應用類費氏數列於準循環低密度奇偶校驗碼之編碼

Abstract

本篇論文介紹了些關於低密度奇偶校驗碼(low-density parity-check codes, LDPC codes)之編碼與解碼的觀念，並且著重於奇偶校驗矩陣(parity-check codes matrix)的建立方式。 現存建立低密度奇偶校驗碼的方式有兩類，一個為隨機產生碼(random codes)，另一個則是特定產生碼(deterministic codes)，兩者方式皆有其各自的利弊。對於隨機產生碼來說，其建立方式主要為電腦搜尋(computer-search)，因此，其可適用於任意長度或是任意比例的碼，但是，因為缺乏特定的奇偶校驗矩陣，其也會有較高的硬體複雜度。另一方面，特定產生碼是利用事先決定好的奇偶校驗矩陣，甚至是更有結構性的準循環架構(Quasi-cyclic form)去建立，如此一來，其擁有較低的硬體複雜度及碼的長度與比例的選擇彈性。所以，我們勢必要在硬體複雜度以及碼的彈性間做平衡以及取捨。 本論文提出了一個應用類費氏數列於準循環低密度奇偶校驗碼的編碼方式，其同樣為特定產生碼的一種，並且提供了對於某些特定長度以及比例的碼，一個擁有低硬體複雜度的選擇。

The thesis introduces the concepts of encoding and decoding about low-density parity-check (LDPC) codes and focuses on the part of code constructions. There are two kinds of code constructions in LDPC codes. One is random codes, and the other is deterministic codes. Both of them have pros and cons. For the random codes, they are constructed by computer-search, so they are more general for constructing any code length and code rate. However, because they do not have certain parity-check matrix, they have higher hardware complexity. On the other hand, the deterministic codes are constructed by deterministic matrices and even more structural matrix, like QC-form, so they have lower hardware complexity but fewer generalizations about code length and code rate. Therefore, we must do some trade-off between the hardware complexity and the generalizations. The thesis proposes a systematic method for constructing QC-LDPC codes based on Fibonacci-like sequences which is also a kind of deterministic codes. Although it cannot suit any code length and code rate, it provides some choices about code length and code rate with lower hardware complexity.