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

这项研究探索了一种保护数字通信和数字存储系统可靠性的新方法。该方法利用了最近的工作(由研究团队和其他人)，该工作根据新的图形表示来公式化数据的“编码”和“解码”；该公式化比用于确保数据完整性的现有技术具有几个优点，包括在非常低的功率下具有更好的性能，并且不存在“差错平台”，即，以递增的功率支出一致地(并且显著地)降低解码的差错概率的能力。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-使用需要更少功率(因此具有更长的电池寿命)和更短的处理延迟的设备。更具体地说，该研究调查了空间耦合稀疏码的使用，即具有稀疏奇偶校验表示的通道(差错控制)码的使用，该稀疏奇偶校验表示由耦合在一起的一系列小“原型图”形成。该方法由研究小组在终止的低密度奇偶校验卷积码的背景下首创，最近已被证明具有特性的独特组合--接近信道容量的迭代译码性能和随块长度线性增长的最小距离--随着码大小变大。研究内容包括四个方面：(1)低延迟/记忆译码策略的设计与分析；(2)译码差错概率性能保证；(3)空间耦合代数结构稀疏码的开发与分析；(4)空间耦合在信道编码直接域外的应用，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.