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In this paper a new sequential decoding algorithm is introduced that uses stack storage at the receiver. It is much simpler to describe and analyze than the Fano algorithm, and is about six times faster than the latter at transmission rates equal to Rcomp the rate below which the average number of decoding steps is bounded by a constant. Practical problems connected with implementing the stack algorithm are discussed and a scheme is described that facilitates satisfactory performance even with limited stack storage capacity. Preliminary simulation results estimating the decoding effort and the needed stack siazree presented.