The introduction of Non-Transmittable Codewords (NTCs) into Viterbi Algorithm Decoder has emerged as one of the best ways of improving performance of the Viterbi Algorithm Decoder. However, the performance has been tested only in hard decision Viterbi Decoder in telecommunication systems, but not in soft decision Viterbi Decoder and storage media. Most storage media use Reed Solomon (RS) Algorithm Decoder. Yet, the field experience still shows failure of the algorithm in correcting burst errors in reading data from the storage media; leading into data loss. This paper introduces the Soft Viterbi Algorithm Decoding enhanced with Non-Transmittable Codewords for storage media. Matlab software was used to simulate the algorithm and the performance was measured by comparing residual errors in a data length of one million bits. Additive White Gaussian Noise model was applied to distort the stored data. The performance comparison was made against the Reed Solomon code, Normal Soft Viterbi and Hard decision Viterbi enhanced with NTCs. The results showed that the Soft Viterbi Algorithm enhanced with NTCs performed remarkably better by 88.98% against RS, 84.31% against Normal Soft Viterbi and 67.26% against Hard Viterbi enhanced with NTCs.