Hadamard Codes Research Articles

A novel carrier index M‐ary differential chaos shift keying modulation scheme

AbstractTo obtain better spectral efficiency and higher bit rate, a novel carrier index M‐ary differential chaos shift keying modulation scheme is proposed. In this system, part of subcarriers is assigned to the chaotic reference so that it can carry extra data bits through carrier index modulation, while one of the remaining subcarriers is activated to transmit the data‐bearing signal. In addition, M‐ary DCSK modulation is also applied to data‐bearing signals based on the constellation theory and Walsh codes. Theoretical bit error rate expressions are derived over the multipath Rayleigh fading and additive white Gaussian noise channels. Simulations and comparisons are performed with various combinations of chaotic sequence lengths, subcarrier numbers and constellation sizes. Results show that the proposed scheme can outperform other counterparts in both spectral efficiency and bit error rate performances.

A novel differential chaos shift keying system based on joint time slot and code index of carrier phase modulation

This paper proposes a novel differential chaos shift keying (DCSK) system that utilizes carrier phase modulation in combination with time slot and code index modulation, referred to as CP-TCIM-DCSK system, to achieve high data rate transmission. In the proposed CP-TCIM-DCSK system, the carrier modulated by the carrier phase is used to transmit the information-bearing signal. In addition to physically transmitted information bits, extra information bits are conveyed through time slot and Walsh code modulation, as well as carrier phase modulation, making full use of the benefits of multidimensional modulation. To successfully estimate carrier phase bits and code index bits, an effective joint detection algorithm for carrier phase and code index tailored for the CP-TCIM-DCSK system is introduced. The theoretical Bit Error Rate (BER) expressions for the CP-TCIM-DCSK scheme are derived for both Additive White Gaussian Noise (AWGN) and multipath Rayleigh fading channels. Furthermore, a comparison of data rates, energy efficiency, and complexity between the CP-TCIM-DCSK system and the most advanced systems in the same category at present is conducted. The results validate the accuracy of theoretical analysis through simulation and demonstrate that the proposed scheme outperforms its competitive systems in terms of BER performance.

Hadamard Coded Multiplane Wave based Ultrafast Doppler for Rat Brain Imaging

Abstract This study explores the application of Hadamard multiplane-wave coding in ultrafast power and color Doppler imaging for enhanced visualization of rat brain vasculature. By implementing an 8-order Hadamard matrix, an approximate 10 dB improvement in signal-to-noise ratio was significantly achieved, particularly in deep brain regions and the hippocampus. The enhanced imaging technique, compared to classical plane wave coherent compounding, demonstrates its potential for applications requiring deep penetration and high sensitivity to small blood flow without compromising the ultrafast frame rate.

Improving deep representation learning via auxiliary learnable target coding

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.

A high-data-rate hybrid index communication system based on quadrature chaos shift keying

To address the rapidly increasing challenges posed by the demands for large-scale data transmission and processing, this paper proposes a high-data-rate hybrid index modulation communication system based on quadrature chaos shift keying (HR-HIM-QCSK). The system employs a hybrid modulation involving carrier index and slot index. In this approach, three mutually orthogonal reference signals are constructed using Walsh codes. These reference signals are then utilized to create three distinct QCSK signals, distinguishing between the activation modes of carriers and time slots. This design allows all slots to carry QCSK signals, significantly enhancing the data rate of the HR-HIM-QCSK system. Theoretical analysis and simulations conducted under additive white Gaussian noise and multipath Rayleigh fading channels demonstrate that the HR-HIM-QCSK system outperforms other competing systems in terms of bit error rate (BER) performance. Further analysis covers aspects such as data rate, spectral efficiency, complexity and covertness, highlighting the superior performance of the HR-HIM-QCSK system in high-data-rate communication. This study provides valuable insights for the design of efficient chaotic communication systems.

Hadamard Error-Correcting Codes and Their Application in Digital Watermarking.

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 ⌊dmin-12⌋ bits, where dmin 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.

Code Index Modulated Chaotic Ambient Backscatter Communication With Differential Walsh Codes

Code Index Modulated Chaotic Ambient Backscatter Communication With Differential Walsh Codes

Design of a brief perceptual loss function with Hadamard codes

Design of a brief perceptual loss function with Hadamard codes

A novel detection method for wheat aging based on the delayed luminescence

Wheat aging plays an important role in assessing storage wheat quality and its subsequent processing purposes. The conventional detection methods for wheat aging are mainly involved in chemical techniques, which are time-consuming as well as waste part of wheat samples for each detection. Although some physical detection methods have obtained gratifying results, it is extremely hard to expand their application fields but to stay in the theory stage. For this reason, a novel nondestructive detection model for wheat aging based on the delayed luminescence (DL) has been proposed in this paper. Specifically, after collecting enough sample data, we first took advantage of certain hyperbolic function to fit DL signal, and then used four parameters of the hyperbolic function to feature the decay trend of the DL signal. Secondly, in order to better feature the DL signal, we extracted other six features together with above four features to form the input feature vector. Finally, as the bidirectional long short-term memory (Bi-LSTM) network lacked error-correcting performance, the Bi-LSTM network based on Walsh coding (Walsh-Bi-LSTM) mechanism was proposed to establish the detection model, which made the detection model have the error-correcting performance by reasonably splitting the multi-classification target task. Shown by experimental results, the newly proposed wheat aging detection model is able to achieve 94.00% accuracy in the testing dataset, which can be used as a green and nondestructive method to timely reflect wheat aging states.

DNA Code Design Based on the Cosets of Codes over Z4

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 Z4. 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.

Partial permutation decoding and PD-sets for [formula omitted]-linear generalized Hadamard codes

It is known that Zps-linear codes, which are the Gray map image of Zps-additive codes (linear codes over Zps), are systematic and a systematic encoding has been found. This makes Zps-linear codes suitable to apply the permutation decoding method. This technique is also based on the existence of r-PD-sets, which are subsets of the permutation automorphism group of the code. In this paper, we study the permutation automorphism group of Zps-linear generalized Hadamard codes of type (n;t1,…,ts) and show how to construct r-PD-sets of size r+1, for all r up to an upper bound, in order to be able to perform a partial permutation decoding for these codes.

A Reliable and Intelligent Deep Learning Based Demodulator for M-Ary Code Shifted Differential Chaos Shift Keying System With Power Allocation

In high-speed railway systems, channel conditions are dramatically changing, which brings great challenges to information transmissions. Our objective is to improve the reliability performances by utilizing the deep learning (DL) scheme to intelligently extract the features of signals to combat the complex dynamically changing channel conditions. In this paper, we propose a DL-aided demodulation scheme for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary code shifted differential chaos shift keying system with power allocation (PA-GCS-MDCSK) to enhance reliability performance. In this design, the deep neural network (DNN) adopts fully-connected layers (FCLs) to conduct the joint de-spreading of Walsh codes and chaotic demodulations. Meanwhile, the long short-term memory (LSTM) unit with the residual structure is constructed to extract the correlation between the chaotic sequences, thus the interferences induced by real-valued chaotic sequences can be suppressed, thereby improving the reliability performance. Then the computational complexity is analyzed and compared with benchmark schemes. Simulation results over both additive white Gaussian noise (AWGN), fading, and railway channels validate that the proposed design can achieve better bit error rate (BER) and robustness performances than benchmark schemes.

Target-to-User Association in ISAC Systems With Vehicle-Lodged RIS

Target-to-user (T2U) association is a prerequisite to fully exploit the potential of the sensing function in communication-centric integrated sensing and communication (ISAC) systems, e.g., for beam and blockage management. This letter proposes to purposely mount a RIS on the roof of the vehicular user equipment (VUE), which can serve as an intentional back-reflector towards the base station. By controlling the reflection pattern over time, it is possible to transmit information to the sensing system, i.e., back-reflection as bit 1, no back-reflection as bit 0. The VUEs are configured to back-reflect a Hadamard code sequence, which enables T2U association. The numerical results confirm the validity of our proposal.

Non-destructive detection method for wheat freshness degree based on delayed luminescence

Accurate identification to freshness degree is one of the preconditions for secure storage of wheat. Up to now, the detection on wheat freshness mainly depends on biochemical methods. However, biochemical methods are always involved in a series of problems, such as long pretreatment processes to wheat samples, poor repeatability, destructive detection and so on, which hardly meet the detection requirements of scientific and intelligent grain storage. Therefore, finding out a simple, accurate, and non-destructive detection method for wheat freshness degree is of necessity. For this reason, we propose a novel wheat freshness degree detection model based on the delayed luminescence (DL) signals of wheat samples in this paper. Furthermore, a bidirectional LSTM network based on Walsh coding (Walsh-Bi-LSTM) is introduced in order to make the detection model have the error-correcting performance by reasonably splitting the multi-classification target task into several binary classification targets. Shown by the experimental results, the classification accuracy rates of the detection model established in this paper achieve 90% and 94% on the test sets of storage wheat and artificial aging seed wheat samples, improving 9% and 12% compared with conventional Bi-LSTM network model respectively, which validates that the proposed model can accurately detect wheat freshness degree.

A Novel Coupled Code Shifted M-ary Differential Chaos Shift Keying Modulation

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.

English

When new data streaming arrives, traditional hashing methods should retrain the hashing functions based on all samples. That leads to high training time complexity. In contrast, the online hashing algorithm re-computes the hashing functions just based on the new arrival streaming data and has been widely applied in large-scale image retrieval tasks. However, differences exist in numbers and labels between new arrival and old datasets, which causes the data imbalance problem while establishing their similarity matrix. This paper proposes a novel supervised online hashing method, Label Projection, based on Hadamard Codes for Online Hashing (LHOH), which jointly employs the label projection and similarity preservation mechanism to solve the data imbalance problem. In addition, LHOH considers the Hadamard codes as the label projection target domains to avoid the problem of difficult discrete optimization of the objective function. Then, LHOH employs the label projection matrix as label weight values, which can solve the data imbalance problem while computing the similarity matrix between new arrival and old datasets and preserve the consistency of Hamming and semantic space similarity. To increase the distinguishability among the hash codes, LHOH designs triple supervision learning mechanisms, including assigning Hadamard codes, projecting labels, and embedding labels. To validate the performance of the proposed LHOH method, this paper sets up the approximate nearest neighbor (ANN) search comparative experiments on two widely used datasets. The final results show that LHOH outperforms six current state-of-the-art online methods.

PERFORMANCE OF MU-MC-DS-CDMA SYSTEM IN RAYLEIGH FADING CHANNEL

The Multi user Multi Carrier Direct sequencing Code Division Multiple Access (MU-MC-DS-CDMA) strategy was developed in response to rising demand for system capacity, higher data rates, and multimedia services. It's essentially a combination of CDMA and OFDM schemes. As a result, MC-CDMA takes the advantages of both CDMA and OFDM technologies. CDMA improves bandwidth consumption performance, whereas OFDM helps to minimize Inter Symbol Interference (ISI) and multipath fading. This dissertation suggests a method for evaluating the performance of multi user MC-DS-CDMA system. BER and PAPR are used to evaluate the results. The Bit Error Rate (BER) output of the proposed method is then examined using MATLAB for various modulation techniques. By using Walsh-Hadamard (W-H) code is used because it eliminates Multiple Access Interference (MAI). In terms of BER, it can be shown that BPSK performs better than QPSK. Key Words: AWGN, BER, ISI, MC-CDMA, Rayleigh Fading Channel, SNR, QPSK, MAI

A Novel Differential Chaos Shift Keying Scheme With Multidimensional Index Modulation

A new differential chaos shift keying scheme with multidimensional index modulation, referred to as MIM-DCSK scheme, is proposed in this paper. This design objective of the proposed MIM-DCSK scheme is to enhance the data rate, energy efficiency, and spectral efficiency of traditional DCSK scheme. In the proposed MIM-DCSK scheme, in addition to the information bits allocated for physical transmission, multidimensional transmission entities, namely the time slot, carrier, and Walsh code are simultaneously considered as indices to convey additional information bits, thus achieving high data rate, spectral efficiency, and energy efficiency. The theoretical bit-error-rate (BER) expressions of the MIM-DCSK scheme are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Furthermore, the data rate, complexity, spectral efficiency, and energy efficiency of the MIM-DCSK scheme are analyzed. Simulation results verify the accuracy of the theoretical analysis and illustrate the superiority of the proposed scheme. The proposed MIM-DCSK scheme is a promising solution for low-power and low-cost short-wireless communications.

Load Estimation Based Dynamic Access Protocol for Satellite Internet of Things

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.

Linearity and classification of [formula omitted]-linear generalized Hadamard codes

The ZpZp2-additive codes are subgroups of Zpα1×Zp2α2, and can be seen as linear codes over Zp when α2=0, Zp2-additive codes when α1=0, or Z2Z4-additive codes when p=2. A ZpZp2-linear generalized Hadamard (GH) code is a GH code over Zp which is the Gray map image of a ZpZp2-additive code. Recursive constructions of ZpZp2-additive GH codes of type (α1,α2;t1,t2) with t1,t2≥1 are known. In this paper, we generalize some known results for ZpZp2-linear GH codes with p=2 to any p≥3 prime when α1≠0, and then we compare them with the ones obtained when α1=0. First, we show for which types the corresponding ZpZp2-linear GH codes are nonlinear over Zp. Then, for these codes, we compute the kernel and its dimension, which allow us to classify them completely. Moreover, by computing the rank of some of these codes, we show that, unlike Z4-linear Hadamard codes, the Zp2-linear GH codes are not included in the family of ZpZp2-linear GH codes with α1≠0 when p≥3 prime. Indeed, there are some families with infinite nonlinear ZpZp2-linear GH codes, where the codes are not equivalent to any Zps-linear GH code with s≥2.