CIF: Small: Moderate Deviations and Exact Asymptotics in Information Theory

CIF：小：信息论中的适度偏差和精确渐近

• 批准号: 1218578
• 负责人: Aaron Wagner
• 金额: $ 49.1万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1218578&HistoricalAwards=false
• 关键词: CIF; Small; Moderate; Deviations; Exact

Information theory describes what is possible in reliable communication and data compression, and it generally does so via asymptotic results. While existing asymptotic results are rightly celebrated, they have two limitations. First, none of these results is directed at the asymptotic regime that is the most practically important. In the case of channel coding, this is the regime in which the error probability tends to zero and the rate approaches capacity as the blocklength increases. Second, existing results are often too coarse to be useful as benchmarks for practical codes because they hide nuisance factors that could be significant at moderate blocklengths.This research will address both of these issues. The project will characterize the performance of optimal channel codes for the regime in which the rate approaches capacity and the error probability simultaneously tends to zero. This will be followed by characterizing the nuisance factors in both this regime and the classical ones by establishing more refined "exact-asymptotic" bounds. These results will also be extended to data compression and multiuser problems, leading to a more precise understanding of the fundamental limits of coding in practical regimes of interest.In additional to advancing the field of information theory, this research will strengthen its connections to coding theory and probability theory, the former by providing more useful performance bounds for moderate blocklengths and the latter by cross-fertilizing ideas between the two fields. The educational component will revamp course offerings in information theory in order to allow the inclusion of recent research results, including those from this project, and to make the subject accessible to a wider audience.

信息论描述了可靠通信和数据压缩的可能性，并且通常通过渐近结果来实现。虽然现有的渐近结果值得庆祝，但它们有两个局限性。首先，这些结果都不是针对实际上最重要的渐近状态。在信道编码的情况下，随着块长度的增加，错误概率趋于零并且速率接近容量。 其次，现有的结果通常过于粗糙，无法用作实际代码的基准，因为它们隐藏了在中等块长度下可能很重要的干扰因素。这项研究将解决这两个问题。该项目将描述速率接近容量且错误概率同时趋于零的情况下最佳信道编码的性能。接下来将通过建立更精确的“精确渐近”界限来表征该机制和经典机制中的有害因素。这些结果还将扩展到数据压缩和多用户问题，从而更准确地理解实际感兴趣的编码的基本限制。除了推进信息论领域之外，这项研究还将加强其与编码理论和概率论的联系，前者通过为中等块长度提供更有用的性能界限，后者通过两个领域之间的交叉传播思想。教育部分将修改信息论课程设置，以便纳入最新的研究成果，包括该项目的研究成果，并使更广泛的受众能够接触到该主题。