低密度奇偶檢查碼的同位校驗矩陣的建構方法有很多種，其中一類是隨機建構的，例如：Gallager Code、Mackay Code，而還有一類就是由代數幾何所構成，例如：歐幾里德幾何(EG-LDPC Code)、投影幾何(PG-LDPC Code)。本論文是利用代數幾何—歐幾里德幾何的方法建構同位校驗矩陣的，以及其矩陣為一個準循環的形式。並分別在不同通道環境中模擬。
在對於有線或無線通訊中，脈衝雜訊是一個重大的問題。由於脈衝雜訊不同於一般的AWGN雜訊，其雜訊能量往往是AWGN雜訊能量的數百倍，而常見的脈衝雜訊有Class A model和Bernoulli-Gaussian通道模型，而這兩種雜訊皆屬於無記憶性型，發生雜訊的時機非常隨機，無法去描述真實通道的特性，故發展出基於馬可夫鏈特性的雜訊Markov-Gaussian(MG)通道模型。而為了解決脈衝雜訊，在本論文中利用了QC EG-LDPC結合了最大後驗機率(MAP)來進行通道估測並且利用和積演算法(SPA)進行解碼來降低位元錯誤率(BER)。

There are many ways to construct parity check matrices for low density parity check codes, one of which is randomly constructed, for example: Gallager Code, Mackay Code, another is algebraic geometry, for example: Euclidean geometry (EG-LDPC Code), projection geometry (PG-LDPC Code). This thesis constructs parity check matrices by means of algebraic geometry - Euclidean geometry, and its matrix is a quasi-cyclic form. And simulation in different channel environment.
Impulse noise becomes one of the problems in the wired and wireless communication systems. As the impulse noise is different from the general AWGN noise, the impulse noise energy is often hundreds of times the energy of the AWGN noise. The common impulse noise such as Middleton class A and Bernoulli-Gaussian noise model. Both of them are memoryless, which mean that their occurrences are random. However, they can’t describe the characteristics of the real channel. A memory channel such as Markov-Gaussian is introduced to address the characteristics of the real channel.
To address the impulsive noise, QC EG-LDPC is used in this paper to combine the maximum a posteriori (MAP) Estimation for channel estimation and to reduce the bit error rate (BER) by using the SPA algorithm.

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