重要取樣技巧應用於MLSDA解碼效能估量之研究

Abstract

在固定長度（constraint length）增加時，迴旋碼的錯誤更正能力隨之快速成長，然而使用長的固定長度將受限於高解碼複雜度。應用於二進位迴旋碼的最大概度軟性決策序列解碼法則（MLSDA）[1]可在長的固定長度下獲得好的效能而且解碼複雜度較不受固定長度影響。估量系統效能時通常需要能產生數百個錯誤的次數，然而在系統錯誤率低時模擬時間將因此需求增長而無法實行。 不同於需要大量模擬次數才能得到有意義的系統效能估量的蒙地卡羅（Monte Carlo）模擬法，重要取樣（Important Sampling）[2,3,4,7]模擬法可以用較少的模擬次數獲得相對精確的量測值。使用重要取樣技巧，針對合適的錯誤事件選擇的通道可以成為有效率的模擬法。 在論文中我們將焦點置於將重要取樣技巧應用在MLSDA時，好的偏壓通道的選取。結果顯示，在我們所做的實驗中最好的IS模擬可以節省相當多的次數，然而不適當的選取IS密度函數將使該模擬法比蒙地卡羅模擬法更沒效率。

It is known that the error correction capability of the convolutional codes grows dramatically as the code constraint length increases. Yet, to employ codes with long constraint length may suffer a high decoding complexity. In [1], the authors proposed the Maximum-Likelihood soft-decision Sequential Decoding Algorithm (MLSDA) [1] for binary convolutional codes, and showed that its computational complexity turns out to be less affected by the code constraint length; therefore, it may apply to convolutional codes with long constraint lengths, and yield a good system performance. In order to evaluate the resultant system performance, sufficient simulation runs, usually requiring to induce hundred of errors, should be taken. This may render an unfeasibly long simulation time if the true system error is indeed low. Unlike the brute-force it Monte Carlo (MC) simulation that often requires a very large number of simulation trials to achieve meaningful estimates of system performance, the Importance Sampling (IS) [2,3,4,7] simulation can achieve relatively accurate estimate with much less simulation trials. For IS technique, well-chosen channels to adapt to suitable error events can result in an efficient simulator. In this thesis, we focused on the selection of good biased channels for Importance Sampling being applied to the MLSDA. By the simulation results, the best IS simulator among those we tried can save fairly large simulation trials, while an improperly chosen IS density may arise an IS simulator that performs even worse than an MC one.