In this paper, by modifying the well-known Viterbi algorithm, an adaptive Viterbi algorithm that is based on strongly connected trellis decoding is proposed. Using this algorithm, the design and a field-programmable gate array implementation of a low-power adaptive Viterbi decoder with a constraint length of 9 and a code rate of 1/2 is presented. In this design, a novel systolic array-based architecture with time multiplexing and arithmetic pipelining for implementing the proposed algorithm is used. It is shown that the proposed algorithm can reduce by up to 70% the average number of ACS computations over that by using the nonadaptive Viterbi algorithm, without degradation in the error performance. This results in lowering the switching activities of the logic cells, with a consequent reduction in the dynamic power. Further, it is shown that the total power consumption in the implementation of the proposed algorithm can be reduced by up to 43% compared to that in the implementation of the nonadaptive Viterbi algorithm, with a negligible increase in the hardware.