A MATLAB Algorithm for Verifying Maximum A Posteriori Probability Decoding of Convolutional Codes

This document presents a verified MATLAB algorithm implementing the Maximum A Posteriori Probability (MAP) decoding algorithm for convolutional codes, complete with detailed annotations throughout the code.

Convolutional codes represent a widely-used error correction coding technique employed in data transmission systems to detect and correct errors. The MAP decoding algorithm serves as a fundamental decoding method that reconstructs original data from received encoded sequences by computing the most probable transmitted information based on probabilistic calculations.

Within this verified MATLAB implementation, we demonstrate the complete MAP decoding workflow for convolutional codes, incorporating explanatory comments at each algorithmic stage. The implementation will include key components such as: state transition probability calculations using log-domain computations to prevent numerical underflow, forward and backward recursion algorithms through trellis structures, and log-likelihood ratio (LLR) computations for final decision metrics. These annotations will help readers understand both the theoretical foundations and practical implementation details of the decoding process.

Through this verification algorithm, we can validate the performance and accuracy of convolutional code MAP decoding under various channel conditions and error patterns. This verification process holds significant importance for further research and algorithmic improvements, including performance comparisons with other decoding methods like Viterbi algorithm, and investigations into turbo code applications where MAP decoding serves as a fundamental component.

We anticipate that this annotated MATLAB implementation will provide readers with comprehensive insights into both understanding and applying MAP decoding algorithms for convolutional codes in practical communication systems, serving as an educational resource and baseline for further developments in channel coding research.