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Common randomness (CR), as a resource, is not commonly used in existingpractical communication systems. In the common randomness framework, bothsender and receiver aim to generate a common random variable observable toboth, ideally with low error probability. The knowledge of this CR allows us toimplement correlated random protocols that can lead to faster and moreefficient algorithms. Previous work on CR focused on Single-Input Single-Output(SISO) channels with finite input and output alphabets. As far as we know, noresults on continuous and Multiple-Input Multiple-Output (MIMO) channels haveyet been established. We characterize CR over Gaussian channels for theirpractical relevance in many communication situations. We first derive the CRcapacity for Gaussian SISO channels. This result is then used for thederivation of the CR capacity in the MIMO case. CR plays a key role in theidentification scheme. In contrast to the classical transmission, the decoderis now interested in knowing \emph{whether} a specific message was sent or not,rather than knowing \emph{what} the received message is. In many newapplications such as several machine-to-machine and human-to-machine systemsand the tactile internet, the identification, also called the post-Shannonscheme, is more efficient than the classical transmission. It has been provedthat through CR generation, the post-Shannon communication task allows us toachieve an enormous performance gain that we can take advantage of in severalapplications.  We consider a correlation-assisted secure identification scheme and develop alower bound on the corresponding secure identification capacity.

Optimal Signal Processing for Common Randomness Generation over MIMO Gaussian Channels with Applications in Identification