臺灣博碩士論文加值系統

根據其它文獻上證明的結果，我們得知隨機旁集(random-coset)非二位元 的低密度同位檢查碼(low-density parity-check code, LDPC codes)及非規則重覆累加碼(irregular repeat-accumulate code, IRA code)在搭配q-ary的非均勻訊號星雲時，可達到無限制的通道極限。而在[19]中可得知隨機旁集IRA碼，因為使用的是簡單的時變累加碼(time-varying accumulate code)編碼，所以複雜度會比LDPC碼還低。且模擬的結果顯示，當我們將變數節點的度數固定為2時，就能得到不錯的效能，這也意味著對於非二位元 重覆累加碼而言，只要將訊息重覆二次即可得到相當好的效能。因為訊息重覆二次，該編碼器就會擁有類似渦輪碼的架構。因此我們預測若將原本渦輪碼(turbo code)中的迴旋碼(convolutional code)改用時變累加碼來代替，應該可以得到不錯的效能。另外，我們也提出了一個新的編碼調變方案(modulation and coding scheme, MCS)，透過特定的轉換器，將累加碼的輸入與輸出限制在一個較小的符號系統(alphabet)，因此相較於一般的累加碼，其輸入輸出都是在整個有限場 ，我們的調變方案使之能更適用於現代通訊系統不同通道條件下的速率適應調整(rate adaptation)。

According to the results of other research, random-coset low-density parity-check (LDPC) codes and irregular repeat-accumulate (IRA) codes with q-ary nonuniform signal constellations, under belief-propagation (BP) decoding, will approach the unrestricted Shannon limit. It has been shown that, random-coset LDPC codes has much higher encoding complexity than the IRA code, because IRA code can be encoded using the concept of time-varying accumulate code as proposed in [19]. And the simulation results show that, the best SNR thresholds of random-coset LDPC or IRA codes are obtained when the average variable node degree as close as possible to 2. This also means that we can get good performance, as long as repeat the information twice, which implies the turbo codes with two branches encoded by two independent time-varying accumulate (RA) codes may have good potential to construct good codes. In addition, compared with conventional repeat accumulate codes with input and output from the entire Galois field , we also proposed a time-varying accumulate codes with input and output restricted to a small-sized alphabet (smaller than ).This construction allows better flexibility of modulation and coding scheme (MCS) for rate matching in modern communication systems.

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 背景簡介 1
1.2 研究動機 1
1.3 論文架構 2
第二章 隨機旁集非二位元碼(Nonbinary Random-Coset Codes) 4
2.1 隨機旁集非二位元 的低密度同位檢查碼(LDPC) 4
2.2 隨機旁集非二位元 的非規則重覆累加碼(IRA) 6
第三章 疊代解碼演算法 11
3.1 伽羅瓦代數(Galois field)的運算與分析 11
3.2 隨機旁集非二位元 IRA碼的BP解碼演算法 12
3.3 隨機旁集非二位元 IRA碼的BCJR解碼演算法 14
第四章 隨機旁集 IRA碼的高斯近似法(Gaussian Approximation) 19
第五章 旁集 IRA碼的設計 21
5.1 LDPC碼和IRA碼基於 的EXIT分析差異 21
5.2 BCJR疊代解碼演算法的EXIT charts設計分析 22
第六章 渦輪碼基於非二位元時變累加碼 27
6.1 LDPC和IRA碼的模擬結果觀察 27
6.2 新的編碼方式─渦輪碼基於非二位元時變累加碼 30
6.3 渦輪碼基於非二位元時變累加碼的碼域轉換 32
第七章 渦輪碼基於非二位元時變累加碼的解碼與EXIT chart設計 33
7.1 渦輪碼基於非二位元時變累加碼的解碼 34
7.2 渦輪碼基於非二位元時變累加碼的EXIT chart設計 38
第八章 模擬結果與結論 41
8.1 渦輪碼基於非二位元時變累加碼模擬結果 41
8.2 結論 45
參考文獻 47
附錄 51

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