臺灣博碩士論文加值系統

低密度同位檢測碼(Low density parity check codes, LDPC)[1][2]為線性區碼，亦為一種錯誤更正碼，其最早在1960年被Robert Gallager提出，為最接近Shannon Limit的碼之一，但由於那時VLSI技術尚未成熟，直到1990年LDPC碼被重新挖掘研究後證實其優異的性能，迅速竄起並成為最受歡迎的錯誤更正碼之一，在通訊界也被廣泛使用如：4G、802.11n和802.16e。

無線通訊裡MIMO通道能提升頻譜利用效率，增加傳輸速率改善通訊品質，但因受衰減通道的影響，系統需做通道估測來降低接收到的位元錯誤率(Bit Error Rate, BER)，但通道估測也有可能發生誤差，於是我們實際模擬碼率為1/2的LDPC碼在此情形下的錯誤性能變化。若通道估計正確，在2根傳送天線和2根接收天線的系統下用BPSK、QPSK和16-QAM調變能夠在SNR為9.2、13.1和16.1(dB)下達到BER=10^(-4)。而在同樣的2×2通道及環境下，假設錯誤的通道矩陣其機率模型為獨立同分佈的複數高斯函數且期望值為0變異數為0.01，此時BER小於某個值後下降會變的很緩慢，即使提高SNR似乎也很難讓BER曲線下降，用BPSK、QPSK和16-QAM調變在SNR為18.2、12.5和16.7(dB)下分別達到BER=10^(-4),10^(-3),10^(-2)，以此為基準相較原系統分別差了9.0、3.5和9.9(dB)。

Low density parity check (LDPC) codes[1][2] are a class of error correcting codes (ECCs). The LDPC codes are first invented by Robert Gallager in 1960. However since the VLSI technology is not fully developed at that time, LDPC codes were slowly forgotten in the following years. It was not until 1990 researchers reinvestigated the LDPC codes and found their near-Shannon limit error performance. Since then, the LDPC code has become one of the most popular ECCs. LDPC codes are also widely used in many communication systems, such as 4G, 802.11n, 802.16e, etc.


In wireless communication, MIMO can improve spectrum efficiency, and increase transmission rate, which can better the quality of communication. Yet, to such end, a channel estimation is required for demodulating the MIMO signals and hence for providing low bit error rate (BER). However, channel estimation can be inaccurate sometimes. In this thesis, a rate 1/2 code LDPC code is used to simulate this situation and to observe the variation of error performance. If the channel estimation is perfect, a MIMO system with two transmit, and two receive antennas can reach BER=10^(-4) at SNR=9.2, 13.1, 16.1 dB by using BPSK,QPSK and 16-QAM, respectively. On the other hand, when the estimation is inaccurate and the entries of error channel matrix are i.i.d. complex Gaussian with zero mean and variance 0.01, we found the required SNRs to reach the BER performances at 10^(-4),10^(-3),10^(-2) are SNR=18.2,12.5,16.7(dB) for BPSK,QPSK and 16-QAM, respectively.

頁碼
誌謝辭 I
中文摘要 II
英文摘要 III
目錄 IV
圖目錄 VI
表目錄 VII
第一章 簡介 1
1.1 動機 1
1.2 論文架構 1
第二章 低密度同位檢測碼(Low density parity check codes, LDPC) 3
2.1 LDPC碼介紹 3
2.2 LDPC碼的建構方式 6
第三章 解映射(Demapping) 9
3.1 訊號調變 9
3.2 SISO下的解映射 10
3.3 MIMO下的解映射 15
3.4 MIMO下通道估測發生錯誤時的解映射 19
第四章 遞迴解碼演算法 21
4.1 概論 21
4.2 機率域．遞迴解碼 22
4.3 對數域．遞迴解碼 27
4.4 最小和演算法 30
第五章 解映射與解碼 31
第六章 模擬結果與討論 33
第七章 總結 42
參考文獻 43

圖目錄
圖 頁碼
1.1 論文架構方塊圖 2
2.1 本例的查核矩陣H和其行列權重 6
2.2 本例的Tanner Graph 6
3.1 BPSK星座圖 9
3.2 QPSK星座圖 10
3.3 16-QAM星座圖 10
3.4 多天線系統架構圖 15
4.1 前半段遞迴示意圖 21
4.2 後半段遞迴示意圖 22
4.3 前半段遞迴訊息傳遞方向 25
4.4 後半段遞迴訊息傳遞方向 25
4.5 phi(x)函式圖 29
5.1 1個位元作調變時的解映射 31
5.2 2個位元作調變時的解映射 32
5.3 4個位元作調變時的解映射 32
6.1 (120,60) irregular LDPC經BPSK調變在SISO通道下的位元錯誤率 34
6.2 (1000,500) irregular LDPC經BPSK調變在SISO通道下的位元錯誤率 34
6.3 (120,60) irregular LDPC經QPSK調變在SISO通道下的位元錯誤率 35
6.4 (1000,500) irregular LDPC經QPSK調變在SISO通道下的位元錯誤率 35
6.5 (120,60) irregular LDPC經QAM調變在SISO通道下的位元錯誤率 36
6.6 (1000,500) irregular LDPC經QAM調變在SISO通道下的位元錯誤率 36
6.7 (120,60) irregular LDPC經BPSK調變在2×2通道下的位元錯誤率 37
6.8 (1000,500) irregular LDPC經BPSK調變在2×2通道下的位元錯誤率 37
6.9 (120,60) irregular LDPC經QPSK調變在2×2通道下的位元錯誤率 38
6.10 (1000,500) irregular LDPC經QPSK調變在2×2通道下的位元錯誤率 38
6.11 (120,60) irregular LDPC經QAM調變在2×2通道下的位元錯誤率 39
6.12 (1000,500) irregular LDPC經QAM調變在2×2通道下的位元錯誤率 39

表目錄
表 頁碼
1 SISO通道下的模擬參數設定及結果 40
2 2×2通道下的模擬參數設定及結果 40

[1] R. Gallager, Low-density parity-check codes, in IRE Trans. Information Theory, Jan, 1962.
[2] W. E. Ryan, An Introduction to LDPC Codes, The University of Arizona, Box 210104, Tucson, AZ 85721, Aug. 19, 2003.
[3] S. ten Brink, J. Speidel, R.-H. Yan, Iterative mapping and Decoding for Mutilevel Modulation, Proc. GLOBECOM, pp. 579-584, Nov. 1998.
[4] J. Wu and H.-N. Lee, Best Mapping for LDPC Coded Modulation on SISO, MIMO and MAC Channels, IEEE Wireless Commun. Networking Conf., vol. 4, Mar, 2004.