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arXiv:2408.09119 · IEEE Information Theory Workshop (ITW)

Identification via Gaussian Multiple Access Channels in the Presence of Feedback

Yaning Zhao, Wafa Labidi, Holger Boche, Eduard Axel Jorswieck, Christian Deppe

Published Nov 24, 2024• 1 citation
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Abstract

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.

DOI
10.1109/itw61385.2024.10806939

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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 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 definitions1nlog⁡M\frac{1}{n}\log Mn1​logM(as defined by Shannon for transmission) and1n log⁡log⁡ M\frac{1}{n}\ \log \log\ Mn1​ loglog 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].
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 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 1nlog⁡M\frac{1}{n}\log Mn1​logM (as defined by Shannon for transmission) and 1n log⁡log⁡ M\frac{1}{n}\ \log \log\ Mn1​ loglog 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].
We consider the covert communication over the two-user Gaussian multiple access channel (GMAC) with causal feedback. It is shown that any causal feedback does not enlarge the covert capacity region and the time-division scheme is optimal for a class of channels, which includes the case where the warden observes what the legitimate receiver receives. For the proof, we derive an outer bound on the covert capacity region of general GMACs with noiseless causal feedback, which implies that the square-root law holds for arbitrary channel gains. Furthermore, the extension to multi-user case is presented.
The feedback capacities of the Gaussian multiple-access channel (GMAC) and the GMAC with noncausal channel state information at the transmitters (NCSIT) are achieved by Ozarow's Schalkwijk-Kailath (SK) type feedback scheme and its extension (also called Rosenzweig's feedback scheme), respectively. In this paper, first, we show that the above Ozarow's and Rosenzweig's feedback schemes, which are not designed with the consideration of secrecy, already achieve the secrecy capacity regions (capacity regions with perfect weak secrecy constraint) of the Gaussian multiple-access wiretap channel (GMAC-WT) with feedback and the GMAC-WT-NCSIT with feedback, respectively. This indicates that for Gaussian multiple-access wiretap channels, the traditional secret key based feedback schemes are not necessary. Next, we show that the feedback capacities of the GMAC with degraded message sets (GMAC-DMS) and the GMAC-NCSIT with degraded message sets (GMAC-NCSIT-DMS) can be achieved by two-step SK type feedback schemes. Furthermore, we show that the above capacity-achieving feedback schemes also achieve the secrecy capacity regions of the GMAC-WT-DMS with feedback and the GMAC-WT-NCSIT-DMS with feedback, i.e., the secrecy capacity regions of the GMAC-WT-DMS with feedback and the GMAC-WT-NCSIT-DMS with feedback equal the capacity regions of the same models without secrecy constraint. Finally, we derive outer bounds on the secrecy capacity regions of GMAC-WT, GMAC-WT-DMS and GMAC-WT-NCSIT-DMS, and show that feedback helps to increase the secrecy capacity regions of GMAC-WT and GMAC-WT-DMS, and in some cases helps to increase the secrecy capacity regions of GMAC-WT-NCSIT and GMAC-WT-NCSIT-DMS. Overall, the main contribution of this paper is to find the inherent secrecy nature of SK-type feedback schemes for the GMACs.
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.