CIF: Medium: Collaborative Research: Spatially Coupled Sparse Codes on Graphs - Theory, Practice, and Extensions

本文研究了一种保护数字通信和数字存储系统可靠性的新方法。这种方法利用了最近的工作（由研究团队和其他人），以一种新颖的图形表示形式制定了数据的“编码”和“解码”；与现有的确保数据完整性的技术相比，这种配方有几个优点，包括在非常低的功耗下具有更好的性能，并且没有“错误下限”，即能够在增加功耗的情况下持续（并且显著）降低解码错误概率。这项研究的最终目标是更可靠地传输数字数据、文本、计算机文件、语音和音频信号、视频等——使用耗电量更少（因此电池寿命更长）和处理延迟更短的设备。更具体地说，该研究调查了空间耦合稀疏码的使用-信道（错误控制）码通过耦合在一起的小“原型”链形成的稀疏奇偶校验表示。这种方法是由研究小组在终止低密度奇偶校验卷积码的背景下首创的，最近已被证明具有独特的特性组合-迭代解码性能接近信道容量和最小距离，随着代码大小的增加，最小距离随块长度线性增长。主要研究方向为：(1)低延迟/内存解码策略的设计与分析；(2)译码错误概率性能保证；(3)具有代数结构的空间耦合稀疏码的开发与分析；(4)信道编码直接域之外的空间耦合应用，包括协同分集、压缩感知和多终端源/信道编码。

This research investigates a new approach to protecting the reliability of digital communication and digital storage systems. This approach takes advantage of recent work (by the research team and others) that formulates the "encoding" and "decoding" of data in terms of a novel graphical representation; this formulation has several advantages over existing techniques for insuring data integrity, including better performance at very low power and the absence of an 'error floor', i.e., the ability to consistently (and significantly) lower the decoded error probability with incremental expenditures of power. The ultimate goal of the research is more reliable delivery of digital data, text, computer files, speech and audio signals, video, etc. - using devices that require less power (and thus have longer battery life) and shorter processing delay.More specifically, the research investigates the use of spatially coupled sparse codes - channel (error control) codes with a sparse parity check representation formed by coupling together a chain of small "protographs". This approach, which was pioneered by the research team in the context of terminated low-density parity check convolutional codes, has recently been shown to possess a unique combination of properties - iterative decoding performance that approaches channel capacity and minimum distance that grows linearly with block length - as the code size gets large. The research follows four tracks: (1) the design and analysis of low latency/memory decoding strategies; (2) decoded error probability performance guarantees; (3) the development and analysis of spatially coupled sparse codes with algebraic structure; and (4) the application of spatial coupling outside the immediate domain of channel coding, including cooperative diversity, compressed sensing, and multi-terminal source/channel coding.