最大概度軟性決策旋序列積碼解碼演算法

Abstract

本篇論文，旨在研習最大概度之軟性決策旋積碼解碼演算法(MLSDA)的表現。本論文中的演算法，捨棄了傳統的費農測度(Fano metrics)，採用魏格納法則(Wagner rule)為基礎，而被稱為符合最大概度解碼法則之第二型態新測度。在 [1] 的原始分析中，假設儲存堆疊的容量為無限大。然而，這個假設在實際的應用上並不可行，而當我們考量儲存堆疊容量為有限的因素時，最大概度之軟性決策旋積碼解碼演算法的效益將無可避免的變差。我們模擬所得的結果指出：當適當儲存堆疊的容量時每個位元的錯誤率幾乎是保持原狀。然而，更進一步的縮減儲存堆疊的容量，每個位元的錯誤率會很明顯的升高。 模擬結果指出：經由模擬所得的曲線和經由理論上限的曲線差別最多為0.67; 因此要將此演算法的效能改善至理論上限的空間是相當有限的，。 最後，為了得知最大概度之軟性決策旋積碼解碼演算法在衰減性的頻道(Fading channel)下的表現，我們導出了形式較為複雜的測度。此外，我們也使用了這個新的測度和之前在加成性白色高斯雜訊頻道(AWGN)下的所導出的測度來比較個別的表現。令人驚訝的，模擬的結果指出，和新測度比較下，舊有的測度在衰減性的頻道下依然有相當的每個位元之錯誤率，但是在計算的複雜度方面，新測度很明顯的保有了相當的優勢。

In this thesis, we study the performance of the {\it maximum-likelihood soft-decision sequential decoding algorithm} (MLSDA) for convolutional codes, which is previously proposed in \cite{HANCHEN98}. Instead of using the conventional Fano metric, the proposed algorithm employs a new metric based on a variation of the Wagner rule, which is referred to as the {\it second form of the maximum-likelihood decoding} rule. The original analysis in \cite{HANCHEN98} assumed infinite stack size. This assumption, however, may not be feasible in practice, and the performance of MLSDA is expected to degrade if finite stack constraint is applied. Our simulation results, however, indicate that the BER (Bit Error Rate) remains almost intact for a moderate stack size (e.g., $512$). Yet, a further decrease in stack size (e.g., 64) may significantly degrade the BER. We also empirically investigate the tightness of the theoretical upper bound for the computational efforts of MLSDA derived in \cite{HANCHEN98}. Simulation results show that the difference between the curves obtained from simulations and from the theoretical upper bound is at most $0.67$; and therefore, the room for improvement to the theoretical upper bound seems prohibitively limited. Finally, a more complex metrics is derived to obtain the performance of the MLSDA under the fading channel. We also provide the performance comparison between the MLSDA using the former metrics for the additive white Gaussian noise (AWGN) channel and that using the new metrics under the same fading channel. Surprisingly, the simulation results show that the former metrics for the AWGN channel is robust for the BER, but the new metrics still have the superiority of computational complexity.