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.
