Abstract: A method for implementing the Viterbi algorithm (Viterbi decoder) for very high data rates/decoding rates. The trellis diagram (original trellis diagram) of the Markov process, the original trellis diagram being the basis of such implementation, is considered over a greater period. Transitions of the original trellis diagram are combined in one multi-step transition (multi-step trellis diagram) per each M. The number of transition branches, which rise exponentially, in such a process with M, is reduced to a smaller number by exploiting fundamental properties of the original trellis diagram forming the basis of the multi-step transitions. This eliminates non-optimal transition branches irrespective of the change from one multi-step transition to another.