Reed-Muller Encoding and Decoding with FHT Algorithm Implementation

This MATLAB program implements Reed-Muller encoding and decoding operations. The implementation is based on Reed-Muller coding theory and utilizes the Fast Hadamard Transform (FHT) algorithm for efficient computation. Reed-Muller coding is a mathematical technique for error correction and encoding that effectively detects and corrects errors in data transmission. The program structure includes separate functions for encoding and decoding processes, where the encoder generates Reed-Muller codewords through logical operations on information bits, while the decoder employs FHT for maximum likelihood decoding. The FHT algorithm, being a fast implementation of Hadamard transform, enables efficient processing of large datasets by reducing computational complexity from O(N²) to O(N log N). Key MATLAB functions used include hadamard matrix generation, logical operations for code construction, and efficient signal processing techniques. By integrating Reed-Muller coding principles with the computational efficiency of FHT, this implementation achieves both accuracy and performance in error correction tasks, making it suitable for communication systems requiring reliable data transmission.