適用於低密度奇偶檢查迴旋碼之改良式差值動態排程解碼演算法

Abstract

前人的研究顯示，具有分式奇偶檢查矩陣的低密度奇偶檢查迴旋碼因為其Tanner圖裡有長度為4的循環，所以位元錯誤率很差。然而我們最近的研究發現，如果透過穿刺的概念將原來的Tanner圖轉換成具有較大的最小循環長的Tanner 圖，那些具有分式奇偶檢查矩陣的低密度奇偶檢查迴旋碼的位元錯誤率可以跟具有多項式奇偶檢查矩陣的低密度奇偶檢查迴旋碼的位元錯誤率一樣好，或者更好。由於以往對於穿刺的低密度奇偶檢查碼的解碼而言，排程法常被用來進一步改善位元錯誤率或是增加解碼的收斂速度，所以我們在現有的排程法中選擇表現較好的排程演算法 (EDS演算法) 來解那些具有分式奇偶檢查矩陣的低密度奇偶檢查迴旋碼，看看是否可以得到更好的位元錯誤率。在這篇論文中，我們首先修改了EDS演算法中的差值方程式，使得解碼過程中的更新順序更洽當。此外，透過觀察我們發現，使用排程法來解碼可能會有不收斂或者是收斂到非最佳碼字的問題，有鑑於此，我們提出兩個方法，分別使用擾動和位元翻轉來解決問題。根據模擬結果，無論是對於具有分式校驗矩陣的低密度校驗迴旋碼還是對於具有多項式校驗矩陣的低密度校驗迴旋碼，我們提出的排程演算法的位元錯誤率都比一些現有排程演算法的位元錯誤率好。

Previous studies on low-density parity-check convolutional codes (LDPC-CCs) revealed that LDPC-CCs with rational parity-check matrices (RPCM) have poor bit-error-rate (BER) performances due to the existence of lenth-4 cycles in their Tanner graphs. In our recent work, we found that we can transform the original Tanner graph of an LDPC-CC with an RPCM into a new Tanner graph with larger girth based on the concept of puncturing such that the LDPC-CC can have a comparable or even better BER performance than those of LDPC-CCs with polynomial parity-check matrices (PPCMs). For the decoding of punctured LDPC codes, sequential schedules are usually used to improve BER performances or speed up the convergence of the decoding. We select the well-performed e?cient dynamic scheduling (EDS) among the available sequential schedules to decode those LDPC-CCs with RPCMs in order to obtain better BER performances. In this thesis, we ?rstly modify the residual function of EDS to have a more appropriate updating order. Besides, since several observations indicate that the decoding based on the original EDS or our improved EDS may not converge or converge to non-optimal codewords, two re?ned strategies based on the perturbation and the bit- ipping are hence proposed to mitigate these problems. Revealed by the simulations results, not only for RPCMs but also for PPCMs, our proposed algorithm can provide better BER performances than those of several existent schemes.