A Comparative Study Between Decoding Methods for First-Order Reed-Muller Codes

Abstract

Encoding is considered one of the fundamental sciences in the fields of communication and data protection, particularly with the advancement of digital data. The primary objective of encoding is to diminish the size of data, enhance the quality of transmission and reception, ensure confidentiality and security, and optimize efficiency and accuracy. Reed-Muller encoding technology stands out as a widely employed and effective technique in various

modern applications, such as satellite communications, security and protection methods, artificial intelligence systems, quantum communications systems, health data, and digital medicine.

Motivated by the significance of Reed-Muller encoding, we embarked on a research study in this domain. The study encompasses an examination of the encoding and decoding processes of Reed-Muller at the first order, employing two distinct methods: majority logic and Hadamard matrices. The comparison between these methods is conducted with respect to performance, efficiency, computational complexity, speed, effectiveness, and error correction capability.