Implementation of the hamming code on pascalabc.net while studying the theoretical foundations of informatics

Theoretical Foundations of Informatics is a classic branch of discrete mathematics taught to students in various information, mathematical and technical fields. The presentation of the material is mainly carried out using matrix algebra. This article describes a methodology for teaching the topic of error correcting coding to pedagogical university students as part of the course on theoretical foundations of informatics and considers an algorithm for obtaining a Hamming code through a tabular template. An original implementation of the considered algorithm in PascalABC. NET is proposed. When writing code, modern techniques are used: dynamic arrays, slices, safe slices, conditional (ternary) operation, foreach loop, sequence methods, lambda expressions, tuples, documenting comments, etc. The functions of the School module from the official delivery of the PascalABC.NET compiler are used to work with binary numbers. The described methodology has been tested in teaching 4-year students of the pedagogical direction, the profile "Mathematics and Informatics" of the Orenburg State Pedagogical University and has shown its applicability. In addition, it is possible to use the proposed approach for teaching schoolchildren at a specialized level or in extracurricular work.

Design of Extended Hamming Code Technique Encryption for Audio Signals by Double Code Error Prediction

Noise can scramble a message that is sent. This is true for both voicemails and digital communications transmitted to and from computer systems. During transmission, mistakes tend to happen. Computer memory is the most commonplace to use Hamming code error correction. With extra parity/redundancy bits added to Hamming code, single-bit errors may be detected and corrected. Short-distance data transmissions often make use of Hamming coding. The redundancy bits are interspersed and evacuated subsequently when scaling it for longer data lengths. The new hamming code approach may be quickly and easily adapted to any situation. As a result, it's ideal for sending large data bitstreams since the overhead bits per data bit ratio is much lower. The investigation in this article is extended Hamming codes for product codes. The proposal particularly emphasises on how well it functions with low error rate, which is critical for multimedia wireless applications. It provides a foundation and a comprehensive set of methods for quantitatively evaluating this performance without the need of time-consuming simulations. It provides fresh theoretical findings on the well-known approximation, where the bit error rate roughly equal to the frame error rate times the minimal distance to the codeword length ratio. Moreover, the analytical method is applied to actual design considerations such as shorter and punctured codes along with the payload and redundancy bits calculation. Using the extended identity equation on the dual codes, decoding can be done at the first instance. The achievement of 43.48% redundancy bits is obtained during the testing process which is a huge proportion reduced in this research work.

Reversible Data Hiding in Encrypted Image Based on (7, 4) Hamming Code and UnitSmooth Detection

With the development of cloud storage and privacy protection, reversible data hiding in encrypted images (RDHEI) plays the dual role of privacy protection and secret information transmission. RDHEI has a good application prospect and practical value. The current RDHEI algorithms still have room for improvement in terms of hiding capacity, security and separability. Based on (7, 4) Hamming Code and our proposed prediction/ detection functions, this paper proposes a Hamming Code and UnitSmooth detection based RDHEI scheme, called HUD-RDHEI scheme for short. To prove our performance, two database sets—BOWS-2 and BOSSBase—have been used in the experiments, and peak signal to noise ratio (PSNR) and pure embedding rate (ER) are served as criteria to evaluate the performance on image quality and hiding capacity. Experimental results confirm that the average pure ER with our proposed scheme is up to 2.556 bpp and 2.530 bpp under BOSSBase and BOWS-2, respectively. At the same time, security and separability is guaranteed. Moreover, there are no incorrect extracted bits during data extraction phase and the visual quality of directly decrypted image is exactly the same as the cover image.

SIMULATION MODEL OF THE SOFTWARE FOR WORKING WITH PERFECT CODES BASED ON HAMMING CODE AND GOLE CODE

This article presents an analytical review of noise-tolerant codes, namely, the perfect codes are considered. Ideal codes can be used to encode and decode information, as they have all the desired properties, namely, resistance to interference and ease of implementation. In conclusion, a simulation model of encoding and decoding the information word is developed.

Study of single event upsets (SEUS) a survey and analysis

Over the last few years evolution in electronics technology has led to the shrinkage of electronic circuits. While this has led to the emergence of more powerful computing systems it has also caused a dramatic increase in the occurrence of soft errors and a steady climb in failure in time (FIT) rates. This problem is most prevalent in FPGA based systems which are highly susceptible to radiation induced errors. Depending upon the severity of the problem a number of methods exist to counter these effects including Triple Modular Redundancy (TMR), Error Control Coding (ECC), scrubbing systems etc. The following project presents a simulation of an FPGA based system that employs one of the popular error control code techniques called the Hamming Code. A resulting analysis shows that Hamming Code is able to mitigate the effects of single event upsets (SEUs) but suffers due to a number of limitations.