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The Association of Warfarin Dosage in Clinical Use and Pharmacogenomics
No full text研究背景
Warfarin是臨床上一個常用來治療及預防血液栓塞疾病的藥物。然而使用warfarin來治療有其風險存在，基本上是因為病患間的個體差異，可歸因於：基因變異、環境、疾病種類及嚴重程度所影響，而使得在劑量的調整相當重要，現在臨床上的作法是監測其國際標準凝血時間比值(INR, international normalized ratio)。為達個別化用藥的目的，我們將討論可能的影響因子。
研究方法
本研究共收集94年7月至94年10月台大醫院內科部有使用warfarin之門診病患，於病情穩定後，抗凝血劑warfarin之使用情形，且收集病患之性別、年齡、適應症、病患用藥、INR值，並檢測病患的基因型，包括CYP1A2、CYP2C9、CYP2C19、CYP3A4、凝血因子Ⅱ、Ⅶ、Ⅸ、Ⅹ、蛋白質C、蛋白質S、EPHX1、GGCX、GSTA1和VKORC1等基因，以及檢測warfarin異構物之血中濃度，研究病患個體化的warfarin用藥與藥物基因體學的相關性。
研究結果
符合受試者條件的病患共計75位，其中73位成功鑑定出所有納入檢測基因之基因型型別。病患處方warfarin之適應症主要為深層靜脈栓塞(deep vein thrombosis)。病患的平均維持劑量為3.9毫克/天，平均之INR值為2.02。基因型與劑量使用之關連性分析發現，VKORC1基因的-1639、1173、2225位置和CYP2C19基因的681位置，與warfarin的維持劑量有高度的相關。且VKORC1基因的-1639、1173、2225三個位置，有鏈鎖不平衡(linkage disequilibrium)現象出現。另外，年齡的因素也和維持劑量的多寡有高度的負相關。
異構物濃度與維持劑量間有顯著的相關性存在，但與療效間卻沒有直接的相關，故無法以監測濃度的方式來調整病患之劑量，仍需採用臨床上使用的INR值(或PT值) 來監測。
結論
Warfarin的維持劑量，是多種因素互相影響所決定的。台灣人的平均維持劑量與西方人不同的原因，可能是因為CYP2C19與VKORC1上SNP位置變異頻率的不同所致。經由迴歸模式的建立，可根據年齡、體重及基因上的變異等因素，計算出適合台灣人所使用的warfarin藥物投與劑量，以減少副作用的產生，增加藥物使用的安全性。Background
Warfarin is an anticoagulant that is prescribed widely for the treatment and prevention of thrombosis. However, risks caused by warfarin vary, depending on the individuals, mainly genetic variations, environment, diseases and the severity of disease. It is important to adjust the dose of warfarin in clinical use based on the International Normalized Ratio (INR) value monitoring. All the possible factors involving dose adjustment will be investigated in this study in order to approach the individualized drug use.
Methods
Outpatients receiving long-term therapy were enrolled in National Taiwan University Hospital from July to October 2005. We collected the data including sex, age, indication, concomitant agents, INR value and the genotype of certain SNP sites in CYP1A2, CYP2C9, CYP2C19, CYP3A4, coagulation factor II, factor VII, factor IX, factor X, protein C, protein S, EPHX1, GGCX, GSTA1 and VKORC1. Furthermore, we detected the concentration of warfarin enantiomers and studied the association of pharmacogenomics and personalized warfarin doses.
Results
There were 75 patients enrolled in the study but two were excluded due to the failure of identifying the genotype. Deep vein thrombosis is the main indication in all patients. The mean maintenance dose was 3.9 mg/day and the mean INR value was 2.02. Results showed the variants of the positions -1639, 1173, 2225 in VKORC1 and the position 681 in CYP2C19 were highly related with warfarin maintenance dose. Also, there was negative relationship between age and warfarin maintenance dose in our study. Linkage disequilibrium of factor IX, GGCX and VKORC1 in certain SNP sites occurred in the study. The concentration of enantiomers was positively related to the maintenance dose of warfarin, but not to drug response. It is not applicable to adjustment of the dose by monitoring the concentration of racemic warfarin, or to its enantiomers.
Conclusion
The maintenance dose of warfarin was determined by multiple factors. The ethnic effect of Taiwanese and Caucasian might be partly caused by the different frequency of SNP sites of VKORC1 and CYP2C19. According to the regression model, we can calculate the warfarin maintenance dose by age and the genotype of these SNP sites so as to decrease the adverse drug effects and increase the safety of the drug.中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅱ
目錄……………………………………………………………………Ⅳ
表目錄……………………………………………………………… Ⅵ
圖目錄…………………………………………………………………Ⅶ
第一章 前言……………………………………………………………1
第二章 文獻探討………………………………………………………3
第一節 Warfarin 總論………………………………………………3
一、化學結構與物化性質……………………………………………3
二、藥理作用機轉………………………………………………………4
三、藥物動力學…………………………………………………………4
四、藥物藥效學…………………………………………………………5
五、適應症、劑量及副作用……………………………………………6
六、藥物交互作用………………………………………………………7
第二節 基因多型性……………………………………………………9
一、單核甘酸多型性(SNP)……………………………………………9
二、Cytochrome P450的基因多型性…………………………………9
三、凝血因子相關的基因多型性……………………………………10
四、與維他命K 循環有關的基因多型性……………………………10
五、基因多型性與warfarin 用藥劑量的關係……………………10
第三章 研究目的………………………………………………………13
第四章 研究方法………………………………………………………14
第一節 試驗設計與流程………………………………………………14
一、研究對象…………………………………………………………14
二、受試者選擇標準…………………………………………………14
三、研究進行流程……………………………………………………14
四、資料來源…………………………………………………………14
第二節 基因型鑑定……………………………………………………15
一、SNPstream 之鑑定……………………………………………15
二、PCR-RFLP 之鑑定………………………………………………17
第三節 Warfarin 異構物的濃度測定：HPLC 分析…………………20
一、檢體處理…………………………………………………………20
二、實驗步驟…………………………………………………………20
三、分析條件…………………………………………………………20
四、標準溶液配製……………………………………………………21
五、標準曲線(Standard curve)製作……………………………… 21
六、校正曲線(Calibration curve)製作……………………………22
七、分析方法之確效…………………………………………………22
八、萃取回收率………………………………………………………22
第四節 試劑配方………………………………………………………24
第五章 研究結果………………………………………………………29
第一節 研究對象的基本資料…………………………………………30
第二節 基因型鑑定……………………………………………………31
第三節 HPLC 異構物濃度分析………………………………………32
一、滯留時間及檢量線水準…………………………………………32
二、萃取回收率………………………………………………………32
三、確效性試驗………………………………………………………32
四、樣本數、異構物平均濃度………………………………………32
第四節 各因子間相關性分析…………………………………………33
一、維持劑量與基因型或其他因子之關聯性………………………34
二、異構物濃度與劑量或其他因子間的關聯性……………………34
第五節 Warfarin 維持劑量投與的模式建立………………………36
一、單變項分析………………………………………………………36
二、多變項分析及迴歸模式的建立…………………………………36
第六章 討論…………………………………………………………50
第一節 研究對象的基本資料…………………………………………50
第二節 基因型鑑定……………………………………………………51
第三節 HPLC 異構物濃度分析………………………………………53
第四節 各因子間相關性分析…………………………………………54
第五節 Warfarin 維持劑量投與的模式建立………………………56
第六節 研究限制………………………………………………………57
第七章 結論及建議……………………………………………………58
第八章 參考文獻………………………………………………………59
附錄一 受試者同意書…………………………………………………65
附錄二 問卷……………………………………………………………69
表目錄
表2-1 維生素K 依賴型蛋白質………………………………………12
表4-1 Primers for polymerase chain reaction-restriction fragment length
polymorphism analysis…………………………………28
表5-1 Demographic and clinical characteristics of the enrolled patients……37
表5-2 Selected SNP sites for genotyping………………………………… 38
表5-3 Genetic variants of the enrolled patients…………………………………39
表5-4 人體血漿中warfarin 異構物及diclofenac 的萃取回收率…………………………40
表5-5 偵測人體血中warfarin 異構物之方法確效參數……………40
表5-6 Warfarin daily dose and INR value in various genotypes……………………41
表5-7 Characteristics of patients with higher or lower warfarin dose requirements…43
表5-8 維持劑量與其它因子關係表………………………………………44
表5-9 影響warfarin 維持劑量之單變項迴歸分析…………………………………44
表5-10 Regression equation for modeling warfarin daily dose requirements……….46
表5-11 Regression equation for modeling warfarin weekly dose requirements
in desired INR value……………………………………………………46
圖目錄
圖2-1 The structure of racemic warfarin……..………………………….……...3
圖2-2 The vitamin K cycle…………………………………………………..…..12
圖4-1 SNPstream®作用原理之圖解………………………………………..…..26
圖4-2 The strategy of RFLP to genotype CYP2C19*2 and *3…………..….27
圖5-1 Warfarin doses for population study…………………………………….47
圖5-2 INR value of patients receiving warfarin…………….……..…………..47
圖5-3 RFLP analysis of CYP2C19……………………………………….…….48
圖5-4 Calibration curve of warfarin enantiomers……….………………........48
圖5-5 Box plot of mean warfarin doses for different age and genotype.…..4
Search for KL decay to light pseudoscalar sgoldstino at E391a
No full text本論文尋找可能的中性K介子衰變至pi0介子以及輕準純量goldstino(代稱X粒子)。所使用數據來自日本國家高能加速器心質子加速器的E391a 偵測器，於九十四年二月至三月間取。由事例重建，我們針對四組可能的質量範圍搜尋，並無發顯著訊號，因此給予90%信心水準之衰變分率上限，分別為r(KL->pi0X(181.7 MeV)) < 2.26e-6r(KL->pi0X(198.0 MeV)) < 1.97e-6r(KL->pi0X(214.3 MeV)) < 1.81e-6r(KL->pi0X(230.6 MeV)) < 1.17e-6With mX = 214.3 MeV as hinted by a previous HyperCPxperiment, we report the first search of the decay KL->pi0X sing the Run2 data sample recorded with the E391a detector t KEK-PS. The particle X has a theoretical interpretation as he pseudoscalar sgoldstino. It is predicted to decay redominantly to two photons. As a result of this search, weet a 90% confidence-level upper limit for its branching atio at B(KL->pi0X)<1.81e-6. We also performed a search for he same mode assuming different mX: 181.7MeV, 198MeV, 30.6MeV and set respective 90% confidence-level upper imits: B(KL->pi0X181.7)<2.26e-6,(KL->pi0X198.0)<1.97e-6 and B(KL->pi0X230.6)<1.17e-6. TheL flux for the E391a Run2 data set is also measured to be (4.83+-0.21)e9 in the fiducial region.Introduction 1.1 The X particle - HyperCP experiment . . . . . . . . . . . . . 1.2 The sgoldstino interpretation . . . . . . . . . . . . . . . . . . 1.3 The Higgs boson interpretation . . . . . . . . . . . . . . . . . 4.4 Hints at decay K0L 0X(X ! - KTeV and NA48 experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 K mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 KEK E391a 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 The Neutral Beam . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Particle Generation . . . . . . . . . . . . . . . . . . . . 8.2.2 The Pencil Beam . . . . . . . . . . . . . . . . . . . . . 9.3 The E391a Detector . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Electromagnetic Calorimeter . . . . . . . . . . . . . . . 11.3.2 Charged Veto . . . . . . . . . . . . . . . . . . . . . . . 14.3.3 Main Barrel . . . . . . . . . . . . . . . . . . . . . . . . 17.3.4 Front Barrel . . . . . . . . . . . . . . . . . . . . . . . . 21.3.5 Collar Counters . . . . . . . . . . . . . . . . . . . . . . 22.3.6 Back Anti . . . . . . . . . . . . . . . . . . . . . . . . . 24.3.7 Beam Hole Charged Veto . . . . . . . . . . . . . . . . . 25.4 Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . 25.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 27.4.2 PMT operation in vacuum . . . . . . . . . . . . . . . . 27.5 Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.5.1 AmpDiscri module . . . . . . . . . . . . . . . . . . . . 29.5.2 Physics trigger . . . . . . . . . . . . . . . . . . . . . . 29.5.3 Other triggers . . . . . . . . . . . . . . . . . . . . . . . 32.5.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . . 33.6 Data Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.6.1 Data taking shifts . . . . . . . . . . . . . . . . . . . . . 34 Monte Carlo Simulation 36.1 Particle generation . . . . . . . . . . . . . . . . . . . . . . . . 36.2 KL propagation and decay . . . . . . . . . . . . . . . . . . . . 37.3 Decay modes and statistics . . . . . . . . . . . . . . . . . . . . 37.3.1 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 38.4 Energy deposit . . . . . . . . . . . . . . . . . . . . . . . . . . 38.5 Accidental activity . . . . . . . . . . . . . . . . . . . . . . . . 40.6 Combination of modes . . . . . . . . . . . . . . . . . . . . . . 40 Analysis Method 41.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 42.2.1 Clustering routine . . . . . . . . . . . . . . . . . . . . . 42.2.2 Kinematic reconstruction . . . . . . . . . . . . . . . . . 43.2.3 Reconstruction results . . . . . . . . . . . . . . . . . . 52.3 Candidate Selection . . . . . . . . . . . . . . . . . . . . . . . . 52.3.1 Signal box . . . . . . . . . . . . . . . . . . . . . . . . . 52.3.2 0 region . . . . . . . . . . . . . . . . . . . . . . . . . . 53.4 Background Suppression . . . . . . . . . . . . . . . . . . . . . 53.4.1 Veto cuts . . . . . . . . . . . . . . . . . . . . . . . . . 54.4.2 Kinematic and MB cuts . . . . . . . . . . . . . . . . . 56.4.3 Cluster quality . . . . . . . . . . . . . . . . . . . . . . 60.4.4 0 tail . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4.5 KL radius at the exit of collimator 6 . . . . . . . . . . 63.4.6 Selection results . . . . . . . . . . . . . . . . . . . . . . 63 Signal Extraction 66.1 Likelihood Method . . . . . . . . . . . . . . . . . . . . . . . . 66.1.1 De nition . . . . . . . . . . . . . . . . . . . . . . . . . 66.1.2 Background PDF . . . . . . . . . . . . . . . . . . . . . 67.1.3 Background normalization . . . . . . . . . . . . . . . . 69.1.4 Signal PDF . . . . . . . . . . . . . . . . . . . . . . . . 70.1.5 Fit results . . . . . . . . . . . . . . . . . . . . . . . . . 70pper Limit Estimation . . . . . . . . . . . . . . . . . . . . . 71.2.1 Systematic error study . . . . . . . . . . . . . . . . . . 71.2.2 Implementation of systematic errors . . . . . . . . . . . 75.2.3 Final tting results . . . . . . . . . . . . . . . . . . . . 75.3Counting Method . . . . . . . . . . . . . . . . . . . . . . . . . 77.4KL Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78onclusions and Prospects 81.1Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Increased data statistics { Run3 data set . . . . . . . . 82.2.2 Increased MC statistics . . . . . . . . . . . . . . . . . . 83.2.3 Finer CsI crystals { E14 experiment . . . . . . . . . . . 84 0Monte Carlo 89inematic Fitting 9
An Analog/Mixed-Signal Circuits Macromodel Technique for Yield Analysis Applications
No full text隨著IC製程進步，電晶體尺寸面積縮小，現今製程變異已是影響良率的重要因素之一。在製程變異的影響下，IC的效能將異於其理想狀況，導致部分產品雖然可以運作，但其效能已不符合規格。蒙地卡羅分析法是一個常用的良率分析方法，藉由了解製程變異的機率分布，大量模擬實際的電路參數組合，來預測電路設計的良率。藉由蒙地卡羅分析法，我們可以預測良率，但是這個分析法卻有著耗費大量電路模擬時間的缺點。
Macromodel技術可用來加速電路模擬，其概念是以較精簡的模型替換電路的內部區塊（例如放大器）來達到模擬速度加快的目的。然而此一技術無法直接應用在良率分析上。因為在蒙地卡羅分析法中，每一個產生的電路參數組合皆有著不同的電路效能，以致於必須耗費大量的時間來產生其替代模型。
在這篇論文中，我們改善了Macromodel技術，加快模型建立速度。對於需要大量電路參數組合的蒙地卡羅分析法，有著顯著的改善效果。在實驗結果分析方面，我們以一Flash ADC做為實驗電路，實驗結果為良率分析速度提升3.7倍，電路模擬速度提升4倍，電路效能是否符合規格的預測準確率在94.17 %左右。As the IC fabrication technology advances, the transistor feature size keeps shrinking and it is possible now to integrate a complete system on a chip. However, as the device size decreases, the inevitable process variations become an important factor of manufacturing yield. Under the influence of process variations, the performances of the fabricated IC's deviate from those of the nominal design. As a result, some IC's may still function, but their specifications are out of the acceptable range. Monte Carlo simulation is a commonly used technique for yield estimation. Given the process variation distribution, a sufficient large number of circuit instances are generated to match the fabrication distribution. Then, all the generated instances are simulated. Then, one can predict the performance distribution and yield based on the simulation results. The problem with Monte Carlo simulation is the required long circuit simulation time.
Macromodel is a commonly used technique to speed up circuit simulation. The idea is to replace a circuit block, e.g., OPAMP, with a reduced model. However, for yield estimation applications, the macro-modeling process has to be performed for each circuit block instance because they are different in the existence of process variations. In this thesis, we propose a macromodel technique which is specially useful for yield estimation applications where a large number of macromodels have to be generated for the same circuit block.
We use a flash ADC to validate our technique, with the proposed macromodeling technique, the speed up of yield estimation is about 3.7 times, the speed up of circuit simulation is 4 times, and the pass/fail classification accuracy is about 94.17%.Table of Contents
Acknowledgement
Abstract
List of Figures
List of Tables
Ch.1 Introduction……………………………………………………...1
Ch.2 Preliminaries…………………………………………………….3
2.1 Yield…………………………………………………………….3
2.2 Variations……………………………………………………….3
2.2.1 Sources of Variations……………………………………...3
2.2.2 Process Variations…………………………………………3
2.2.3 Global and Local Variations………………………………6
2.2.4 Static Analysis of Process Variations……………………..6
2.3 Macromodeling Techniques…………………………………….7
2.3.1 Types of Macromodel……………………………………..8
2.3.2 The Macromodeling Process………………………………9
2.3.3 Application of Macromodeling to Yield Estimation……..10
Ch.3 Process Variations Macromodeling……………………………11
3.1 Basic Ideas……………………………………………………..13
3.2 Mapping Function Construction Flow…………………………13
3.3 Classify Considerable Performances of Functional Block…….15
3.4 Global Variations Analysis……………………………………15
3.5 Local Variations Analysis…………………….……………….23
3.6 Mapping Function…………………….……………………….25
Ch.4 Experiment and Result Analysis……………………………….30
4.1 OPAMP Macromodel Template……………………………….30
4.2 A/D Converters…………………………………………………32
4.3 Process Variation……………………………………………….34
4.4 Experiment Results…………………………………………….34
4.4.1 Process Variations Macromodeling……………………...34
4.4.2 A/D Converters Simulation Result……………………….37
Ch.5 Conclusions and Future Work…………………………………39
Reference………………………………………………………………..4
Theory and Performance of ML Decoding for LDPC Codes Using Genetic Algorithm
No full text低密度奇偶校驗碼近幾年來吸引廣大研究者的關注，許多人先後投入這個領域，其中，最主要的原因在於優越的解碼能力。傳統的解碼器主要運用訊息傳遞的原理，藉由眾人的力量更正因雜訊干擾而錯誤的資訊。最大概度解碼則是編碼理論中公認最佳的解碼器。雖然前者的方法有不錯的更正效果，但是始終無法達到最大概度解碼的能力，而後者卻又因為複雜度太高無法實行。因此，如何求出低密度奇偶校驗碼中最佳解碼器的更錯效果就是本篇論文研究的重點。 相關研究指出，此種編碼方法整體效果可能達到通道容量，但我們還是想知道某些特定編碼的極限值。此外，渦輪碼的最大概度解碼研究也在某些論文中提出，他們成功找出錯誤率1.5*10^(-4)以下的解碼表現，這些成就也成為本篇論文參考及學習方向。 我們發現在錯誤率10^(-5)以下的地方，干擾解碼演算法可以有效達到出最大概度解碼的能力，但是當錯誤率較高時，這樣的方法就不太有效，因此我們提出加入額外資訊的概念及可行性研究。這些資訊稱做gift，主要協助解碼器產生其他高度可能的答案。為了更有效率找到這些額外資訊，本篇論文根據基因演算法的概念，設計出兩種新的解碼演算法。 基因解碼演算法中的染色體由一群已知的0、1或未知的基因組成，傳統的遞迴解碼器用來評斷這些染色體的好壞，運用「物競天擇、適者生存」的原理，留下最優良的基因，多代演化後，能夠幫忙解出真正傳送編碼的染色體就會出現。同時我們也提出平行基因解碼演算法，每個初始染色體獨自演化，最終解回真正的傳送資訊。 對我們而言，基因解碼演算法最重要的地方是任何人用模擬的方式求出特定低密度奇偶校驗碼的最大概度解碼能力。根據我們的模擬結果，此種解碼方法比傳統方法好上0.1dB以上，並且成功在錯誤率10^(-5)以下的地方找到解碼能力的極限值。此外，此法也比先前提到的干擾解碼演算法好上0.02~0.03dB，並擁有和球體裝填極限一樣的型式。只要複雜度允許，本文提出的方法就可以用來改善傳統解碼方法的能力。Low-density parity-check (LDPC) codes drawn large attention lately due to their exceptional performance. Typical decoders operate based on the belief-propagation principle. Although these decoding algorithms work remarkably well, it is generally suspected that they do not achieve the performance of ML decoding. The ML performance of LDPC codesemains unknown because efficient ML decoders have not been discovered.lthough it has been proved that for various appropriately chosen ensembles of LDPC codes, low error probability and reliable communication is possible up to channel capacity, we still want to know the actual limit for one specificode. Thus, in this thesis, our goal is to establish the ML performance. t a word error probability (WEP) of 10^{-5} or lower, we find that perturbed decoding can effectively achieve the ML performance at reasonable complexity. In higher error probability regime, the complexity of PD becomes prohibitive. In light of this, we propose the use of gifts. Proper gifts can induce high likelihood decoded codewords.e investigate the feasibility of using gifts in detail and discover that the complexity is dominated by the effort to identify small gifts that can pass the trigger criterion. A greedy concept is proposed to maximize the probability for a receiver to produce such a gift. Here we also apply the concept of gift into the genetic algorithm to find the ML bounds of LDPC codes. n genetic decoding algorithm (GDA), chromosomes are amount of gift sequence with some known gift bits. A conventional SPA decoder is used to assign fitness values for the chromosomes in the population. After evolution in many enerations, chromosomes that correspond to decoded codewords of very high likelihood emerge. We also propose aarallel genetic decoding algorithm (P-GDA) based on the greedy concept and feasibility research of gifts. The most important aspect of GDA, in our opinion, is that one can utilize the ML bounding technique and GDA to empirically determine an effective lower bound on the error probability with ML decoding. ur results show that GDA and P-GDA outperform conventional decoder by 0.1 ~ 0.13 dB and the two bounds converge at a WEP of . Our results also indicate that, for a practical block size of thousands of bits, the SNR-error probability relationship of LDPC codes trends smoothly in the same fashion as the sphere packing bound. The abrupt cliff-like error probability curve is actually an artifact due to the ineffectiveness of iterative decoding. If additional complexity is allowed, our methods can be applied to improve on the typical decoders.1 Introduction 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Contribution and organization . . . . . . . . . . . . . . . . . . . . . . 5 Background 7.1 Low-density parity-check code . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Sparse parity matrix . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Regular LDPC codes . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 Irregular LDPC Codes . . . . . . . . . . . . . . . . . . . . . . 8.2 Tanner graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Decoding of LDPC codes . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.2 Concept of belief propagation . . . . . . . . . . . . . . . . . . 10.3.3 Sum-product algorithm . . . . . . . . . . . . . . . . . . . . . . 11.3.4 Iterative decoding . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 ML bounding technique . . . . . . . . . . . . . . . . . . . . . . . . . 16.4.1 Bounding ML WEP through simulation . . . . . . . . . . . . 16.4.2 Multiple-output decoding . . . . . . . . . . . . . . . . . . . . 18.5 Genetic decoding algorithm . . . . . . . . . . . . . . . . . . . . . . . 19.6 Sphere packing bound(SPB) . . . . . . . . . . . . . . . . . . . . . . . 22 Bounding ML performance using perturbation noises 25.1 Perturbed decoding for LDPC codes . . . . . . . . . . . . . . . . . . 25.2 Genetic decoding with additive noise as chromosomes . . . . . . . . . 29 Feasibility of gifts in facilitating ML performance bounding 33.1 Gift-assisted decoding for LDPC codes . . . . . . . . . . . . . . . . . 34.2 Complexity analysis of randomly selected gifts . . . . . . . . . . . . . 37.3 Gift selection based on a priori bit probability . . . . . . . . . . . . . 39.4 Feasibility of evolutionary algorithm . . . . . . . . . . . . . . . . . . . 42.5 Concentration of useful gift bits . . . . . . . . . . . . . . . . . . . . . 44 Genetic decoding algorithm 49.1 Gift-assisted genetic decoding algorithm for LDPC codes . . . . . . . 49.2 ML bound using genetic decoding algorithm . . . . . . . . . . . . . . 52.3 Parameters and procedures for genetic decoding algorithm . . . . . . 53.4 Simulation results of genetic decoding algorithm . . . . . . . . . . . . 54 Parallel genetic decoding algorithm 57.1 Parallel genetic decoding algorithm for LDPC codes . . . . . . . . . . 57.2 Parameter and procedure for parallel genetic decoding algorithm . . . 60.3 Simulation results of parallel genetic decoding algorithm . . . . . . . 63 Summary 65 Conclusions and future works 67.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68ibliography 7
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