The ACS computation and the survivor memory are most power critical, consuming about 90% power in the Viterbi decoder. Based on the low power mechanisms, the scarce state transition (SST) technique and the variable truncation length, we present a Viterbi decoder for the MB-OFDM UWB applications. The SST scheme lowers state transition as well as signal switches in the ACS units. Moreover, the decoding with variable truncation length leads to the access reduction in the survivor memory. The experimental results show more than 30% power reduction under high SNRs as compared to those without SST and variable truncation length.