Correction Codes Research Articles

Assessment of chemistry knowledge in large language models that generate code.

In this work, we investigate the question: do code-generating large language models know chemistry? Our results indicate, mostly yes. To evaluate this, we introduce an expandable framework for evaluating chemistry knowledge in these models, through prompting models to solve chemistry problems posed as coding tasks. To do so, we produce a benchmark set of problems, and evaluate these models based on correctness of code by automated testing and evaluation by experts. We find that recent LLMs are able to write correct code across a variety of topics in chemistry and their accuracy can be increased by 30 percentage points via prompt engineering strategies, like putting copyright notices at the top of files. Our dataset and evaluation tools are open source which can be contributed to or built upon by future researchers, and will serve as a community resource for evaluating the performance of new models as they emerge. We also describe some good practices for employing LLMs in chemistry. The general success of these models demonstrates that their impact on chemistry teaching and research is poised to be enormous.

A Revisit of Linear Network Error Correction Coding

A Revisit of Linear Network Error Correction Coding

КОМПЛЕКСНИЙ АНАЛІЗ ВЛАСТИВОСТЕЙ КОДУ ХЕММІНГА В СУПЕРПОЗИЦІЇ ТЕОРІЙ КОДУВАННЯ, ЗАВАДОСТІЙКОСТІ ТА ІНФОРМАЦІЇ

In the modern era, the task of transferring and preserving information is extremely important. Errors can often occur when data is transmitted over channels with interference or when it is stored on an unreliable medium. Scientific studies of the properties of electrical signals, which are information carriers in electronic communication systems, traditionally have three directions: the theory of immunity, the theory of information, and the theory of probability. Each of these theories has its own historical lineage, outstanding achievements and untapped potential. But the peculiarity of these studies is that more often they are implemented independently of each other, using their own set of initial parameters, criteria and performance indicators, quantitative characteristics. The article examines the properties of Hamming codes, which have been actively used in practice for more than 70 years, in the context of determining their most effective area of use in various fields. The specific interest in Hamming codes is also caused by the fact that they have a unique property: they are - according to the classical definition - perfect codes. The difficulty lies in the fact that the concept of "the most effective area of use" in each of the mentioned theories is special, therefore, a comprehensive analysis of the properties of the Hamming code in the superposition of the theories of coding, immunity and information is a relevant and interesting research task. From the standpoint of coding theory, Hamming codes have the same correcting ability - they correct only one error in a block. After all, as the length of the block n increases, the redundancy decreases. At the same time, the degree of closeness of the Hamming codes to the Plotkin limit increases. Therefore, preference according to these criteria should be given to Hamming codes with the largest block length n. From the standpoint of the theory of immunity, the best is the code that provides the best correction indicators at the smallest value of the data transmission channel parameter h2 (signal/noise ratio) under the conditions of ensuring the required reliability. Compared to the case of no coding, the shortest code – the Hamming code (7,4) – gives the greatest gain. From the point of view of information theory, the transmission of signals using Hamming codes requires speed correction (acceleration) in the communication channel in order to prevent the loss of source symbols due to the redundancy of the correction code. At the same time, the advantage of the Hamming code (7,4) over other, longer codes remains. According to the integral indicator - the energy costs to achieve the required reliability without losing the speed of information transmission from the source - preference should be given to the Hamming code with parameters (7, 4) with a gain in the signal-to-noise ratio Δh2 = 2.72 dB compared to the case without coding.

Разработка математической модели отказоустойчивого преобразователя invsubbytes в полиномиальной системе классов вычетов

The article is devoted to the issue of improving the fault tolerance of the InvSubBytes procedure of SPN converters. Describes the possibility of applying a corrective code in a polynomial system of residue classes as a tool for detecting and eliminating the consequences of failures in the operation of replacement blocks.

A VHDL Code for Offset Pulse Position Modulation Working with Reed Solomon System by Using ModelSim

Error correction codes, often known as ECC, play a significant part in the process of detecting and correcting data mistakes that occur through communication channels that are unreliable or noisy. The essential concept behind error correction through ECC is to supplement the message that is being sent by the transmitter with redundant bits, the values of which are determined by the parameters n and k. These bits can then be utilized by the receiver to identify and correct specific types of errors. ECC is utilized in a wide variety of applications, including but not limited to data storage, the Internet, and telecommunications. There are numerous variations of ECC, including linear block, convolutional, and turbo codes, among others. The results of a simulation of a linear block reed Solomon, for example, with offset pulse position modulation have been presented in this study. The simulation was carried out in very high-speed integrated circuit hardware description language (VHDL), and a field-programmable gate array was used (FPGA) It made use of a Boolean function to function to program code for an algorithm that is working. Because of its performance, time to market, cost, reliability, and long-term maintenance benefits, FPGA is an appropriate platform for implementing error correction code (ECC). As a part of this project, the technique of offset Pulse Position Modulation (Offset PPM) was invented as an outstanding solution to code the fiber-optic applications and Reed Solomon (RS) codes apply to ModelSim SE-64 10.5 software. In addition, this coding scheme has been approved by the simulation and is matched with theory, and it is expected to be implemented shortly. The study begins with a concise introduction to RS encode/decode about design and performance and then moves on to discuss the development result of simulation and hardware implementation.

Development of a Shorted Interleaved Reed-Solomon Codes (siRS) for data downlink in Stratospheric Probes and Nano-Satellites

In the last 10 years, the advancement in the electronics have made possible the development of more sophisticated unmanned vehicles and probes, manufactured using Components-Of-The-Shelf (COTS) available to public, whether be for industrial of scientific purposes. In the matter of aerospace exploration, the CubeSats are the best example of sophisticated devices partially of entirely developed using this commercial COTS. The financial cost of some components is still a point of consideration in the design, but it is not entirely a show-stopper since some low-cost components can be optimized to meet the necessary requirements and increase the reliability. In the case of stratospheric probes and nano-satellites, the Telemetry, Tracking and Command (TT&C) subsystem, in charge of the data uplink/ downlink, can be improved by including an Error Correcting Code (ECC), making possible to use commercial transceivers of low-power are low-cost. In this article we describe an implementation of an interleaved and shortened Reed-Solomon Code, which we called siRS, to improve the image and telemetry downlink in stratospheric probes and nano-satellites, using entirely low-cost commercial RF transceivers and an ARM-based mini-PC.

Decoding of linear codes for single error bursts correction based on the determination of certain events

Introduction: In modern systems for communication, data storage and processing the error-correction capability of codes are estimated for memoryless channels. In real channels the noise is correlated, which leads to grouping error in bursts. A traditional method to fight this phenomenon is channel decorrelation, which does not allow developing of coding schemes, mostly utilizing the channel capacity. Thus the development of bursts decoding algorithms for arbitrary linear codes is the actual task. Purpose: To develop a single error burst decoding algorithm for linear codes, to estimate the decoding error probability and computational complexity. Results: Two approaches are proposed to burst error correction. The first one is based on combining the window sliding modification of well-known bit-flipping algorithm with preliminary analysis of the structure of parity check matrix. The second one is based on the recursive procedure of constructing the sequence of certain events which, in the worst case, performs the exhaustive search of error bursts, but in many cases the search may be significantly decreased by using the proposed heuristics. The proposed recursive decoding algorithm allows a guaranteed correction of any single error bursts within burst-correction capability of the code, and in many cases beyond the burst-correction capability. The complexity of this algorithm is significantly lower than that of a bit flipping algorithm if the parity-check matrix of the code is sparse enough. An alternative hybrid decoding algorithm is proposed utilizing the bit-flipping approach and showing the error probability and completion time comparable to the recursive algorithm, however, in this case the possibility of a guaranteed burst correction hardly can be proved. Practical relevance: The proposed decoding methods may be used in modern and perspective communication systems, allowing energy saving and increasing reliability of data transmission by better error performance and computational complexity.

Relaxed Locally Correctable Codes with Nearly-Linear Block Length and Constant Query Complexity

Locally correctable codes (LCCs) are codes C: Σk → Σn which admit local algorithms that can correct any individual symbol of a corrupted codeword via a minuscule number of queries. One of the central problems in algorithmic coding theory is to construct O(1)-query LCC with minimal block length. Alas, state-of-the-art of such codes requires exponential block length to admit O(1)-query algorithms for local correction, despite much attention during the last two decades. This lack of progress prompted the study of relaxed LCCs, which allow the correction algorithm to abort (but not err) on small fraction of the locations. This relaxation turned out to allow constant-query correction algorithms for codes with polynomial block length. Specifically, prior work showed that there exist O(1)-query relaxed LCCs that achieve nearly-quartic block length n = k4+α, for an arbitrarily small constant α > 0. We construct an O(1)-query relaxed LCC with nearly-linear block length n = k1+α, for an arbitrarily small constant α > 0. This significantly narrows the gap between the lower bound which states that there are no O(1)-query relaxed LCCs with block length n = k1+o(1). In particular, this resolves an open problem raised by Gur, Ramnarayan, and Rothblum (ITCS 2018).

Implementation of Error Correction on IBM Quantum Computing Devices

Quantum noise cannot be avoided in the quantum computing devices due to unstable nature of qubits and signals. The error caused by quantum noise can be detected and corrected using different error correcting codes. In this work, we have tested the feasibility and accuracy of three qubit bit flip and phase flip error correcting code in quantum computer provided by International Business Machine Quantum Experience (IBM QX) cloud platform. Among five quantum processors, ibmq_ourense is found to have highest average accuracy 77.9% ± 3.09% on all qubits simultaneously. Three qubits bit flip error correction circuit gave correct output 89.9% ± 1.01% of the time on average. Similarly three qubits phase flip error correction circuit give 88.05% ±1.89%. The measurement error mitigation has improved the accuracy of bit flip and phase flip error correction code by 5.01% and 7.01% respectively on average. The error rate shows that the error in quantum computations are random in nature and can be corrected. IBM QX quantum computer are suitable for only small scale quantum computation and demonstrate purpose. Furthermore, the accuracy of error correction codes can be increased with the use of higher accuracy quantum qubits and quantum gates.

Historical and legal conditions of functioning and evolution of criminal correspondence institutions in the Ukrainian SSR

Purpose. The purpose of the study is to determine the historical and legal conditions for the development of penal institutions in the Soviet period, their evolution in the context of the transformation of correctional labor legislation, as well as the main types of violations of the rights of persons who served sentences. Methods. The methodological basis of the research was a complex of general scientific, special scientific and philosophical methods, as well as the principles of historicism and objectivity. Results. It has been established that in relation to the Soviet criminal-executive system, it is expedient to apply the concept of the penal-correctional system, because from the first years of the formation of Soviet power, the maintenance of persons serving punishment was carried out primarily in labor colonies, and physical labor was understood as the main and effective way of atonement. The first legal act regulating the penal system was adopted on October 23, 1925, the Correctional Labor Code of the USSR, which established the priority of educational tasks for prisoners and the idea of correction of convicts. The Central Directorate of Correctional Labor Camps and Labor Settlements of the NKVD («GULAG») became a certain symbol of Soviet power and a vivid example of the fact that the penal system was totalitarian. Throughout June 1941, we can talk about deliberate acts of terror and mass murders of prisoners in correctional facilities in Western Ukrainian regions. The post-war penal system was a combination of correctional labor colonies, separate camps (detention for a term of three years or more), labor colonies for minors, prisons, and transit and transfer points. The last normative-legal act that consolidated the structure of the Soviet criminal-executive system was adopted in 1970 «Correctional Labor Code of the Ukrainian SSR». Originality. The main stages of the development of the criminal correctional system of the Ukrainian SSR, as well as the historical and legal conditions for the emergence of criminal correctional institutions, have been established. Practical significance. The results of the research can be used in the process of historical and legal research, preparation of special courses.

Construction Technique and Evaluation of High Performance t-bit Burst Error Correcting Codes for Protecting MCUs

The occurrences of Multiple Cell Upset (MCU) are more liable to arise in modern memory systems with the continuous upgradation of microelectronics technology from micron to deep submicron scales. These MCUs are mainly induced due to radiations in memory systems. Error Correcting Codes (ECCs) with lower design complexity are generally preferred for the mitigation of MCUs. The major drawback of the existing ECC is requiring higher overheads as error correction capability increases. In this paper, authors have proposed a new class of high performance [Formula: see text]-bit Burst Error Correcting (BEC) codes. Parity check matrices ([Formula: see text]) have been proposed for 3-bit and 4-bit BEC codes with word lengths of 16-bit, 32-bit and 64-bit. Also a simplified decoding scheme has been introduced for these codes. The proposed codecs have been designed and implemented in FPGA and ASIC platforms. The proposed codecs are compact in area, faster in speed and efficient in power compared to existing related schemes. But these lower design constrains are achieved at the cost of increase in redundancy. So, the proposed codecs can be employed in applications where redundancy is not the only constrain for correcting [Formula: see text]-bit burst errors caused by MCUs.

VLSI Implementation of Multi-Bit Error Detection and Correction Codes for Space Communications

VLSI Implementation of Multi-Bit Error Detection and Correction Codes for Space Communications

Laser Induced Single Event Upset (SEU) Testing of Commercial Memory Devices with Embedded Error Correction Codes (ECC)

Results of laser-induced single event upset testing of devices with embedded error correction codes are described. Specifically, the memory system, consisting of a Micron MT41K256M16TW-107 IT: P 32 Meg×16×8 banks Dual Dynamic Random Access Memories (DDRs) was tested on a self-made test board. Two samples of each memory system or device type were irradiated with a pulsed laser. The units were irradiated by using a continual read/write correct loop in several bit patterns. Results for both correctable and uncorrectable errors are presented along with soft error data records.

Quantum Teleportation Error Suppression Algorithm Based on Convolutional Neural Networks and Quantum Topological Semion Codes

Quantum error correction (QEC) is a key technique for building scalable quantum computers that can be used to mitigate the effects of errors on physical quantum bits. Since quantum states are more or less affected by noise, errors are inevitable. Traditional QEC codes face huge challenges. Therefore, designing an error suppression algorithm based on neural networks (NN) and quantum topological error correction (QTEC) codes is particularly important for quantum teleportation. In this paper, QTEC codes: semion codes—a greater than 2 dimensional (2D) error correction code based on the double semion model—are used to suppress errors during quantum teleportation, using a NN to build a decoder based on semion codes and to simulate the quantum information error suppression process and the suppression effect. The proposed convolutional neural network (CNN) decoder is suitable for small distance topological semion codes. The aim is to optimize the NN for better decoder performance while deriving the relationship between decoder performance and slope and pseudothreshold during training and calculate the thresholds for different noise areas when the code distances are the same, P t h r e s h o l d = 0.082 for A r e a < 0.007 d B and P t h r e s h o l d = 0.096 for A r e a < 0.01 d B . This paper demonstrates the ability of CNNs to suppress errors in quantum transmission information and the great potential of NNs in the field of quantum computing.

Combating Errors in Propagation of Orbital Angular Momentum Modes of Light in Turbulent Media

There is a wealth of simulation, experimental and analytical studies on propagation of orbital angular momentum (OAM) modes through atmospheric and oceanic turbulence.} Using the data of these studies and generalising the framework proposed in [Bala et al., [arXiv:2208.04555] for error-immune information transfer, we accomplish two tasks. First, we identify invariants for propagation of OAM modes through atmospheric and oceanic turbulence, in which error-immune information can be encoded. A closer look at the data reveals two universal features: (i)coherence lasts for a much longer distance in turbulence than entanglement, and, (ii) the crosstalk among different OAM modes depends very weakly on the initial OAM mode index in the weak turbulence regime. Keeping these in mind, we next develop a method for combating errors in what we call an idealised crosstalk channel. In an idealised crosstalk channel, the crossover probabilities are independent of the initial mode index (IMI). We lay down a procedure that allows to retrieve full information in a state by identifying invariant quantities. Finally, we construct quantum error correction and rejection codes for idealised crosstalk channels, without any need for multiparty entanglement.

Triage Grading and Correct Diagnosis Are Critical for the Emergency Treatment of Anaphylaxis.

Anaphylaxis is one of the most frequent and misdiagnosed emergencies in the pediatric emergency department (PED). We aimed to assess which factors play a major role for a correct diagnosis and an appropriate therapy. We reviewed the records of children discharged with a diagnosis of anaphylaxis or an allergic reaction over 11 years from 3 hospitals in the Bologna city area. One hundred and sixteen cases matched the criteria (0.03% of the total admittances) and were divided according to the patients' symptoms at arrival: active acute patients [AP], n = 50, or non-acute patients ([NAP], n = 66). At the patients' discharge, anaphylaxis was diagnosed in 39 patients (33.6%). Some features seemed to favor a correct diagnosis: active symptoms at arrival (AP vs. NAP, p < 0.01), high-priority triage code (p < 0.01), and upper airway involvement (p < 0.01). Only 14 patients (12.1%), all in the AP group, received epinephrine, that was more likely administered to patients recognized to have anaphylaxis (p < 0.01) and with cardiovascular, respiratory, or persistent gastrointestinal symptoms (p < 0.02), as confirmed by logistic regression analysis. Anaphylaxis is still under-recognized and under-treated. Correct triage coding and a proper diagnosis seem to foster an appropriate treatment. Physicians often prefer third-line interventions. Specific training for nurses and physicians might improve the management of this disease.

Rectangle stabbing and orthogonal range reporting lower bounds in moderate dimensions

We study the orthogonal range reporting and rectangle stabbing problems in moderate dimensions, i.e., when the dimension is clog⁡(n) for some constant c. In orthogonal range reporting, the input is a set of n points in d dimensions, and the goal is to store these n points in a data structure such that given a query rectangle, we can report all the input points contained in the rectangle. The rectangle stabbing problem is the “dual” problem where the input is a set of rectangles, and the query is a point.Our main result is the following: assume using S(n) space, we can solve either problem in d=clog⁡n dimensions, c≥4, using Q(n)+O(t) time in the pointer machine model of computation where t is the output size. Then, we show that if the query time is small, that is, Q(n)=n1−γ, for γ≥22+log⁡c, then the space must be Ω(n1−γncγ/e−o(cγ)). Interestingly, we obtain this lower bound using a non-constructive method, and we show the existence of some codes that generalize a specific aspect of error correction codes. Our result overcomes the shortcomings of the previous lower bounds in the pointer machine model for non-constant dimension [3–5,13], as the previous results could not be extended for d=Ω(log⁡n).The only known lower bounds for rectangle stabbing, when the dimension is non-constant, are based on conditional lower bounds upon the best-known results on CNF-SAT [21]. Therefore, our lower bound is the first non-trivial unconditional lower bound for orthogonal range reporting and rectangle stabbing with non-constant dimension.

New low power and fast SEC-DAEC and SEC-DAEC-TAEC codes for memories in space application

Multiple cell upset (MCU) caused by cosmic radiation is a serious issue related to the reliability of static random access memories (SRAMs) in space application. Due to radiation, single cell or multiple cells of a memory are corrupted. The chances of errors in more than one memory cells are also increasing due to continuous down scaling of technology. Single error, double or triple adjacent errors are most common in this case. Several error correction codes are already introduced for protecting the memories. But many existing error correcting codes have either higher delay and/or power consumption and/or decoder error rate. In this paper, we have introduced 16-bit, 32-bit and 64-bit information length, uniquely decodable single error correction-double adjacent error correction (SEC-DAEC) and single error correction-double adjacent error correction-triple adjacent error correction (SEC-DAEC-TAEC) codes with lower power consumption and delay. In our design, same H-matrix is used for implementing both SEC-DAEC and SEC-DAEC-TAEC codes. Both FPGA and ASIC based synthesis results show that proposed SEC-DAEC and SEC-DAEC-TAEC codes with dimensions (24, 16), (41, 32) and (75, 64) are better compared to existing same dimension codes with respect to area, power and delay. Since, the proposed SEC-DAEC and SEC-DAEC-TAEC codes have low encoder and decoder delay which corresponds to low writing and reading time, consume significantly low power and have zero decoder error rate, so proposed codec can be used for memories in space application.

Imaging Stars with Quantum Error Correction

The development of high-resolution, large-baseline optical interferometers would revolutionize astronomical imaging. However, classical techniques are hindered by physical limitations including loss, noise, and the fact that the received light is generally quantum in nature. We show how to overcome these issues using quantum communication techniques. We present a general framework for using quantum error correction codes for protecting and imaging starlight received at distant telescope sites. In our scheme, the quantum state of light is coherently captured into a nonradiative atomic state via stimulated Raman adiabatic passage, which is then imprinted into a quantum error correction code. The code protects the signal during subsequent potentially noisy operations necessary to extract the image parameters. We show that even a small quantum error correction code can offer significant protection against noise. For large codes, we find noise thresholds below which the information can be preserved. Our scheme represents an application for near-term quantum devices that can increase imaging resolution beyond what is feasible using classical techniques.

Tinjauan Ketepatan Kode Diagnosis Pada Kasus Bedah Pasien Rawat Inap di RSKD Duren Sawit

Based on Kenmenkes RI in 2014, it explains about coding which has the meaning as an activity of providing main diagnosis codes and secondary diagnoses in accordance with ICD-10 and providing procedure codes in accordance with ICD-9CM. Coding inaccuracies can affect the financing of health services, this study was conducted to see the accuracy of the main and secondary diagnosis codes of surgical cases of inpatients at Duren Sawit Hospital using descriptive research methods with a quantitative approach, namely writing aims to describe the results obtained on the accuracy of diagnosis codification. Informants in this study were inpatient coders at RSKD Duren Sawit, data collection in this study using interviews and observation methods. The results of this study indicate that the coding SPO uses the latest procedures based on an electronic system, the educational background of the coder at RSKD Duren Sawit has an important role in the quality of the correct code. The competence of the coder at RSKD Duren Sawit still has to undergo deeper learning, in the results of coding research on surgical cases of inpatients, it was found that the average dignosis code that had accuracy was 58 (63.74%) and 33 (36.26%) were inappropriate, and it was also found that the results of the accuracy of the secondary diagnosis were 84 (92.30%) and 7 (7.70%) were inappropriate. Based on the 4 characters, the inaccuracy occurred in the main diagnosis of the majority in the 4th character as many as 31 (34.7%). There are factors that become obstacles to the identification of 5M, namely the man factor, the lack of accuracy of doctors in inputting diagnoses and the lack of accuracy of officers in re-examining incorrect diagnosis codes and having to undergo learning related to coding more deeply for diagnosis coding officers who are not from academic graduates of medical records.