Modified Reed-Muller Codes for Multiple Error Correction Approach

Abstract

Reed-Muller codes (RM for shorten), are very popular in the domains of electrical engineering and computer science. Their versatility makes them essential, especially in the area of wireless communication. Within the

context of 5G mobile networks, Reed-Muller codes contribute significantly to optimizing data transmission efficiency and reliability. Moreover, these codes play a crucial role in deep-space communication. Thus, the decoding of RM codes still attracts the researchers till now. This paper aims to decode these codes, by providing a modification to binary RM codes. The resulting code allows us to correct the receiving word twice:

The first correction approach: The modified code yields an easily compute parity check matrix, which is used to correct errors in the received word.

The second correction approach: after we correcting the errors with the previous approach, the word will become much closer to the sent word, and now the majority logic technique will be much more useful.