Implementation of Galois Field for Application in Wireless Communication Channels

Abstract

This paper discusses the implementation of Galois Field based codes for application in wireless communication channel. It discusses the use of Galois Fields outlining the basic performance of a digital communication system in terms of BER curves. The work further discusses the performance of these codes in Gaussian and Rayleigh Fading Channels.

Comparison of communication performance of block coding methods in different channels using DWT

“…The error correction feature of LBC is controlled with different digital modulations. In [9], channel coding performances of some Galois based codes (BCH and Hamming) for AWGN and Rayleigh fading channels are given by BER curves. The authors concluded that Hamming coding showed the best results in the presence of the Galois field.…”

“…For any positive integers m ≥ 3 and t < 2 m−1 , there exists a binary BCH code with the following parameters:• Block length: n = 2 m −1 • Number of parity-check digits: n − k ≤ mt • Minimum distance: d min ≥ 2t + 1A finite field Galois Field GF(q) is fixed, where q is a prime power for a general BCH code. m i x is the minimal polynomial over GF(q) of α(i), α is a primitive nth root of unity in GF(q m ), for all i[9].2.5 Reed-Solomon codesRS codes are cyclic and non-binary codes. These codes comprise of symbols containing m bit sequences, where m > 2.…”