Viterbi Decoding Algorithm Implementation for (2,1,7) Tail-Biting Convolutional Code in MATLAB

This MATLAB implementation demonstrates the Viterbi decoding algorithm for (2,1,7) tail-biting convolutional codes. The algorithm begins by processing the received codeword with zero-termination, then applies the Viterbi algorithm to decode the tail-biting sequence. The Viterbi algorithm employs dynamic programming principles, comparing path metrics across different state transitions to select the optimal decoding path. In the MATLAB implementation, key functions include: - Zero-termination processing to handle the circular nature of tail-biting codes - Branch metric calculation using Hamming or Euclidean distance - Path metric accumulation and comparison through trellis traversal - Traceback mechanism to recover the original information sequence The algorithm implementation involves creating a trellis structure with 64 states (2^(7-1)) and processing the received sequence through forward path metric computation and backward traceback operations. This approach provides an effective decoding method for tail-biting convolutional codes while offering practical insights into their operational principles. The code structure allows for clear understanding of how convolutional encoding and Viterbi decoding work together in communication systems.