以優先權為基礎之消去迴圈演算法建構低密度同位元檢查碼

Abstract

低密度同位元檢查碼具有優異的解碼能力及硬體實現的低複雜度，近年來受到廣大討論與研究，其中一部分研究為設計具有較大周長或是消除更多的短迴圈的同位檢查矩陣以得到更好的解碼效能。本論文提出以優先權為基礎的消去迴圈演算法，統計每個元素包含的迴圈數量高低排列優先順序，如此可有效率打斷迴圈的連結，故本改良式演算法能大幅降低建構矩陣的運算量。此外設計低編碼長度的位元檢查矩陣時因為優先權的機制能更有效率打斷迴圈，因此相較其它兩者類似架構的演算法能消除更多的迴圈，得到效能上的增進，尤其是在較高訊號雜訊比的情況下差異較為明顯，適用於低功耗或低運算量等通訊系統。

In recent years, Low-Density Parity-Check Codes have attracted a lot of attention and discussion due to great decoding ability and low complexity of hardware implementation. Some research focuses on performance improvement by designing high performance coding with large girth. In this thesis, we propose a priority based cycle elimination algorithm. It is efficient to eliminate cycle by setting the priority based on the number of dependent cycles. As shown in the results, the proposed algorithm can significantly reduce the complexity in operation. It can also construct high-performance codes and eliminate more cycles than traditional approaches for short code-length applications. Comparing with the other algorithms, the proposed algorithm can have better decoding performance, especially in high SNR environment; hence, our algorithm can satisfy the requirement of low-power communication systems.