DECODING OF NOISE-RESISTANT CYCLIC CODES IN THE SPECTRAL DOMAIN

Abstract

The ability of a code to detect errors and correct them is assessed not only by the characteristics of speed and minimum code distance but also by the inherent ability to build high-speed decoding methods for it with low computational complexity by reducing the number of arithmetic operations. There are many effective ways to decode a linear block BFR code. The choice of a particular code decoding method depends not only on the parameters (length, minimum distance), but also on which part of the algorithm is implemented in hardware and which in software, and on the required speed and even the cost of the available circuit blocks. In particular, optimizing the implementation of such algorithms in hardware requires careful consideration of processing power, energy consumption, and memory allocation as these factors directly influence the feasibility of deploying these methods in real-world applications. Therefore, the development of new fast algorithms for decoding block FFT codes that increase the reliability of information transmission is an urgent task. The paper analyzes the existing methods for decoding linear FFT codes and estimates the computational complexity of both frequency and time algorithms. These analyses are critical as they form the foundation for identifying opportunities to enhance performance and reduce delays, particularly in systems requiring high throughput and low latency. A method for solving the key equation (one of the decoding stages) and efficiently calculating the error polynomial in the spectral domain is considered. An algorithm is proposed for finding the n-2t spectral components of the error vector using the known t coefficients of the error locator polynomial and the known 2t syndrome components calculated at the first stage of decoding.