  A common problem on sequential-type decoding is that at the signal-to-noise
ratio (SNR) below the one corresponding to the cutoff rate, the average
decoding complexity per information bit and the required stack size grow
rapidly with the information length. In order to alleviate the problem in the
maximum-likelihood sequential decoding algorithm (MLSDA), we propose to
directly eliminate the top path whose end node is $\Delta$-trellis-level prior
to the farthest one among all nodes that have been expanded thus far by the
sequential search. Following random coding argument, we analyze the
early-elimination window $\Delta$ that results in negligible performance
degradation for the MLSDA. Our analytical results indicate that the required
early elimination window for negligible performance degradation is just twice
of the constraint length for rate one-half convolutional codes. For rate
one-third convolutional codes, the required early-elimination window even
reduces to the constraint length. The suggestive theoretical level thresholds
almost coincide with the simulation results. As a consequence of the small
early-elimination window required for near maximum-likelihood performance, the
MLSDA with early-elimination modification rules out considerable computational
burdens, as well as memory requirement, by directly eliminating a big number of
the top paths, which makes the MLSDA with early elimination very suitable for
applications that dictate a low-complexity software implementation with near
maximum-likelihood performance.
