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In this paper, the design and FPGA implementation of a low-power adaptive Viterbi decoder with a constraint length of 9 and 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 adaptive Viterbi algorithm is used. A scheme for providing a tolerance to clock-to-data skew to avoid timing violation is proposed. A process of eliminating spurious toggles, for reducing power consumption, is also developed. It is shown that the total power consumption in the implementation of the adaptive algorithm can be reduced by up to 43% compared to that in the implementation of a corresponding non-adaptive Viterbi algorithm, with a negligible increase in the hardware.