| Summary: | 博士 === 國立交通大學 === 電信工程系所 === 96 === In this work, the maximum-likelihood sequential-search decoding algorithm proposed in [17] is revisited. By replacing the conventional Fano metric with one that is derived based on the Wagner rule, the sequential-search decoding in [17] guarantees the maximum-likelihood (ML) performance, and was therefore named the maximum-likelihood sequential decoding algorithm (MLSDA). It was then concluded by simulations that when the MLSDA is operated over the convolutional code trellis, its software computational complexity is in general considerably smaller than that of the Viterbi algorithm.
A common problem on sequential-type decoding is that at the signal-to-noise ratio (SNR) below the one corresponding to the cut off rate, the average decoding complexity and the required stack size grow rapidly with the information length [25]. This problem, to some extent, prevents the practical use of sequential-type decoding from codes with long information sequence. In order to alleviate the problem in the MLSDA, we propose to directly eliminate the top path whose end node is ∆-trellis-level prior to the farthest one among all nodes that have been expanded thus far by the sequential search, which we termed the early elimination. We then analyze the early-elimination window that results in negligible performance degradation for the MLSDA. Our asymptotic-based analytical result indicates that the required early elimination window for negligible performance degradation is around three times (resp. 2.2-fold) of the constraint length for rate one-half convolutional codes under additive white Gaussian (resp. binary symmetric) channel. For rate one-third convolutional codes, the required early-elimination window reduces to two times (resp. 1.2-fold) of the constraint length for the same channel. The theoretical level thresholds almost coincide with the simulation results.
As a consequence of 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. This makes the MLSDA with early elimination suitable for applications that dictate a low-complexity software implementation with near maximum-likelihood performance. The upper bounds of decoding complexity of both the MLSDAs with and without early elimination are subsequently derived by utilizing the Berry-Esseen inequality. Both the upper bound and the simulated complexity indicate that the average decoding complexity per output bit for the MLSDA with early elimination is almost irrelevant to the memory order, as well as the message length, for medium to high SNRs.
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