Coding for efficient information transmission in optical and wireless systems

该奖项支持的长期研究计划专注于设计高效的编码和解码技术，以便在各种类型的信道上可靠地传输信息，包括无线信道、光信道和分组网络信道。挑战在于实现这样的编码方案：(A)具有接近信息论极限的效率；以及(B)可以用实际算法进行编码和解码。研究挑战之所以出现，是因为不同的渠道往往需要截然不同的方法。对于建立基本限制和构建最合适的编码方案而言，实现对信道的操作的良好理解变得至关重要。由于差错控制编码是每个现代通信系统的中心组件，这项工作有可能提高现有和新兴通信系统的效率，使服务提供商具有竞争优势，并为他们的用户提供更好(更便宜、更快、更可靠)的服务。 有三个分项目旨在实现这一长期目标。其中一个目标是在公共安全、灾难恢复和战术无线电场景中出现的高度动态的无线多跳或网状网络。另一个目标是使用基于逆散射变换的新方法在光纤上有效地传输信息。第三部分研究了一类基于非交换斜多项式环的新型纠错码的性质和应用。 在所有情况下，都非常重视人才的培训(从本科生到研究生，再到博士后研究员)。

The long-term research program supported by this award is focused on devising efficient encoding and decoding techniques for reliable information transmission over a variety of channel-types, including wireless channels, optical channels, and packet-network channels. The challenge is to achieve coding schemes that (a) have an efficiency approaching information-theoretic limits; and (b) can be encoded and decoded with practical algorithms. Research challenges arise because different channels often require quite different approaches. It becomes essential to achieve a good understanding of the operation of the channel, both to establish fundamental limits and to construct the most suitable coding schemes. Since error-control coding is a central component of every modern communications system, this work has the potential to improve the efficiency of existing and emerging communications systems, giving service-providers a competitive advantage, and giving their users better (cheaper, faster, more reliable) service. Three sub-projects are aimed at achieving this long-term objective. One of them targets highly dynamic wireless multi-hop or mesh networks that arise in public safety, disaster recovery, and tactical radio scenarios. Another targets the efficient transmission of information over optical fibers using a novel approach based on the Inverse Scattering Transform. The third aims to examine the properties and applications of a new class of error-correcting codes based on non-commutative skew polynomial rings. In all cases, the training of people (from undergraduate students, to graduate students, to postdoctoral fellows) is given significant emphasis.