Soft-Output Viterbi Algorithm (SOVA) is one type of recovery memory-less Markov Chain and is used widely to decode convolutional codes. Fundamentally, conventional SOVA is designed on the basis of Maximum A-Posteriori probability (MAP) under Additive White Gaussian Noise (AWGN) interference. Therefore, the use of conventional Gaussian-based SOVA performs inefficiently and generates high BER (Bit Error Rate) in the presence of Symmetric Alpha Stable noise SαS. The poor performance of the Gaussian-based SOVA can be attributed to the mathematical quadratic cost function of the receiving mechanism. The quadratic cost function at the receiving end is statistically vulnerable and inefficient to guard SOVA component decoder against the entries of the outliers which are superimposed on the transmitted signal from hostile SαS channel. The author studies and improves the performance of conventional SOVA with the introduction of Bayesian Cauchy metric calculation. Substantial performance improvement was observed from Mento Carlo Simulation for SOVA running on the platform of parallel turbo codes.