MAP Algorithm Implementation for Turbo Codes in MATLAB

This MATLAB simulation implements the MAP (Maximum A Posteriori) algorithm for Turbo codes using a 1/2 code rate Recursive Systematic Convolutional (RSC) encoder and a 2-random interleaver. The implementation includes comprehensive BER (Bit Error Rate) performance analysis under various signal-to-noise ratio conditions. The simulation models the complete Turbo coding chain: RSC encoding, interleaving, AWGN channel transmission, and iterative MAP decoding with extrinsic information exchange. Key functions implemented include: - RSC encoder with polynomial representation [1, 5/7] in octal - 2-random interleaver generation using permutation matrices - Log-MAP algorithm implementation for soft-decision decoding - Iterative decoding with stopping criteria based on CRC or maximum iterations The simulation evaluates Turbo code performance by analyzing BER curves, convergence behavior, and the impact of different parameters such as interleaver size, number of iterations, and signal conditions. The decoding process employs the BCJR algorithm variant with forward-backward recursion for probability calculations. Performance optimization techniques include adaptive iteration control and early termination mechanisms. Through detailed analysis of Turbo code characteristics, this study provides insights for improving communication system reliability and data transmission rates, with practical applications in wireless communications and deep-space telecommunications.