利用Berry-Esseen不等式分析序列译码复杂度
Analysis of Sequential Decoding Complexity Using the Berry-Esseen Inequality
摘要：
他的研究提出了一种新的技术来估计计算复杂性的顺序解码使用贝里-埃辛定理。不同于传统的中心极限定理参数，这往往只适用于足够大的码字长度所确定的理论界限，从贝里-埃辛定理获得的新的界限是有效的任何块长度。新的边界的准确性，然后检查两个顺序解码算法，一个排序自由的变体的广义Dijkstra算法（GDA）（或简化GDA）和最大似然顺序解码算法（MLSDA）。经验研究的小块长度的代码显示，简化的GDA的理论上限几乎匹配的仿真结果的信号噪声比（SNR）每信息比特（$γ_b$）是大于或等于8 dB。然而，当$γ_b$较小时，理论界可能会明显高于模拟的平均复杂度。对于MLSDA，对于高SNR（$γ_b\geq 6$ dB）和低SNR（$γ_b\leq 2$ dB），理论上界与仿真结果非常接近。即使对于中等SNR，仿真结果和理论界在$\log_{10}$尺度上最多相差\makeblue{0.8}。
英文摘要：
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 ($γ_b$) is greater than or equal to 8 dB. However, the theoretical bound may become markedly higher than the simulated average complexity when $γ_b$ is small. For the MLSDA, the theoretical upper bound is quite close to the simulation results for both high SNR ($γ_b\geq 6$ dB) and low SNR ($γ_b\leq 2$ dB). Even for moderate SNR, the simulation results and the theoretical bound differ by at most \makeblue{0.8} on a $\log_{10}$ scale.
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