This thesis briefly introduces the theory of TCM. By using the Euclidean Weight of error sequences as the coding metric, the algorithm of the Free Euclidean Distance in traditional coding schemes is improved, and the Viterbi Maximum- Likelihood decoding algorithm is optimized by simplifying the calculation of the conditional decoding probability, thus the improvement has been made in the performance of the whole system. Finally, it is verified that this scheme can get higher asymptotic coding gain through MATLAB simulation, which makes the system performance approach the asymptotic limit in theory compared with the traditional scheme.