Cooperation in communication and compression [electronic resource]
Keywords: Electrical Engineering.

With a heavy proliferation of connected devices all across the globe, cooperation among entities of the network components cannot be neglected. Especially when the available resources are scarce, system components must cooperate to exchange information strategically, in order to push the overall network performance to its ultimate performance limits. In this thesis, we study new models of cooperation in both multi-user communication and compression networks, which are two broad categories classifying Network Information Theoretic problems. The common precept for the proposed models of cooperation is that of \textit{partial or deterministic-function cribbing}, where the entities in the network (transmitters or receivers) cooperate with each other by sensing a deterministic function of each others' signals. In the first part of the thesis, we investigate the role of cooperation in multi-user communication systems. Specifically, we study the Multiple Access Channel (MAC), a canonical communication model in Network Information Theory, where multiple transmitters or encoders wish to communicate their private messages to a single receiver or decoder over a channel, which here is a shared wireless noisy medium. We consider a two-encoder model, and introduce cooperation between the encoders via deterministic-function cribbing, that is when an encoder senses a deterministic function of the channel input symbols of the other encoder (and/or {\it vice versa}), and uses them to send encoded symbols over the channel. We derive fundamental limits by constructing essentially optimal schemes and show via examples that cooperation helps in boosting the performance. In the second part of the thesis, the role of cooperation in multi-user compression systems is investigated. Specifically, we consider the Successive Refinement (SR) setting as the compression setup, where a single encoder describes a source, to multiple decoders, with different levels of refinement. That is, while all decoders may receive common description of information about the source, only some of the decoders may receive a refined description of information about the source. The decoders need to reconstruct the source under a given distortion criterion. Here we consider a two-decoder model and allow cooperation between the decoders, via deterministic-function cribbing, that is, the decoder with crude (less) information about the source (the one which receives only the common information), gets auxiliary information in the form of a deterministic function of the reconstruction symbols of the other decoder (the one which has access to both common and refined information). We derive the fundamental limits, as well as formalize new coding schemes which are optimal. Examples are also given which show that cooperation results in a much better rate-distortion tradeoff than that without cooperation. Finally, in the third part of the thesis, we connect the dots to understand the dualities between the two settings considered, that is, Multiple Access Channel with Encoder Cooperation and Successive Refinement with Decoder Cooperation. The duality proposed is comprehensive in the sense that one setting can be completely transformed into another, including dual schemes, cooperating strategies and rate regions.