MATLAB Implementation of Arithmetic Coding with Performance Metrics

In this documentation, we will implement arithmetic coding using MATLAB and calculate its average code length, entropy, and coding efficiency. Arithmetic coding is a data compression technique that transforms input data into a real number between 0 and 1, achieving efficient compression through probability-based interval subdivision. The MATLAB implementation will involve key algorithmic steps including probability calculation, interval initialization, iterative range narrowing, and final binary code generation. For performance evaluation, we will compute the average code length to assess compression effectiveness by measuring the average number of bits required per symbol. Entropy calculation will quantify data uncertainty using Shannon's entropy formula H(X) = -Σp(i)log2p(i), revealing the theoretical information content. Coding efficiency will be determined as the ratio between entropy and average code length, indicating how closely the implementation approaches theoretical compression limits. Through these metrics, we can conduct comprehensive performance analysis of arithmetic coding, including probability model optimization and compression ratio verification using practical test cases.