Computation Codes - A New Tool for Multi-user Communication

大型无线网络的一个主要潜力是合作：来自单个节点的传输不仅会被预定的接收器听到，而且会被附近所有其他节点听到；通过类比，任何接收器不仅从预定的发射器捕获信号，还从附近所有其他发射器捕获信号。悲观主义者对这些事实的看法影响了过去几十年的通信网络设计：设计出了巧妙的算法和协议来避免干扰。然而，最近的研究揭示了许多情况，在这些情况下，只要形状合适，干扰是有益的。这通常被称为物理层合作。迄今为止提出的大多数合作方案都收集了潜在信号的统计依赖性。相比之下，在本项目中，开发了新的代码，允许利用干扰的代数结构，从而能够高效可靠地计算所涉及消息的功能。这样的代码称为计算代码。它们在明确要求计算的应用中具有独立的意义，例如传感器网络。更一般地说，计算编码视角用于为更大的网络开发新的框架：在网络内部，传递消息的明智选择的函数（而不是消息本身）。只要接收者有足够多的函数，它就可以推断出底层的消息（即比特）。这让人想起了所谓的网络编码，重要的区别在于，在新的框架中，应该根据实际的干扰特性来决定消息的哪些功能应该被传递，这可以带来显著的收益。

A major potential in large wireless networks is cooperation: A transmission from a single node is overheard not only by the intended receiver, but by all other nearby nodes; by analogy, any receiver not only captures the signal from the intended transmitter, but from all other nearby transmitters. The pessimist's perspective on these facts has shaped communication network designs of the past decades: Clever algorithms and protocols have been devised to avoid interference. Recent work, however, has revealed many scenarios under which interference turns out to be beneficial, provided it is suitably shaped. This is often referred to as physical-layer cooperation. Most of the cooperation schemes that have been proposed to date harvest the statistical dependence of the underlying signals. By contrast, in this project, novel codes are developed that permit to exploit the algebraic structure of the interference, enabling efficient and reliable computation of functions of the involved messages. Such codes will be referred to as computation codes. They are of independent interest in applications that explicitly call for computation, such as sensor networks.More generally, the computation coding perspective is used to develop a new framework for larger networks: Inside the network, judiciously chosen functions of the messages (rather than the messages themselves) are being passed around. As soon as a receiver has sufficiently many functions, it can infer the underlying message (i.e., the bits). This is reminiscent of so-called network coding, with the important difference that in the new framework, the question of which functions of the messages should be passed around is decided according to the actual interference characteristics, which can lead to significant gains.