Hamming Code Implementation: Encoding, Decoding, and Error Correction with MATLAB Simulation

This article introduces Hamming code, an encoding technique used for encoding, decoding, and error correction in digital communications. Hamming codes are error-correcting codes capable of detecting and correcting errors during data transmission. We employ MATLAB software to simulate Hamming code operations and calculate its bit error rate (BER) and error correction performance. The implementation includes generating parity-check matrices using the hammgen() function, encoding data with encode() or custom generator matrices, and decoding with syndtable() for syndrome-based error correction. Through MATLAB simulations, we demonstrate how to compute the code's minimum distance and analyze its error detection/correction capabilities using biterr() and berawgn() functions. Additionally, we discuss various error-correction coding techniques and their applications in digital communication systems. This study provides comprehensive insights into encoding and error correction technologies in digital communications, serving as valuable reference for future research in channel coding and communication system design.