linear codes over Z 2 , Z 4 , or Z 2 s in general. A Z p s -linear generalized Hadamard (GH) code is a GH code over Z p which is the image of a Z p s -additive code by a generalized Gray map. In this paper, we generalize some known results for Z p s -linear GH codes with p = 2 to any odd prime p. First, we show some results related to the generalized Carlet's Gray map. Then, by using an iterative construction of Z p s -additive GH codes of type (n ; t 1 , ... , t s) , we show for which types the corresponding Z p s -linear GH codes of length p t are nonlinear over Z p . For these codes, we compute the kernel and its dimension, which allow us to give a partial classification. The obtained results for p ≥ 3 are different from the case with p = 2 . Finally, the exact number of non-equivalent such codes is given for an infinite number of values of s, t, and any p ≥ 2 ; by using also the rank as an invariant in some specific cases. [ABSTRACT FROM AUTHOR]

A Noise Suppression aided Multi-Carrier $M$ -ary Differential Chaos Shift Keying (NS-MC-MDCSK) system is proposed here where each information subcarrier transmits an $M$ -ary information-bearing signal and the $M$ -ary constellation symbols are constructed by orthogonal Walsh codes to improve the energy efficiency. Exploiting the redundant information available in the received signal, we propose a noise suppression algorithm to suppress channel noise in the reference and $M$ -ary information-bearing signals. In the proposed algorithm, correlation coefficients detected between the received reference and information-bearing signals are fed back to suppress the noise corrupting the signal received. This method reduces the channel noise significantly and provides an outstanding Bit Error Rate (BER) performance. A performance analysis is performed for the NS-MC-MDCSK system over Additive White Gaussian Noise (AWGN) and multipath fading channels. Finally, the BER performance of the NS-MC-MDCSK system is compared to that of other chaotic communications systems. It is shown that the NS-MC-MDCSK system offers better BER performance than its competitors. [ABSTRACT FROM AUTHOR]

Herein, a new space–time block coding technique is proposed for a MIMO 2 × 2 multiple-input multiple output (MIMO) system to minimize the bit error rate (BER) in Rayleigh fading channels with reduced decoding complexity using ZF and MMSE linear detection techniques. The main objective is to improve the service quality of wireless communication systems and optimize the number of antennas used in base stations and terminals. The idea is to exploit the correlation product technique between both information symbols to transmit per space–time block code and their own orthogonal Walsh–Hadamard sequences to ensure orthogonality between both symbol vectors and create a full-rate orthogonal STBC code. Using 16 quadrature amplitude modulation and the quasi-static Rayleigh channel model in the MATLAB environment, the simulation results show that the proposed space–time block code performs better than the Alamouti code in terms of BER performance in the 2 × 2 MIMO system for both cases of linear decoding ZF and MMSE. [ABSTRACT FROM AUTHOR]

Adversarial images have become an increasing concern in real-world image recognition applications with deep neural networks (DNN). We observed that all the architectures in DNN use one-hot encoding after a softmax layer. The attacker can make minute modifications in the adversarial example rendering those changes imperceptible to a human observer. The Hamming distance between pairs of one-hot codes is two, independent of the number of classes, and we gather this is at the heart of a successful attack. This paper proposes increasing the Hamming distance between class codes as a generic defense against adversarial attacks from the above observation. It is only natural to use error-correcting codes for this task. We present an experimental comparison of our proposal against SOTA adversarial defenses. We conducted tests for six types of white-box attacks and one black-box scenario described in the literature. In all the experiments, our proposal’s precision surpasses the state-of-art defenses by a wide margin.

Code‐index modulation (CIM) uses the index of spreading code to convey information, which can be integrated with different kinds of MIMO systems to achieve higher throughput. This paper proposes a novel CIM‐integrated space time shift keying scheme called CIM‐STSK. The CIM‐STSK system employs three types of resources to transmit information bits, which are Hadamard codes, dispersion matrix indexes and QAM constellation symbols. The mathematical expression of the bit error rate of the CIM‐STSK system is derived, and the theoretical analysis is validated with Monte Carlo simulation results. Compared with the corresponding CIM‐SS, STSK, CIM‐SM, and CIM‐QSM systems, CIM‐STSK scheme can not only improve spectrum efficiency, but also achieve a better error performance. [ABSTRACT FROM AUTHOR]

We initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure‐resilient and tolerant property testing. We first investigate local list‐decoding in the presence of erasures. We prove an analog of a famous result of Goldreich and Levin on local list‐decodability of the Hadamard code. Specifically, we show that the Hadamard code is locally list‐decodable in the presence of a constant fraction of erasures, arbitrarily close to 1, with list sizes and query complexity better than in the Goldreich–Levin theorem. We further study approximate locally erasure list‐decodable codes and use them to construct a property that is erasure‐resiliently testable with query complexity independent of the input length, n, but requires nΩ(1) queries for tolerant testing. We also investigate the general relationship between local decoding in the presence of errors and in the presence of erasures. [ABSTRACT FROM AUTHOR]

A subset of a vector space $\mathbb {F}_{q}^{n}$ is additive if it is a linear space over the field $\mathbb {F}_{p}$ , where $q=p^{e}$ , $p$ prime, and $e>1$. Bounds on the rank and dimension of the kernel of additive generalised Hadamard (additive GH) codes are established. For specific ranks and dimensions of the kernel within these bounds, additive GH codes are constructed. Moreover, for the case $e=2$ , it is shown that the given bounds are tight and it is possible to construct an additive GH code for all allowable ranks and dimensions of the kernel between these bounds. Finally, we also prove that these codes are self-orthogonal with respect to the trace Hermitian inner product, and generate pure quantum codes. [ABSTRACT FROM AUTHOR]

Non-orthogonal multiple access (NOMA) is a prominent 5G wireless communication technique which ensures higher spectral efficiency, low latency and user fairness. As power-domain NOMA exploits different power levels assigned to each user for decoding, therefore, performance of this scheme degrades badly in a network having approximately equidistant users. To address this challenge, a novel hybrid CDMA–NOMA scheme for 5G downlink is proposed in this paper. Superposition coding is done at the transmitter side while successive interference cancellation (SIC) is performed at the receiver. The proposed scheme differentiates inter-cluster users on the basis of spreading codes, whereas intra-cluster users are differentiated on the basis of different power levels. Interference in the system is mitigated through two different techniques, inter-cluster interference through spreading codes (PN and Walsh codes) while intra-cluster interference through SIC technique. We implement an accurate power allocation strategy with users clustering best with poor model (users with nearest and farthest distances to BS) which is based on the distance of each user from base station. Considering user's distance and channel coefficient, the proposed technique adapts intelligently among NOMA and hybrid CDMA–NOMA. BER performance of the hybrid CDMA–NOMA system is analyzed in NYUSIM channel model. The proposed approach improves the capacity without increasing the bandwidth and/or number of antennas, and results in reduced interference in congested NOMA systems. [ABSTRACT FROM AUTHOR]

A multimodal medical image fusion algorithm based on multiple latent low-rank representation is proposed to improve imaging quality by solving fuzzy details and enhancing the display of lesions. Firstly, the proposed method decomposes the source image repeatedly using latent low-rank representation to obtain several saliency parts and one low-rank part. Secondly, the VGG-19 network identifies the low-rank part's features and generates the weight maps. Then, the fused low-rank part can be obtained by making the Hadamard product of the weight maps and the source images. Thirdly, the fused saliency parts can be obtained by selecting the max value. Finally, the fused saliency parts and low-rank part are superimposed to obtain the fused image. Experimental results show that the proposed method is superior to the traditional multimodal medical image fusion algorithms in the subjective evaluation and objective indexes. [ABSTRACT FROM AUTHOR]

This paper investigates the error probability of our proposed modulation technique which is produced by combining the existing pulse position modulation (PPM) technique with Hadamard code (HC). Moreover, the HC is also combined with differential PPM (DPPM). The error performances of existing technique and the proposed technique are compared at high-order modulation (HOM) and low-order modulation. The results show that the error performance of the proposed technique outperforms at HOM at the cost of higher bandwidth. This error performance is improved due to the bipolar nature of HC and it reduces the power requirements of the system. [ABSTRACT FROM AUTHOR]

In this paper, the existence, uniqueness and stability of solutions to a boundary value problem of nonlinear FDEs of variable order are established. To do this, we first investigate some aspects of variable order operators of Hadamard type. Then, with the help of the generalized intervals and piecewise constant functions, we convert the variable order Hadamard FBVP to an equivalent standard Hadamard BVP of the fractional constant order. Further, two fixed point theorems due to Schauder and Banach are used and, finally, the Ulam-Hyers-Rassias stability of the given variable order Hadamard FBVP is examined. These results are supported with the aid of a comprehensive example. [ABSTRACT FROM AUTHOR]

Aiming at the problem of insufficient separation accuracy of aliased signals in space Internet satellite ground communication scene, a stacked time domain convolutional network (Stacked-TCN) separation method based on deep learning is proposed. Firstly, the coding feature representation is extracted from the mixed signal. Then, the deep feature mask of the source signal is trained through the time-domain convolution network. The mask of each signal source and the coding feature of the mixed signal are multiplied by Hadamard to obtain the coding feature representation of the source signal. Finally, 1-D convolution is used to decode the characteristics of the source signal to obtain the original waveform. In the experiment, the negative scale invariant source to noise ratio is used as the loss function of network training, that is, the evaluation index of single channel blind source separation performance. The results show that the Stacked-TCN method has better separation accuracy and noise robustness than the other four algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codes — a type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying Hadamard constraints to the check nodes in a generalized protograph-based LDPC code, followed by lifting the generalized protograph. We name the codes formed protograph-based LDPC Hadamard (PLDPC-Hadamard) codes. We also propose a modified Protograph Extrinsic Information Transfer (PEXIT) algorithm for analyzing and optimizing PLDPC-Hadamard code designs. The proposed algorithm further allows the analysis of PLDPC-Hadamard codes with degree- 1 and/or punctured nodes. We find codes with decoding thresholds ranging from −1.53 dB to −1.42 dB. At a BER of 10−5, the gaps of our codes to the ultimate-Shannon-limit range from 0.40 dB (for rate = 0.0494) to 0.16 dB (for rate = 0.003). Moreover, the error performance of our codes is comparable to that of the traditional LDPC-Hadamard codes. Finally, the BER performances of our codes after puncturing are simulated and compared. [ABSTRACT FROM AUTHOR]

Quasi-complementary sequence sets (QCSSs) play an important role in multi-carrier code-division multiple-access (MC-CDMA) systems. They can support more users than perfect complementary sequence sets in MC-CDMA systems. It is desirable to design QCSSs with good parameters that are a trade-off of large set size, small periodic maximum magnitude correlation and small alphabet size. The main results are to construct new infinite families of QCSSs that all have small alphabet size and asymptotically optimal periodic maximum magnitude correlation. In this paper, we propose three new constructions of QCSSs using additive characters over finite fields. Notably, these QCSSs have new parameters and small alphabet sizes. Using the properties of characters and character sums, we determine their maximum periodic correlation magnitudes and prove that these QCSSs are asymptotically optimal with respect to the lower bound. [ABSTRACT FROM AUTHOR]