Vectorial Boolean functions and codes are closely related, and each corresponding domain gives been to each other. On the one hand, various requirements of binary linear codes are needed for their theatrical interests but, more importantly, for their practical applicants (such as few-weight codes or minimal codes for secret sharing, locally recoverable codes for storage, etc.). On the other hand, various criteria and tables have been introduced to analyse the security of S-boxes that are related to vectorial Boolean functions, such as the Differential Distribution Table (DDT), the Boomerang Connectivity Table (BCT), and the Differential-Linear Connectivity Table (DLCT). In previous years, two new tables have been proposed for which the literature was pretty abundant: the $c$-DDT to extend the DDT and the $c$-BCT to extend the BCT. In the same vein, we propose extended concepts to study further the security of vectorial Boolean functions, especially the $c$-Walsh transform, the $c$-autocorrelation, and the $c$-differential-linear uniformity, and its accompanying table, the $c$-Differential-Linear Connectivity Table ($c$-DLCT). We study these properties of the novel functions at their optimal level concerning these concepts and describe the $c$-DLCT of the crucial inverse vectorial (Boolean) function case. Finally, the derived functions could lead to new families of binary minimal codes, as the recent achievements on minimal codes from low differential uniformity. We draw new avenues for future research toward linear code designs.

This research highlights the importance of error-correcting codes in ensuring secure and efficient data transmission over noisy channels. It discusses the application of Convolutional codes and the Viterbi algorithm for error detecting and correcting in applications where the data rate is high and the error probability is relatively low. This research extends beyond previous studies by conducting a comparative analysis of Convolutional codes, the Viterbi algorithm, and alternative coding methods utilized in satellite communication systems, by evaluating their effectiveness and efficiency relative to other coding approaches like BCH, LDPC, and turbo codes. The evaluation encompasses key performance metrics including error correction capabilities, computational complexity, and robustness against various error types. Additionally, practical implementation factors such as power consumption, computational requirements, and compatibility with existing hardware are considered. The analysis sheds light on the advantages and disadvantages of each coding method, offering insights into why convolutional codes and the Viterbi algorithm are particularly suitable for GPS systems.

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. Recently, Arikan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. Simulation results show that PAC codes, resulting from the combination of these ideas, are close to finite-length lower bounds on the performance of any code under ML decoding. One of our main goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size $L$ is moderately large (say, $L \geq 128$). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed-Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as $\nu = 2$.

Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine-learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, each decoder specializes in decoding words from a specific region of the channel words' distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high SNRs.

We address security and privacy problems for digital devices and biometrics from an information-theoretic optimality perspective, where a secret key is generated for authentication, identification, message encryption/decryption, or secure computations. A physical unclonable function (PUF) is a promising solution for local security in digital devices and this review gives the most relevant summary for information theorists, coding theorists, and signal processing community members who are interested in optimal PUF constructions. Low-complexity signal processing methods such as transform coding that are developed to make the information-theoretic analysis tractable are discussed. The optimal trade-offs between the secret-key, privacy-leakage, and storage rates for multiple PUF measurements are given. Proposed optimal code constructions that jointly design the vector quantizer and error-correction code parameters are listed. These constructions include modern and algebraic codes such as polar codes and convolutional codes, both of which can achieve small block-error probabilities at short block lengths, corresponding to a small number of PUF circuits. Open problems in the PUF literature from a signal processing, information theory, coding theory, and hardware complexity perspectives and their combinations are listed to stimulate further advancements in the research on local privacy and security.

Good estimators are characterized as robust, unbiased, efficient, and consistent. However, the commonly used estimators are weak or lack one or more of these properties. In this article, eight (8) estimators for statistical and geometrical estimations of symmetry/asymmetry, similarity/dissimilarity, identity/unidentity, and feature transformation were proposed following Kabirian-based optinalysis and other operations. The proposed estimators are characterized as invariant (robust) under scaling, location shift, and rotation or reflection. A computing code was written in python language for each of the proposed estimators so that peers can have working codes for application and performance evaluation.

Medical health systems have been concentrating on artificial intelligence techniques for speedy diagnosis. However, the recording of health data in a standard form still requires attention so that machine learning can be more accurate and reliable by considering multiple parameters. The aim of this study is to develop a general framework for recording diagnostic data in an international standard format to facilitate auto-prediction of eye diseases. Efforts were made to ensure error-free data entry by developing a user-friendly interface. Furthermore, different machine learning algorithms were used to analyze patient data based on multiple parameters, including age, illness history, and clinical observations. This data was formatted according to structured hierarchies designed by medical experts, whereas diagnosis was made as per the ICD-10 coding developed by the American Academy of Ophthalmology. Furthermore, the system is designed to evolve through self-learning by adding new classifications for both diagnosis and symptoms. The classification results from tree-based methods demonstrated that the proposed framework performs satisfactorily given a sufficient amount of data. The random forest and decision tree algorithms predicted more accurately as compared to neural networks and the na{\"i}ve Bayes algorithm owing to structured data arrangement.

Iterative Stochastic decoding is an alternative to standard fixed-point decoding of Low-density parity check codes (LDPC) to reduce inter-node routing. In this paper, we propose a Flexible Field-Programmable Gate Array (FPGA)-Based Stochastic decoding (SD) hardware architecture for LDPC codes in the Fifth-Generation (5G) New Radio (NR) Standard that supports decoding of set of various code rates. This decoder’s runtime flexibility is desirable to switch a better performing code rate automatically based on the channel conditions without the extra time needed for reprogramming of FPGA. An offline design method is implemented to generate the hardware description language (HDL) code description of the decoder for the required code-rate set, which is further synthesized and integrated into the Xilinx Kintex-7 series FPGA board to determine the hardware resource utilisation and processing throughput. The Synopsys design tools were employed during both the simulation and synthesis stages, in combination with TSMC 65-nm CMOS standard cell technology, to facilitate comparative analysis. Compared with state-of-the-art designs, the proposed architecture reduces hardware utilization by up to 26% and achieved energy efficiency by 52%.

Bamboo is the building material of the past and future. It offers numerous properties that make it versatile for various applications, including construction. Its impressive strength-to-weight ratio enables it to bear substantial loads and stresses, while its good elasticity allows efficient energy absorption. However, its mechanical properties can vary based on factors such as species, age, locations, methods, and treatment. Treating bamboo is essential to enhance its properties and durability. The literature provides various natural and chemical treatments which enhanced some of the properties but also reported a drawbacks on higher temperature, content and duration. This paper reviewed 57 articles from Scopus database, specifically focusing on article-document type publications from the years 2003 to 2023. Additional references were also incorporated to address concerns in properties, treatment and standards to provide systematic understanding. MATLAB was utilized for data text analytics. With extensive assessment on the articles, the following gaps and concerns were observed and recommends for further study and assessment such as for bamboo properties, the development of centralized guidelines and procedures for the preparation and processing; exploration of alternative materials to reinforce bamboo without compromising its ductility; development of joint connections, and testing of mechanical properties considering seismic, wind and vibration. For treatment methods, the standardization of procedures using natural, chemical or combination. Lastly, for bamboo codes and standards, assessment of existing codes and standards for testing the mechanical properties of bamboo highlighting the potential limitations and areas, uniformity, differences with all existing similar standards. By filling these gaps, it can support the reliability and robustness of bamboo as a sustainable material, fostering its promotion and adoption in construction industry.

The paper investigates new robust code constructions based on bent functions and spline–wavelet transformation. Implementation of bent functions in codes construction increases the probability of error detection in the data channel and cryptographic devices. Meanwhile, use of spline–wavelets theory for constructing the codes gives the possibility to increase system security from the actions of an attacker. Presented constructions combines spline–wavelets functions and bent functions. Developed robust codes, compared to existing ones, have a higher parameter of maximum error masking probability. Illustrated codes are ensuring the security of transmitted information. Some of the granted constructions were implemented on FPGA.

The conceptual and theoretical backbones of symmetry/asymmetry detections or similarity/dissimilarity, and identity/unidentity study are automorphism or isomorphism respectively. However, the development of equations and methods for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures deviates from these backbones. In this article, an equation was proposed for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures, and proved that its isoreflective pairs-points are functionally bijective and inverse. The proposal, called Kabirian-based optinalysis, is based on the conceptual and theoretical frameworks of automorphism and isomorphism. The Kabirian-based optinalysis is also proven and characterized as invariant (robust) under translation (i.e., scaling and location shift), and rotation or reflection. Computing codes were written in python language for Kabirian-based optinalysis to serve as working codes for application and verification.

The Indorama Eleme Petrochemical Limited (IEPL) is found in the southern part of Nigeria more specifically on the Rivers State southern religion Nigeria. It consists of five distinct units, each of which generates its own unique trash at a rate of around 3115.98 tonnes per year. This study had the goal of concentrating on the management of the processing wastes in order to minimize the negative effects that they have on the environment. It is necessary to have an understanding of the number, nature, and make-up of IEPL's industrial wastes in order to effectively manage and regulate the development of waste there. As a result, we decided to collect data through the use of questionnaires. The classification of industrial wastes was accomplished by doing a comparative study and synthesis of research that were relevant to the management of petrochemical waste. Because an individual coding system is required for the integrated management of industrial waste, we gave each type of trash a code that consists of thirteen digits. The primary components of trash were catalysts (9.58 percent), metallic materials (7.62 percent), plastic barrels (35.77 percent), coke (12.66 percent), wood (4.47%), oil (4.15%), glass (0.028 percent), cooling tower packaging (6.7 percent), and other material (18.83 percent). According to the findings of the investigation into the physical qualities of the wastes, only 11.81% of these residues were liquid, while 88.19% were solid. The current handling of these wastes has been experiencing significant difficulties as of late. garbage management at IEPL was particularly challenging due to the wide variety of wastes produced there and the dangerous nature of the wastes themselves (88.19% of garbage was hazardous waste). Recycling and reuse of garbage may have been the greatest decision in some situations; yet, incineration and disposal of waste are also necessary options.

The digital representation of various signals allows, at the subsequent stages of their transmission, to apply correction codes that provide protection against possible errors arising from the action of interference in the communication channel. At the same time, it is important that, with the required correcting ability, these codes have the maximum possible speed. The article presents the results of calculations for linear codes, showing their really achievable limiting capabilities.

The origin of the genetic code is the key to revealing the origin of life on Earth, as it is a prerequisite for the existence of life. More than half a century has passed since the discovery of the genetic code, but its origin is still one of the greatest mysteries. Is the origin of the genetic code truly unknowable? Does the code truly require external design? Here, a hypothesis is proposed, according to which ATP is at the origin of the genetic code by its coevolution with the pristine biochemical system. ATP has several properties that make it suitable as a plausible initiator of the genetic code. First, ATP is the only energetic product of photosynthesis. Second, ATP is at the heart of the extant biochemical systems. Third, ATP serves as a carrier of both energy and information. Fourth, ATP could energetically elongate chains of both polynucleotides and polypeptides, thus providing a bridge between these molecules and eventually mediating prebiotic biochemical innovation from energy transformation to informatization. This hypothesis shows how primitive life emerged through a series of processes from energy to information flow mediated by ATP. Informatization (processes for creating and managing information) was inevitably coupled with structuralization (processes for organizing or incorporating cellular structures), cyclizing polynucleotides and polypeptides into a feedback loop of reciprocal causation. The triplet codon might be only for stereochemical handling of amino acids through, e.g., Watson–Crick pairing interactions. It is only the evolutionary completion of the genetic code from RNA to DNA that, contrary to the central dogma, marked the dawn of cellular life, when Darwinian evolution began to operate. The ATP hypothesis sheds light on the origin of life, together with the formation of both photosynthetic and biochemical systems, which remains largely unknown thus far.

We consider a coded compressed sensing protocol for unsourced massive random access (URA) that concatenates a shared Patterned Reed-Muller (PRM) inner codebook to an outer error-correction code. In this paper, an iterative list PRM projection algorithm is proposed to supplant the signal detector associated with the inner PRM sequences. In particular, we first propose an enhanced paths-saving algorithm called list PRM projection detection for the single-user scenario that keeps multiple candidates for the first few layers to remedy the risk of spreading errors. On this basis, we further propose an iterative list PRM projection algorithm for the multi-user scenario. The vectors for PRM codes and channel coefficients are jointly detected in an iterative manner, which offers significant improvements regarding the convergence rate for signal recovery. Furthermore, the performances of the proposed algorithms are analyzed mathematically, and we verified that the theoretical simulations are consistent with the numerical simulations. Finally, we concatenate the inner PRM codes that employ the iterative list detection to two practical error-correction outer codes. According to the simulation results, we conclude that the packetized URA with the proposed iterative list projection detection works better than benchmarks in terms of the number of active users it can support in each slot and the amount of energy needed per bit to meet an expected error probability.

Information theory is widely used in various disciplines, and effective calculation of Shannon mutual information is typically not an easy task for many practical applications, including problems of neural population coding in computational and theoretical neuroscience. Asymptotic formulas based on Fisher information may provide accurate approximations to mutual information but this approach is restricted to continuous variables because the calculation requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations based on Kullback-Leibler divergence and Rényi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding, and these asymptotic formulas hold true for discrete variables as there is no requirement for differentiability. In particular, one of our approximation formulas has consistent performance and good accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating mutual information between the discrete variables or stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.

The Victorian Government Inquiry into wildfires that killed 173 people in 2009 has driven an Australian policy shift from self-evacuation or staying and defending a well-prepared property (‘go or stay’) to self-evacuation under catastrophic fire weather (‘leave early’). The Inquiry also led to the establishment of national ‘performance standards’ for Private Fire Shelters (PFS, that also known as bunkers). Nonetheless, incorporation of PFS into national bushfire policy remains embryonic with only Victoria having streamlined accreditation and planning approval processes. Arguments against PFS include potentially engendering complacency about preparing dwellings to survive fire and encourage risky behavior in response to a fire threat. Counteracting these arguments is research that shows that residents without PFS have low engagement with bushfire preparation and typically delay evacuation. In any case, because wildfire is unpredictable it is accepted that self-evacuation plans must have fallback positions that include sheltering ‘in place’ from the bushfire, making properly used and well maintained PFS an important element of bushfire safety. A less discussed barrier to PFS uptake outside Victoria appears to hinge on a lack of clarity about obligations for their design, certification, and consistency with planning approvals. The escalating Australian fire crisis demands much greater research and development in legal frameworks, policy and planning processes for PFS, as well as design and construction standards.

The aim of this study was to evaluate the acceptability and feasibility of a theory-derived sedentary workplace intervention (single arm, pre-post design) for police office staff. Twenty-four staff participated in an 8-week intervention incorporating an education session, team competition with quick response (QR) codes, team trophy, and weekly leaderboard newsletters, a self-monitoring phone app, and electronic prompt tools. The intervention supported participants to reduce and break up their sitting time with three minutes of incidental movement every 30 minutes at work. Feasibility and acceptability were assessed using mixed methods via the RE-AIM QuEST and PRECIS-2 frameworks. The intervention was highly pragmatic in terms of eligibility, organisation, adherence, outcome, and analysis. It was slightly less pragmatic on recruitment and setting. Delivery and follow-up were more explanatory. Reach and adoption indicators demonstrated feasibility among police staff, across a range of departments, who were demographically similar to participants in previous office-based multi-component interventions. The intervention was delivered mostly as planned with minor deviations from protocol (Implementation fidelity). Participants perceived the intervention components as highly acceptable. Preliminary results showed improvements in workplace sitting and standing, as well as small improvements in weight and positive affect. Evaluation of the intervention in a fully powered randomised controlled trial to assess behaviour and health outcomes is recommended.

This article is devoted to the problem of genetically coding of inherited cyclic structures in biological bodies, whose life activity is based on a great inherited set of mutually coordinated cyclic processes. The author puts forward and arguments the idea that the genetic coding system is capable of encoding inherited cyclic processes because it itself is a system of cyclic codes connected with Boolean algebra of logic. In other words, the physiological processes in question are cyclical because they are genetically encoded by cyclic codes. In support of this idea, the author presents a set of his results on the connection of the genetic coding system with cyclic Gray codes, which are one of many known types of cyclic codes. This opens up the possibility of using for modeling inherited cyclic biostructures those algebraic and logical theories and constructions that are associated with Gray codes and have long been used in engineering technologies: Karnaugh maps, Hilbert curve, Hadamard matrices, Walsh functions, dyadic analysis, etc. Additionally, the connections of these constructions with statistical rules of genomic DNAs and binary-genomic numbers are considered.

Appropriate estimation of soil settlement is of significant importance since it directly influences the performance of building and infrastructures that are built on soil. In particular, the settlement of fine-grained soils is critical because of low permeability and continuous settlement with time. Coefficient of consolidation (Cc) is a key parameter to estimate settlement of fine-grained soil layers. However, estimation of this parameter is time consuming, needs skilled technicians, and specific equipment. In this study, Cc was estimated using several soil parameters such as liquid limit (LL), plastic limit (PL), and initial void ratio (e0). Estimating such parameters in laboratory is straight forward and needs substantially less time and cost compared to conventional tests to estimate Cc such as Oedometer test. This study presents a novel prediction model for Cc of fine-grained soils using gene-expression programming (GEP). GEP is a biologically inspired technique capable of offering closed-form solution for the optimal solution. A database consisted of 108 different data points was used to develop the model. A closed-form equation solution was derived to estimate Cc based on LL, PL, and e0. The performance of developed GEP-based model was evaluated through coefficient of determination (R2), root mean squared error (RMSE), and mean average error (MAE). High R2 and low error values indicated the descent performance of the model. Furthermore, the model was evaluated using the additional performance measures and met all the suggested criteria. Furthermore, the model had a better performance in terms of R2, RMSE, and MAE compared to most of existing models. It is expected that the developed model will decrease the time and cost associate with determining Cc of fine-grained soils.

Appropriate estimation of soil settlement is of significant importance since it directly influences the performance of building and infrastructures that are built on soil. In particular, the settlement of fine-grained soils is critical because of low permeability and continuous settlement with time. Coefficient of consolidation (C_c) is a key parameter to estimate settlement of fine-grained soil layers. However, estimation of this parameter is time consuming, needs skilled technicians, and specific equipment. In this study, C_c was estimated using several soil parameters such as liquid limit (LL), plastic limit (PL), and initial void ratio (e₀). Estimating such parameters in laboratory is straight forward and needs substantially less time and cost compared to conventional tests to estimate C_c such as oedometer test. This study presents a novel prediction model for C_c of fine-grained soils using gene-expression programming (GEP). GEP is a biologically inspired technique capable of offering closed-form solution for the optimal solution. A database consisted of 108 different data points was used to develop the model. A closed-form equation solution was derived to estimate C_c based on LL, PL, and e₀. The performance of developed GEP-based model was evaluated through coefficient of determination (R²), root mean squared error (RMSE), and mean average error (MAE). High R² and low error values indicated the descent performance of the model. Furthermore, the model was evaluated using the additional performance measures and met all the suggested criteria. Furthermore, the model had a better performance in terms of R², RMSE, and MAE compared to most of existing models. It is expected that the developed model will decrease the time and cost associate with determining C_c of fine-grained soils.Keywords: evolutionary model, gene-expression programming (GEP), prediction, soil compression index, estimation, soil engineering, soil informatics, civil engineering, machine learning, data science, big data, soft computing, deep learning, forecasting, subject classification codes, construction informatics, computational intelligence (CI), artificial intelligence (AI), estimation