Efficient computing methods are exploited for parallel processing of the most important trellis search algorithm, i.e. the Viterbi decoding algorithm (VA). The complicated data transfer scheme and the rather time-consuming computations caused by dynamic trellis search procedures are reorganized into matrix operations. The well-developed systolic processors for matrix operations can be well adapted to implement the whole decoding procedures of VA. A certain amount of AND/EOR operations for maximum likelihood estimation are saved. Flexible time/area performances are provided and T times speedup can be obtained with T consecutive stages being parallelized.