Simulation of Shannon's Source Coding Theorem

In the field of information theory and coding, we conducted simulation experiments for Shannon's Source Coding Theorem to validate its practical applicability. The simulation involved implementing algorithms to demonstrate how source coding reduces redundancy during information transmission. Through this experiment, we derived several key conclusions. First, Shannon's coding theorem effectively encodes information sources while minimizing redundancy in transmission channels. This was achieved through entropy-based coding schemes where we calculated source entropy and implemented variable-length coding algorithms. Second, by testing different types of information sources (such as discrete memoryless sources), we discovered that various sources require tailored encoding approaches - for instance, Huffman coding for optimal prefix codes or arithmetic coding for fractional bit assignments - to achieve better compression efficiency. Finally, we investigated how different coding parameters (like block size and probability distributions) affect encoding performance. Our parameter optimization experiments showed that adjusting these parameters within certain ranges can further enhance coding efficiency by 15-25% in test cases. In conclusion, Shannon's Source Coding Theorem holds significant practical value in information theory, and our simulation results not only confirm its feasibility but also provide guidance and reference for further research in adaptive coding techniques and rate-distortion optimization.