Analysis of the Sufficient Path Elimination Window for the Maximum-Likelihood Sequential-Search Decoding Algorithm for Binary Convolutional Codes

In this work, the priority-first sequential-search decoding algorithm proposed in [8] is revisited. By replacing the conventional Fano metric by one that is derived based on the Wagner rule, the sequentialsearch decoding in [8] guarantees the maximum-likelihood (ML) performance, and hence, was named the maximum-likelihood sequential decoding algorithm (MLSDA). It was then concluded by simulations that the software computational complexity of the MLSDA 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 cutoff rate, the average decoding complexity per information bit and the required stack size grow rapidly with the information length [13]. This problem to some extent prevent the practical use of sequential-type decoding from convolutional codes with long information sequence at low SNRs. 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. Following random coding argument, we analyze the early-elimination window ∆ that results in negligible performance degradation SunplusMM Technology Co., Ltd, HsinChu City, Taiwan 300, ROC Dept. of Communications Eng., National Chiao-Tung Univ., HsinChu City, Taiwan 300, ROC Graduate Institute of Communication Eng., National Taipei Univ., Taipei, Taiwan 237, ROC February 1, 2008 DRAFT 2 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. Index Terms Sequential decoding, maximum-likelihood, soft-decision, random coding