MATLAB Implementation of Viterbi Hard Decision Decoding

In this article, we will discuss the implementation of the Viterbi hard decision decoding program. We begin by introducing the fundamental concepts of the Viterbi algorithm, which employs dynamic programming to find the most likely sequence of states in a Markov process. The MATLAB implementation involves creating trellis structures and computing path metrics through efficient matrix operations. We will explore the detailed MATLAB implementation of the Viterbi hard decision decoder, including functions for trellis generation, branch metric calculation, and survivor path selection. The code utilizes MATLAB's vectorization capabilities for efficient computation of path metrics and traceback operations. The article provides a comprehensive discussion on plotting signal-to-noise ratio (SNR) curves, which involves generating test signals, adding controlled noise, and measuring bit error rates across different SNR values. The MATLAB implementation includes functions for signal generation, noise addition, and BER calculation using histogram-based error counting. We will examine how these SNR curves determine optimal hard decision thresholds through threshold sweeping algorithms and minimum BER detection. The code implementation demonstrates automatic threshold optimization using MATLAB's fminsearch function or grid search methods. Additionally, we will discuss performance optimization techniques for the Viterbi algorithm, including memory-efficient traceback implementation, parallel processing using MATLAB's parfor, and algorithm acceleration through precomputation of branch metrics. The article addresses common implementation challenges such as numerical stability issues, handling of tie-breaking situations in path metric comparisons, and techniques for reducing computational complexity through truncated Viterbi decoding. Through this article, you will learn how to implement a complete Viterbi hard decision decoding system in MATLAB, gaining deep understanding of the algorithm's implementation details, performance optimization strategies, and practical debugging techniques for real-world communication systems.