Svitlana Matsenko

In this paper, we propose a new method for the binomial adaptive compression of binary sequences of finite length without loss of information. The advantage of the proposed binomial adaptive compression method compared with the binomial compression method previously developed by the authors is an increase in the compression rate. This speed is accompanied in the method by the appearance of a new quality—noise immunity of compression. The novelty of the proposed method, which makes it possible to achieve these positive results, is manifested in the adaptation of the compression ratio of compressible sequences to the required time, which is carried out by dividing the initial set of binary sequences into compressible and incompressible sequences. The method is based on the theorem proved by the authors on the decomposition of a stationary Bernoulli source of information into the combinatorial and probabilistic source. The last of them is the source of the number of units. It acquires an entropy close to zero and practically does not affect the compression ratio at considerable lengths of binary sequences. Therefore, for the proposed compression method, a combinatorial source generating equiprobable sequences is paramount since it does not require a set of statistical data and is implemented by numerical coding methods. As one of these methods, we choose a technique that uses binomial numbers based on the developed binomial number system. The corresponding compression procedure consists of three steps. The first is the transformation of the compressible sequence into an equilibrium combination, the second is its transformation into a binomial number, and the third is the transformation of a binomial number into a binary number. The restoration of the compressed sequence occurs in reverse order. In terms of the degree of compression and universalization, the method is similar to statistical methods of compression. The proposed method is convenient for hardware implementation using noise-immune binomial circuits. It also enables a potential opportunity to build effective systems for protecting information from unauthorized access.

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.

This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) and the method of their formation for reliable digital signal processing (DSP), transmission, and data storage. The method is obtained based on the general theory of positional number systems (PNS) with conditions and number functions for converting BNS with a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, and multivalued number systems. Generated by BNS, binomial numbers possess the error detection property. A characteristic property of binomial numbers is the ability, on their basis, to form various combinatorial configurations based on the binomial coefficients, e.g., compositions or constant-weight (CW) codes. The theory of positional binary BNS construction and generation of binary binomial numbers are proposed. The basic properties and possible areas of application of BNS researched, particularly for the formation and numbering of combinatorial objects, are indicated. The CW binomial code is designed based on binary binomial numbers with variable code lengths. BNS is efficiently used to develop error detection digital devices and has the property of compressing information.

Given the need to improve the efficiency of data transfer, there are requirements to ensure their reliability and quality under interference. One way to improve data transfer efficiency is to use noise-resistant codes, which include a closed-form expression of the Fibonacci code, a parity code, and a permanent weight code. The result of applying these types of coding produces interference-resistant end-to-end processing and transmission of information, which is a promising approach to improving the efficiency of telecommunications systems in today's environment. This paper reports the estimation of the error detecting code capability of the Fibonacci code in a closed-form expression, as well as its comparative characteristic with a parity code and a permanent weight code for a binary symmetrical channel without memory. To assess an error detecting capability of the Fibonacci code in a closed-form expression, the probability of Fibonacci code combinations moving to the proper, allowable, and prohibited classes has been determined. The comparative characteristic of the indivisible error-detecting codes is based on an average probability method, for the criterion of an undetectable error probability, employing the MATLAB and Python software. The method has demonstrated the simplicity, versatility, and reliability of estimation, which is close to reality. The probability of an undetectable error in the Fibonacci code in a closed-form expression is V=5×10-7; in a code with parity check, V=7.7×10-15; and in a permanent weight code, V=1.9×10-15, at p10=3×10- 9. The use of the average probability method makes it possible to effectively use indivisible codes for detecting errors in telecommunications systems

In this paper, through the development of the simulation model, we researched the schemes of forward error correction (FEC) code based on the Reed-Solomon (RS-FEC) code within the 25 Gb/s intensity-modulated non-return-to-zero on-off-keying (NRZ-OOK) modulated wavelength division multiplexed fiber-optical transmission system (WDM FOTS). The performance of error correction of RS- FEC code schemes such as RS (255, 227) with 12% overhead (OH), RS (255, 239) with 6.7% OH, RS (255, 235) with 8.5% OH and RS (511, 479) with 6.7% OH and with block interleaver was evaluated. The performance of implemented RS-FEC code schemes was investigated by using the bit error rate (BER) monitoring based on the Monte Carlo (MC) method.

This paper aims to review recent developments in the field of doped fiber-based optical amplifiers and serve as a reference for promising optical signal amplification techniques that may be useful for practical implementation in high-capacity and cost-efficient telecommunications systems. The main focus is put on different rare-earth dopant elements, double-clad fibers, and optical couplers for cladding-pumping technique. It is found that codoped double-clad fiber-based amplifiers currently have attained the main research interest and show possible application also in multichannel fiber optical transmission systems. Additionally, we have compared different free space and waveguide construction optical coupling techniques suitable for doped double-clad fiber amplifiers.

Today telecommunication systems (TS) use a large number of different codes, among which error detection codes (EDC) are distinguished, which are relatively simple to implement. Some of the error control codes (ECC), for example, cyclic codes, which have high noise immunity, require complex methods of encoding and decoding code combinations. As a result, the implementation of these methods in information transfer systems leads to an increase in their cost and a decrease in reliability and speed. In addition, most encoding and decoding devices, as a rule, do not possess the property of self-control. Therefore, it is difficult to implement end-to-end (E2E) control of information on their basis, covering both its processing and transmission using the same code. Such control makes it possible to reduce hardware costs and increase the speed of existing telecommunication systems. However, the existing codes designed to transmit information do not possess the property of E2E control. In this paper, for the E2E monitoring of telecommunication systems, the Fibonacci code is used in a minimal form, which has a simple structure and a fairly high error detection ability. An important task necessary for telecommunication systems using a Fibonacci code is the ability to convert it to binary code for communication with binary digital systems and vice versa the ability to convert binary code to a Fibonacci code. It is these tasks that are solved in this paper. To convert data, we propose and develop the Fibonacci-octal code, which consists of a sequence of 4-bit codes - modules containing 8 Fibonacci numbers. An important feature of the Fibonacci-octal code is those code combinations (Fibonacci numbers) of the modules are relatively easy to convert to the numbers of 3-bit binary modules and vice versa. This simplifies the conversion of Fibonacci numbers to binary numbers and vice versa and makes it faster and more reliable.

With the volumes of transmitted information growth, the task of increasing the noise immunity and reliability of data transmission networks arises. The presence of interference such as nonlinear loss, chromatic dispersion, polarization mode dispersion, and inter-channel interference decreases the performance of fiber optical communication systems. Forward Error Correction (FEC) codes are vital in optical communication systems to achieve highly efficient and highly reliable communication. The paper presents research on a simulation model where FEC channel-coding schemes based on the Bose-Chaudhuri-Hocquenghem (BCH) cycling block code are integrated with non-return-to-zero on-off-keying (NRZ-OOK) modulated wavelength division multiplexed (WDM) fiber optical communication systems. The results highlight the selection of coding parameters in the adopted FEC approach. In our paper, the BCH (255, 231), BCH (255, 223), and BCH (255,191) FEC channel-coding schemes are chosen for integration in the NRZ-OOK modulated WDM optical transmission system. The paper shows the main advantages and drawbacks of the selected FEC coding scheme and provides a comparison of the proposed schemes based on their main features, such as bit error ratio (BER), which were obtained through the simulations of 25 Gbit/s NRZ-OOK WDM fiber optical system. The dynamics of changes in BER was investigated using the Monte Carlo (MC) method for precise results. The paper shows that integration of FEC channel-coding schemes based on the BCH codes improves the noise immunity and reliability of the WDM Fiber Optical Communication Systems.

The paper presents the improved method of noise immune Fibonacci counting in the minimal form of representation. The method was tested and investigated in the developed noise immune pulse counter based on a minimal form of Fibonacci code with a fractal decoding device. The proposed device, which is simulated in the NI Multisim software, possesses a homogenous structure, increased noise immunity, performance and detection of bit errors in the process of its operation.

In this paper, we consider a high-speed Fibonacci-decimal modular counter, which makes it possible to detect errors, both directly during the count, and during the transmission of the received information via communication channels. Along with this, it makes it possible to use the modular principle of building counters and equipment, where they are applied, which reduces the cost of production and operation. It can effectively be used in various radio electronic devices and, especially, in measuring technology.