We study the problem of common randomness (CR) generation in a fundamental two-party communication scenario, where a sender and a receiver seek to agree-with high probability-on a shared random variable. Both parties observe independent and identically distributed (i.i.d.) samples from sources defined over a Polish alphabet with an arbitrary joint distribution. Communication is restricted to a unidirectional, minimally interactive exchange over a noisy, memoryless channel. For this setting, we establish single-letter lower and upper bounds on the CR capacity. These bounds coincide except possibly at a countable set of points where discontinuities may arise.

In contrast to Shannon transmission codes, the size of identification (ID) codes for discrete memoryless channels (DMCs) experiences doubly exponential growth with the block length when randomized encoding is used. Additional enhancements within the ID paradigm can be realized through supplementary resources such as quantum entanglement, common randomness (CR), and feedback. Joint transmission and sensing demonstrate significant benefits over separation-based methods. Inspired by the significant impact of feedback on the ID capacity, our work delves into the realm of joint ID and sensing (JIDAS) for state-dependent multiple access channels (SD-MACs) with noiseless strictly casual feedback. Here, the senders aim to convey ID messages to the receiver while simultaneously sensing the channel states. We establish a lower bound on the capacity-distortion region of the SD-MACs. An example shows that JIDAS outperforms the separation-based approach.

We investigate message identification over a K-sender Gaussian multiple access channel (K-GMAC). Unlike conventional Shannon transmission codes, the size of randomized identification (ID) codes experiences a doubly exponential growth in the code length. Improvements in the ID approach can be attained through additional resources such as quantum entanglement, common randomness (CR), and feedback. It has been demonstrated that an infinite capacity can be attained for a single-user Gaussian channel with noiseless feedback, irrespective of the chosen rate scaling. We establish the capacity region of both the K-sender Gaussian multiple access channel (K-GMAC) and the K-sender state-dependent Gaussian multiple access channel (K-SD-GMAC) when strictly causal noiseless feedback is available.

We study a two-source model for common randomness (CR) generation in which the sender Alice and the receiver Bob generate a common random variable with a high probability of agreement by observing independent and identically distributed (i.i.d.) samples of correlated sources on countably infinite alphabets. The two parties are additionally allowed to communicate over a noisy memoryless channel. In our work, we establish a single-letter lower and upper-bound on the CR capacity for the proposed model. This is a challenging scenario because some of the finite alphabet properties, namely of the entropy can not be extended to the countably infinite case. We use a generalized typicality criterion, called unified typicality, which can be applied to random variables on countably infinite alphabets.

In the identification (ID) scheme proposed by Ahlswede and Dueck, the receiver only checks whether a message of special interest to him has been sent or not. In contrast to Shannon transmission codes, the size of ID codes for a Discrete Memoryless Channel (DMC) grows doubly exponentially fast with the blocklength, if randomized encoding is used. This groundbreaking result makes the ID paradigm more efficient than the classical Shannon transmission in terms of necessary energy and hardware components. Further gains can be achieved by taking advantage of additional resources such as feedback. We study the problem of joint ID and channel state estimation over a DMC with independent and identically distributed (i.i.d.) state sequences. The sender simultaneously sends an ID message over the DMC with a random state and estimates the channel state via a strictly causal channel output. The random channel state is available to neither the sender nor the receiver. For the proposed system model, we establish a lower bound on the ID capacity-distortion function.

We analyze deterministic message identification via channels with non-discrete additive white noise and with a noiseless feedback link under both average power and peak power constraints. The identification task is part of Post Shannon Theory. The consideration of communication systems beyond Shannon’s approach is useful in order to increase the efficiency of information transmission for certain applications. We propose a coding scheme that first generates infinite common randomness between the sender and the receiver. If the channel has a positive message transmission feedback capacity, for given error thresholds and sufficiently large blocklength this common randomness is then used to construct arbitrarily large deterministic identification codes. In particular, the deterministic identification feedback capacity is infinite regardless of the scaling (exponential, doubly exponential, etc.) chosen for the capacity definition. Clearly, if randomized encoding is allowed in addition to the use of feedback, these results continue to hold.

We study the problem of common randomness (CR) generation in the basic two-party communication setting in which the sender and the receiver aim to agree on a common random variable with high probability by observing independent and identically distributed (i.i.d.) samples of correlated Gaussian sources and while communicating as little as possible over a noisy memoryless channel. We completely solve the problem by giving a single-letter characterization of the CR capacity for the proposed model and by providing rigorous proof of it We prove that the CR capacity is infinite when the Gaussian sources are perfectly correlated.

We analyze message identification via Gaussian channels with noiseless feedback, which is part of the Post Shannon theory. The consideration of communication systems beyond Shannon's approach is useful in order to increase the efficiency of information transmission for certain applications. If the noise variance is positive, we propose a coding scheme that generates infinite common randomness between the sender and the receiver. We show that any identification rate via the Gaussian channel with noiseless feedback can be achieved. The remarkable result is that this applies to both rate definitions $\frac{1}{n}\log M$ (as defined by Shannon for transmission) and $\frac{1}{n}\ \log \log\ M$ — (as defined by Ahlswede and Dueck for identification). We can even show that our result holds regardless of the selected scaling for the rate. A detailed version with all proofs, explanations and more discussions can be found in [1].

Common randomness (CR), as a resource, is not commonly used in existing practical communication systems. In the common randomness framework, both sender and receiver, often described as terminals, aim to generate a common random variable observable to both, perhaps with low error probability. The knowledge of this CR allows to implement correlated random protocols that could lead to faster and more efficient algorithms. We characterize CR over Gaussian channels for their practical relevance in many communication situations by deriving the CR capacity for both Gaussian Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) cases. Furthermore, CR plays a key role in the identification scheme. In many new applications such as several machine-to-machine and human-to-machine systems and the tactile internet, which demand ultra-reliable low latency, the identification or also called post-Shannon scheme is proved to be more efficient than the classical transmission. It has been proved that through CR generation, the post-Shannon communication task allows to achieve an enormous performance gain. We consider a correlation-assisted secure identification scheme over Gaussian wiretap channels (GWC) and develop a lower bound on the corresponding secure identification capacity.

New applications in modern communications are demanding robust and ultra-reliable low latency information exchange such as machine-to-machine and human-to-machine communications. For many of these applications, the identification approach of Ahlswede and Dueck is much more efficient than the classical transmission scheme proposed by Shannon. Previous studies concentrate mainly on identification over discrete channels. We focus on Gaussian channels for their known practical relevance. We deal with secure identification over Gaussian channels. In particular, we provide a suitable coding scheme for the Gaussian wiretap channel (GWC) and determine the corresponding secure identification capacity.