A numerical method for calculating coefficients of a positional weight-valued number system for performing the inverse transform and error correction in a modular code

Abstract

One of the effective methods of increasing the performance of digital signal processing systems is the use of parallel arithmetic codes, in particular, polyalphabetic polynomial modular codes. In these codes, performing modular operations (addition, subtraction, multiplication) requires less time compared to performing these operations in positional codes. This is achieved by independently executing these operations across code modules. However, such an organization of calculations requires a translation from positional codes to polyalphabetic polynomial modular codes, and after the calculations, performing the reverse translation. It is known that the latter operation requires quite a lot of time and circuit costs. To eliminate this problem, in this work, we develop a numerical method for calculating the coefficients of a positional weighty number system from a polyalphabetic polynomial modular code combination, which makes it possible to efficiently perform the reverse transformation. The coefficients obtained using this method can also be used to find and correct errors that occur during calculations in digital signal processing. The use of the isomorphism of the Chinese remainder Theorem has made it possible to reduce the time and circuit costs in calculating the coefficients of the positional weighty number system from the modular code.