Analysis of Sequential Decoding Complexity Using the Berry-Esseen Inequality

Abstract

his study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem. Unlike the theoretical bounds determined by the conventional central limit theorem argument, which often holds only for sufficiently large codeword length, the new bound obtained from the Berry-Esseen theorem is valid for any blocklength. The accuracy of the new bound is then examined for two sequential decoding algorithms, an ordering-free variant of the generalized Dijkstra's algorithm (GDA)(or simplified GDA) and the maximum-likelihood sequential decoding algorithm (MLSDA). Empirically investigating codes of small blocklength reveals that the theoretical upper bound for the simplified GDA almost matches the simulation results as the signal-to-noise ratio (SNR) per information bit ($\gamma_b$) is greater than or equal to 8 dB. However, the theoretical bound may become markedly higher than the simulated average complexity when $\gamma_b$ is small. For the MLSDA, the theoretical upper bound is quite close to the simulation results for both high SNR ($\gamma_b\geq 6$ dB) and low SNR ($\gamma_b\leq 2$ dB). Even for moderate SNR, the simulation results and the theoretical bound differ by at most \makeblue{0.8} on a $\log_{10}$ scale.