A decoding apparatus, decoding method, data-receiving apparatus, and a data-receiving method for performing a maximum-likelihood decoding process based on a Viterbi algorithm on a data train completing a convolution-encoding process. The apparatus includes a computation device for performing a trellis computation for decoding a data train completing the convolution-encoding process. The decoding apparatus further includes a control device for controlling the trellis computation to be carried out by the computation device with processing timings in processing units each corresponding to a process carried out on n bits of pre-encoding data, in which each of the processing units is parallel processing carried out on computation results obtained for 2ⁿ states with one of the processing timings immediately preceding a present one of the processing timings to find the computation results with the present processing timing for the 2ⁿ states.