運用籬笆解碼演算法於低密度校驗碼之解碼效能改進

Abstract

低密度奇偶校驗碼是近幾年來為人所熟知的一個解碼效能強大的錯誤更正碼。由於其奇偶校驗矩陣有非零元素稀疏的特性，所以可以針對它的田納圖使用圖形疊代解碼演算法，例如和積演算法，來進行解碼。然而若田納圖之中含有循環路徑的結構，會造成和積演算法的資訊更新公式失準進而導致解碼效能偏離最大似然估計的效果。論文中我們以籬笆解碼的觀點，提出了幾種方法可將造成和積演算法失效的關鍵短循環路徑以特殊的籬笆結構進行替代，並將相關籬笆解碼器與田納圖中剩下的位元節點與校驗節點繼續進行疊代解碼。模擬結果顯示，本論文提出之新式解碼器可針對低密度奇偶校驗區塊碼與迴旋碼獲得不錯的解碼效能改進。

Low-density parity-check (LDPC) codes are well-known error-correcting codes in recent years, which have been shown to achieve capacity-approaching performance. Because LDPC codes are constructed using sparse tanner graphs, they usually use the graph-based iterative decoding schemes, for example the sum-product algorithm. However if the tanner graph contains cycles, it will violate the independence hypothesis in the sum-product algorithm, and then cause a serious performance degradation from the maximum-likelihood decoding. In this thesis we replace the affective short cycles by simple trellis decoders to improve the performance of iterative decoding. Verified by the simulation results, good decoding performance can be obtained for the LDPC block and convolutional codes based on our new methods.