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

本研究探讨一种新的方法来保护数字通信和数字存储系统的可靠性。 这种方法利用了最近的工作（由研究团队和其他人），该工作以新颖的图形表示形式制定了数据的“编码”和“解码”;这种制定方法与现有技术相比具有几个优点，用于确保数据完整性，包括在非常低的功率下具有更好的性能，并且没有“错误楼层”，即，随着功率消耗的增加而一致地（并且显著地）降低解码错误概率的能力。 研究的最终目标是更可靠地传递数字数据、文本、计算机文件、语音和音频信号、视频等--使用需要更少电力的设备（并且因此具有更长的电池寿命）和更短的处理延迟。更具体地，研究了利用空间耦合稀疏码信道具有稀疏奇偶校验表示的（差错控制）码，该稀疏奇偶校验表示通过将一系列小的“原模图”耦合在一起而形成。 这种方法是由研究团队在终止低密度奇偶校验卷积码的背景下开创的，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块长度线性增长-随着代码大小变大。 本研究分为四个部分：（1）低延迟/存储器解码策略的设计和分析;（2）解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和分析;以及（4）空间耦合在信道编码直接域之外的应用，包括协作分集，压缩感知和多终端信源/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.