Towards a New Era in Network Information Theory: A New Approach to Converse

迈向网络信息理论的新时代：一种新的对话方法

• 批准号: RGPIN-2016-04154
• 负责人: Xie, LiangLiang
• 金额: $ 2.62万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=669057
• 关键词: Towards; New; Era; Network; Information

Network information theory provides the fundamental guidance to the optimal design of all kinds of multiuser information systems, including wireless networks. As a theory, it has made many very successful progresses, and has dramatically transformed our view of how to develop communication systems when multiple users are present. Technologies originated from these theoretical studies include the famous code-division multiple-access (CDMA), which has become the standard for all advanced cellular networks.***However, this useful theory has met with many difficult problems in its own development, some of which have been long standing for many years. Although we can already learn a lot of interesting results from this theory, many of which are to provide significant improvement for practice, the theory itself has not completely solved its own basic problems. In fact, many of the best results we know so far are still those obtained in 1970s.***This is really a frustrating situation for people working in this field. For one thing, it is without doubt that this field of research is of pivotal importance in this information age, when information is such an indispensable part of our daily life, and networking among multi-users becomes such an essential character of modern societies. This pure reason has attracted many talented and hard-working people into the field. However, after decades of effort without real breakthroughs, any determined mind will doubt the worth of it. In fact, it has become no secret in the field that more and more people are turning away from the fundamental problems, to more hopeful new application topics. However, for the theory itself, when it cannot solve its own basic problems, it may not be far from dying. *** Is it already hopeless? In retrospect, efforts in network information theory have been mostly concentrated on achievability results. Here, I will focus more on the converse. Instead of the classical approach of using Fano's inequality, I will develop a new approach to the converse. Actually, if one really thinks about it, one may find it a real surprise that Shannon's single user capacity result can be proved by a perfect match between two completely different approaches from both sides: typical sequences for achievability from the lower side and Fano's inequality for converse from the upper side. Is it a general rule or more like a coincidence? If this perfect match has not happened in general except in a very small number of isolated cases, one has to question the generality of this approach. ***The idea I have for the new approach to converse can be briefly put as follows: Develop a way of proving the converse also based on typical sequences. Once this can be done, it will no longer be a surprise that the two sides can easily match, because they are based on the same approach. The way of proving one will always hint on the other. This will provide a general solution to many basic problems in network information theory.**

网络信息论为包括无线网络在内的各种多用户信息系统的优化设计提供了基本的指导。作为一种理论，它已经取得了许多非常成功的进展，并极大地改变了我们对如何开发多用户通信系统的看法。源自这些理论研究的技术包括著名的码分多址（CDMA），它已成为所有先进蜂窝网络的标准。然而，这一有用的理论在其自身的发展过程中遇到了许多难题，其中一些问题已经存在多年。虽然我们已经可以从这一理论中学习到很多有趣的结果，其中很多都是为实践提供了重大的改进，但这一理论本身并没有完全解决其自身的基本问题。事实上，迄今为止我们所知道的许多最好的结果仍然是20世纪70年代获得的结果。这对在这个领域工作的人来说确实是一个令人沮丧的情况。首先，毫无疑问，这一研究领域在信息时代具有至关重要的意义，信息是我们日常生活中不可或缺的一部分，多用户之间的网络成为现代社会的一个重要特征。这种纯粹的原因吸引了许多有才华和勤奋的人进入这个领域。然而，经过几十年的努力，没有真实的突破，任何有决心的人都会怀疑它的价值。事实上，越来越多的人正在从根本问题转向更有希望的新应用主题，这在该领域已经不是什么秘密。但是，对于理论本身来说，当它不能解决自身的基本问题时，它可能离消亡也就不远了。* *回顾过去，网络信息理论的努力主要集中在可验证性结果上。在这里，我将更多地关注匡威的情况。而不是使用法诺不等式的经典方法，我将开发一个新的方法来匡威。实际上，如果人们认真思考，人们可能会发现这是一个真实的惊喜，香农的单用户容量结果可以通过两种完全不同的方法之间的完美匹配来证明：从下侧的可互换性的典型序列和从上侧的匡威Fano不等式。这是一个普遍规律，还是更像是一个巧合？如果除了极少数个别情况外，这种完美的匹配一般都没有发生，人们就不得不质疑这种方法的普遍性。* 我对新的匡威方法的想法可以简单地表述如下：开发一种基于典型序列的逆向证明方法。一旦能够做到这一点，双方能够轻松匹配就不再是一件令人惊讶的事情了，因为他们基于相同的方法。证明一个的方法总是暗示另一个。这将为网络信息论中的许多基本问题提供一个普遍的解决方案。