Collaboration with Yaming Yu - entropy inequalities and thinning

与亚明合作 - 熵不等式和细化

• 批准号: EP/H002200/1
• 负责人: Oliver Johnson
• 金额: $ 0.93万
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH002200%2F1
• 关键词: Collaboration; Yaming; Yu; entropy; inequalities

Entropy quantifies the way in which, for example, the outcome of tossing a fair coin is harder to predict than with a biased one. It plays a fundamental role in understanding how information is transmitted over noisy communication networks, and how large amounts of information can be stored in as small devices as possible (data compression). Entropy is studied in the field of information theory, and this project aims to resolve two major outstanding conjectures, using techniques from various areas of pure mathematics. These conjectures describe the entropy of the sums of random events. It is a familiar fact that while randomness cannot be predicted, by summing or averaging random events, the unpredictability cancels out. Thus, for example, while a single coin toss is impossible to predict, we can be confident that in 1,000,000 fair coin tosses, there will be between 498,000 and 502,000 heads. This project will consider the behaviour of the entropy in such settings, helping understand such effects.More specifically, many models of information transmission suppose that noise is added to the signal, due to physical processes beyond the control of transmitter or receiver. The ultimate aim is to clean up the received message, that is to remove the noise, in order to receive the full content sent by the transmitter. If we are able to prove the conjectures mentioned above, there would be implications in certain communications networks, including enabling a better quality of live streaming video on the Internet. For example, Stankovic describes a model where such video is broadcast via a wireless link to a number of servers, which compress the information locally. The algorithms which work best are based on the so-called Entropy Power Inequality, which we seek to extend here.

熵量化了一种方式，例如，投掷公平硬币的结果比有偏见的更难预测。它在理解信息如何在嘈杂的通信网络中传输，以及如何将大量信息存储在尽可能小的设备中（数据压缩）方面发挥着重要作用。熵是在信息论领域研究的，这个项目的目的是解决两个主要的突出问题，使用纯数学的各个领域的技术。这些图描述了随机事件之和的熵。一个熟悉的事实是，虽然随机性无法预测，但通过对随机事件进行求和或平均，不可预测性就被抵消了。因此，举个例子，虽然掷一枚硬币是不可能预测的，但我们可以确信，在100万次公平的掷硬币中，将有498,000到502,000次正面朝上。这个项目将考虑熵在这种情况下的行为，帮助理解这种影响。更具体地说，许多信息传输模型假设，由于发射机或接收机无法控制的物理过程，噪声被添加到信号中。最终目的是清理接收到的消息，即去除噪声，以便接收发射机发送的全部内容。如果我们能够证明上述假设，将对某些通信网络产生影响，包括在互联网上实现更好的实时流媒体视频质量。例如，Stankovic描述了一个模型，其中这样的视频通过无线链路广播到多个服务器，这些服务器在本地压缩信息。最好的算法是基于所谓的熵权不等式，我们在这里寻求扩展。

项目成果

Monotonicity, thinning and discrete versions of the Entropy Power Inequality

熵幂不等式的单调性、细化和离散版本

• DOI: 10.48550/arxiv.0909.0641
• 发表时间: 2009
• 作者: Johnson O