Noncoherent decoding of trellis codes using multiple-symbol overlapped observations was shown to achieve close to the coherent performance. Optimal decoding by the Viterbi algorithm (VA) for L-symbol observations requires a number of states which grows exponentially with L. In this paper two novel suboptimal algorithms are presented, based on the VA, for which the number of states is the same as the original code, yielding complexity depending weakly on L. The first algorithm, is called the basic decision feedback algorithm (BDFA). It uses feedback from previous decisions to achieve low complexity. Due to the feedback, it suffers from error propagation. A modification of the BDFA called the modified decision feedback algorithm (MDFA) serves to greatly reduce the error propagation and improve the bit error rate performance. >