MATLAB Implementation of Reed Muller Coding with Bit Error Rate Curve Plotting

This MATLAB implementation demonstrates Reed Muller coding and generates bit error rate (BER) performance curves. Reed Muller coding is an error detection and correction technique based on Boolean functions and polynomial theory, which transforms input data into polynomial form and applies Boolean functions for encoding to enhance error correction capabilities.

The MATLAB code implementation involves several key steps: defining input data vectors, converting them into polynomial representations using appropriate transformation algorithms, and applying Boolean function-based encoding routines. The encoder structure typically utilizes generator matrices constructed from Boolean monomials, where coding parameters like order (r) and length (m) determine the error correction capacity.

Through MATLAB programming, you can efficiently implement the Reed Muller encoding algorithm by defining input data sequences, transforming them into polynomial formats using functions like dec2bin for binary conversion, and applying encoding functions that employ Boolean operations such as XOR and AND gates. The encoded output is generated through matrix multiplication between the input vector and the generator matrix.

For performance evaluation, the code incorporates BER curve plotting functionality by simulating transmission through noisy channels (like AWGN) with varying SNR levels. The implementation includes Monte Carlo simulations where errors are introduced and corrected using Reed Muller decoding algorithms, with BER calculated as the ratio of erroneous bits to total transmitted bits.

By analyzing BER curves across different SNR conditions, you can evaluate how Reed Muller coding performance varies with code order selections. The implementation allows comparison between different coding schemes (varying r and m parameters) to determine optimal configurations for specific application requirements, demonstrating the trade-off between coding complexity and error correction capability.

This MATLAB-based approach provides practical understanding of Reed Muller coding applications, enabling researchers and engineers to implement and optimize error correction systems for digital communication scenarios.