论文标题
拓扑驱动的方法用于构建多层类型的方法（带有淋巴结的多编码）准环状低密度均等 - 无线渠道，WDM Long-Haul和档案全息记忆的代码
Topologically Driven Methods for Construction Of Multi-Edge Type (Multigraph with nodes puncturing) Quasi-Cyclic Low-density Parity-check Codes for Wireless Channel, WDM Long-Haul and Archival Holographic Memory
论文作者
论文摘要
在本博士学位论文中，讨论了具有给定误差校正（“瀑布，误差 - 层”）和复杂性（根据循环尺寸和调整器的平行级级别）的现代方法满足QC-LDPC代码（“瀑布，误差 - 地板”）和复杂性（平行性水平）概述：1。重量枚举器优化，使用密度进化，MI（P/exit-exim-Chart）和Is exim-Chart和Is Is of Inim and Is of Inimatian and Is Is of Inim and Is exim and Is Inim and Is Inim and Is Inim and Is It）。相互通道近似等； 2。协方差演变及其近似； 3。QC代码构建的提升方法：钉子，嘉宾和测试，带有腰围，EMD，ACE优化的爬山； 4。使用CPU/GPU的代码距离估计及其并行实现的上限和下限； 5。BROUWER-ZIMMERMAN和数字几何代码距离估计方法； 6。对于误差地板估计的重要性抽样； 7。基于循环组分解的QC代码的长度和速率适应方法； 8。相互作用筛选的方法，可以改善BP下的性能（去倍率变量），并且是近似值。我们提出了几种最先进的方法：MET QC-LDPC代码构建的模拟退火解放；快速EMD和代码距离估计；地板尺度模块化提升，以适应Lenght的适应；由于SNR的估计误差，代码构建的阈值和IT硬件友好压缩的阈值和IT硬件友好压缩的快速有限长度协方差的演变率。我们发现，在匹配的度量空间下，使用拓扑增厚（连续和离散曲率的同型）发现了拓扑原因，从而可以将此思想推广到信号处理和机器学习的一类非线性代码中。使用所提出的算法构建了几代WDM长HAUL误差校正代码。它用于“ 5G EMBB” 3GPP TS38.212和其他应用程序，例如闪存存储，压缩传感测量矩阵。
In this Phd thesis discusses modern methods for constructing MET QC-LDPC codes with a given error correction ("waterfall, error-floor") and complexity (parallelism level according circulant size plus scheduler orthogonality of checks) profiles: 1. weight enumerators optimization, protograph construction using Density Evolution, MI (P/Exit-chart) and it approximation: Gaussian Approximation, Reciprocal-channel approximation and etc; 2. Covariance evolution and it approximation; 3. Lifting methods for QC codes construction:PEG, Guest-and-Test, Hill-Climbing with girth, EMD, ACE optimization; 4. Upper and lower bounds on code distance estimation and its parallel implementation using CPU/GPU; 5. Brouwer-Zimmerman and Number Geometry code distance estimation methods; 6. Importance Sampling for error-floor estimation; 7. Length and rate adaption methods for QC codes based on cyclic group decomposition; 8. Methods for interaction screening which allow to improve performance (decorrelate variables) under BP and it's approximation. We proposed several state-of-the-art methods: Simulated Annealing lifting for MET QC-LDPC codes construction; fast EMD and code distance estimation; floor scale modular lifting for lenght adaption; fast finite-length covariance evolution rate penalty from threshold for code construction and it hardware friendly compression for fast decoder's LLRs unbiasing due SNR's estimation error. We found topology reason's of efficient of such methods using topology thickening (homotopy of continuous and discrete curvature) under matched metric space which allow to generalize this idea to a class of nonlinear codes for Signal Processing and Machine Learning. Using the proposed algorithms several generations of WDM Long-Haul error-correction codes were built. It was applied for "5G eMBB" 3GPP TS38.212 and other applications like Flash storage, Compressed sensing measurement matrix.
