MATLAB Implementation of Reed-Solomon Code with BER-SNR Performance Analysis

This document presents a detailed implementation of Reed-Solomon codes using MATLAB software. The simulation involves generating RS codewords using MATLAB's communication toolbox functions like rsenc() for encoding and rsdec() for decoding. The implementation includes adding AWGN (Additive White Gaussian Noise) to simulate different channel conditions and comparing original vs decoded data to calculate bit error rates. Key algorithmic components include Galois field arithmetic operations, syndrome calculation for error detection, and the Berlekamp-Massey algorithm for error location and correction. The performance evaluation systematically tests RS code behavior across varying SNR conditions, employing Monte Carlo simulation techniques for statistical reliability. The resulting BER-SNR relationship plot provides visual analysis of the code's error correction capability, demonstrating how increasing SNR improves error performance. This implementation serves as an educational tool for understanding RS code principles, including parameters like code length (n), message length (k), and error correction capacity (t), while offering practical insights into their applications in digital communication systems. The plotting functionality utilizes MATLAB's semilogy() function for logarithmic BER scale representation, with proper axis labeling and grid settings for clear data interpretation. Through this comprehensive simulation, users can experimentally verify theoretical RS code performance and study the trade-offs between code rate and error correction robustness under different noise conditions.