位元擷取低密度校驗碼之解碼效能改進

Abstract

低密度校驗碼已被證明可提供極佳的錯誤更正能力，並廣泛被大家所討論且使用在不同的通訊系統。傳統上，低密度校驗碼的校驗矩陣因為非零元素稀疏的特性，利用田納圖做圖形疊代解碼，例如和積演算法，有著不錯的解碼效能。為了因應不同通道的狀況，擷取技巧可以用在低密度校驗碼來調整碼率，以增加頻寬之使用效率，但位元擷取低密度校驗碼直接使用和積演算法時，會造成解碼效能衰退。為了改善位元擷取低密度校驗碼之解碼錯誤率，本文提供一個方法，透過籬笆解碼的觀點對和積演算法做修改；藉由適當的選擇一些與擷取節點有連接到的校驗節點，將其替換為小型籬笆結構，並與田納圖中剩下的校驗節點與位元節點共同疊代訊息，即可使得疊代解碼效能會比原先的和積演算法還來的好。經過模擬結果顯示，我們提出的修正方法可對位元擷取低密度校驗碼有不錯的解碼效能改進。

Low-density parity-check (LDPC) codes have been proved to provide the excellent error-correcting capability and are widely used in many communication systems. Because of the sparsity of parity-check matrices, LDPC codes can employ iterative decoding schemes, such as the sum-product algorithm (SPA), in the Tanner graph to achieve good decoding performance. In order to adapt to the different channel conditions, the puncturing technique can be used to adjust the code rate of an LDPC code, but for the punctured LDPC codes, using SPA directly will degenerate the decoding performance. To improve the decoding error rate of the punctured LDPC codes, this thesis proposes a modification of the SPA from the viewpoint of trellis decoding. The proposed algorithm appropriately selects some check nodes which are connected to the punctured nodes and replace the corresponding subgraph by an equivalent trellis to conduct the trellis-based decoding. The trellis decoders then cooperate with the rest of check and bit nodes in the Tanner graph by the SPA for further iterative decoding. Simulation results, show that the proposed algorithm can improve the decoding efficiency of the punctured LDPC codes.