CIF:Small: Design and Analysis of Spatially-Coupled Coding Systems

数字信息的存储和传输在当今社会无处不在，在现代信息技术基础设施中发挥着重要作用。纠错码是有效、可靠地存储和传输数字信息的基础设施组件的关键部分。空间耦合是一种用于设计纠错码的新技术，在某些情况下，它已被证明可以通过低复杂度的译码实现近乎最佳的性能。本研究的重点是设计和分析基于空间耦合码的数字信息存储和传输的创新技术。这项研究分为三大重点。第一个重点是概括空间耦合码的最新证明技术，以包括空间耦合图形模型上的广泛类别的推理问题。第二个重点是考虑多用户通信问题的通用空间耦合码的设计，包括噪声睡眠狼问题和多址通信。第三个重点是针对带有侧信息的源和信道编码问题，并着重于具有增强消息传递解码的嵌套空间耦合代码。空间耦合似乎也是一个普遍的原则，它广泛适用于涉及消息传递和因子图推理的问题。因此，这项研究有望对信号处理和机器学习等通信以外的科学和工程学科产生影响。

The storage and transmission of digital information is now ubiquitous in our society and plays a valuable role in the modern information-technology infrastructure. Error-correcting codes are a key part of infrastructure components that efficiently and reliably store and transmit digital information. Spatial coupling is a new technique for designing error-correcting codes that has been shown in some cases to achieve near-optimal performance with low-complexity decoding. This research focuses on the design and analysis of innovative techniques for the storage and transmission of digital information based on spatially-coupled codes.The research is broken into three broad thrusts. The first thrust focuses on generalizing recent proof techniques for spatially-coupled codes to include a wide class of inference problems on spatially-coupled graphical models. The second thrust considers the design of universal spatially-coupled codes for multiuser communication problems including the noisy Slepian-Wolf problem and multiple-access communication. The third thrust targets source and channel coding problems with side information and focuses on nested spatially-coupled codes with enhanced message-passing decoding.Spatial coupling also appears to be a general principle that is broadly applicable to problems involving message passing and inference on factor graphs. Therefore, this research is expected to have an impact on science and engineering disciplines beyond communications such as signal processing and machine learning.