Theory and Performance of ML Decoding for Turbo Codes using Genetic Algorithm

雖然渦輪碼使用最大概度解碼可以產生最低的錯誤率，但因為有效率的渦輪碼最大概度解碼器仍未被發明，所以渦輪碼使用最大概度解碼至今仍是件不可能的事情，在這篇論文中，我們提出了一個新的實驗模擬技術去尋找渦輪碼最大概度解碼器的效能極限，也針對渦輪碼提出了一個新的基因解碼演算法。 本文提出的效能極限實驗模擬技術可以針對最大概度解碼器的最佳與最差錯誤率效能做一評估。基因解碼演算法的理論則結合了干擾解碼與基因演算法。在基因解碼演算法中，染色體是隨機可加性的干擾雜訊，而傳統的渦輪解碼器被用來為每個染色體評定個別的適應環境分數，經過許多世代的演化後，非常好的染色體就會出現，而這些好的染色體相對應到的是被解碼後的碼字，而這些碼字是非常好的且有可能是對的。 基因解碼演算法在某些狀況下可以是一個實際可行的解碼演算法，基因解碼演算法同時也是一個多重輸出的解碼器。在我們的認知下，基因解碼演算法最重要的貢獻是可以利用它和我們所提出的最大概度解碼效能極限實驗技術來得到一個最大概度解碼的錯誤率最佳效能極限，而且是透過實驗模擬的方式得到。從我們的實驗結果中可以知道在錯誤率等於10-4附近，我們提出的基因解碼演算法已經可以達到最大概度解碼的效能，也可以確定在這個錯誤率區間，針對WCDMA規範的渦輪碼最大概度解碼器的效能僅比傳統遞回式解碼器來得好一些。Although yielding the lowest error probability, ML decoding of turbo codes has been considered unrealistic so far because efficient ML decoders have not been discovered. In this thesis, we propose an experimental bounding technique for ML decoding and the Genetic Decoding Algorithm (GDA) for turbo codes. The ML bounding technique establishes both lower and upper bounds for ML decoding. GDA combines the principles of perturbed decoding and genetic algorithm. In GDA, chromosomes are random additive perturbation noises. A conventional turbo decoder is used to assign fitness values to the chromosomes in the population. After generations of evolution, good chromosomes that correspond to decoded codewords of very good likelihood emerge. GDA can be used as a practical decoder for turbo codes in certain contexts. It is also a natural multiple-output decoder. The most important aspect of GDA, in our opinion, is that one can utilize the ML bounding technique and GDA to empirically determine a effective lower bound on the error probability with ML decoding. Our results show that, at a word error probability of 10^{-4}, GDA achieves the performance of ML decoding. Using the ML bounding technique and GDA, we establish that an ML decoder only slightly outperforms a MAP-based iterative decoder at this word error probability for the block size we used and the turbo code defined for WCDMA.1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . 2 1.2 History . . . . . . . . . . . . . . . . . . . . 3 1.3 Related works . . . . . . . . . . . . . . . . . 6 1.4 Contribution and Organization . . . . . . . . . 7 2 Background 9 2.1 Parallel Concatenated Convolutional Codes . . . 9 2.2 Maximal-a priori (MAP) Iterative Decoding Algorithm .10 2.3 Perturbed Decoding Algorithm . . . . . . . . . 11 2.4 Genetic Algorithm . . . . . . . . . . . . . . . 13 3 ML bounding technique 17 4 Perturbed Decoding for Turbo Codes 22 5 Genetic Decoding Algorithm 25 5.1 Genetic Decoding for Turbo Codes . . . . . . . 25 5.2 ML bound using GDA . . . . . . . . . .. . . . . 26 5.3 Complexity Aspects for GDA . . . . . . . . . . 30 3 4 CONTENTS 6 Simulation Results 31 6.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . 31 6.2 Parameters and Procedures for GDA . . . . . . . 31 6.3 Performance of GDA . . . . . . . . . . . . . . 34 7 Conclusions 38 7.1 Conclusions . . . . . . . . . . . . . . . . . . 38 7.2 Future works . . . . .. . . . . . . . . . . . . 40 Bibliography 4