Development of the Fibonacci-Octal Error Detection Code for Telecommunication Systems

Abstract

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.