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Globecom

Common Randomness Generation and Identification over Gaussian Channels

Rami Ezzine, Wafa Labidi, Holger Boche, Christian Deppe

Published Dec 1, 2020• 27 citations
Publisher

Abstract

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.

DOI
10.1109/globecom42002.2020.9322460

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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 message transmission scheme proposed by Shannon. Previous studies concentrate mainly on identification over discrete channels. For discrete channels, it was proved that identification is robust under channels uncertainty. Furthermore, optimal identification schemes that are secure and robust against jamming attacks have been considered. However, no results for continuous channels have yet been established. That is why we focus on the continuous case: the Gaussian channel for its known practical relevance. We deal with secure identification over Gaussian channels. Provable secure communication is of a high interest for future communication systems. A key technique for implementing secure communication is the physical layer security based on information theoretic security. We model this with the wiretap channel. In particular, we provide a suitable coding scheme for the Gaussian wiretap channel (GWC) and determine the corresponding secure identification capacity. We also consider Multiple-Input Multiple-Output (MIMO) Gaussian channels and provide an efficient signal-processing scheme. This scheme allows a separation of signal-processing and Gaussian coding.
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.
Common randomness (CR) is a valuable resource for enhancing the trustworthiness of 6G communication systems. This article highlights the role of CR in improving scalability, security, and resilience in distributed 6G architectures. It provides an overview of information-theoretic two-source models for CR generation and summarizes known capacity results, together with their implications for practical systems under different communication settings, including one-way, two-way, helper-assisted, and interactive scenarios. Furthermore, the article explores CR-assisted secure identification over Gaussian channels as an application and highlights selected open research problems in CR generation for next-generation wireless systems. The article targets researchers and practitioners interested in bridging information-theoretic tools with emerging 6G communication systems.
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.
Common randomness (CR) is an important resource for future communication paradigms. Identification is one such future communication paradigm, and it has been proven that CR-assisted identification can improve identification capacity by a double exponential factor. To achieve this, the common source of observation must be perfectly correlated and contain sufficient entropy. Channel reciprocity-based CR generation (alternatively termed Physical Layer Secret Key (PLSK) generation) is one such CR generation scheme. Existing high-rate CR generation is based on the Carrier Frequency Offset (CFO); for practical implementation, CFO-based CR generation would require a re-design of the existing protocol stacks to pass the CFO from the physical layer to the higher protocol layers. In contrast, we develop high-rate CR generation based on the Received Signal Strength Indicator (RSSI), which is highly practical as the RSSI is passed to and widely used by the higher protocol layers in existing communication protocol stacks. For RSSI-based CR generation, we demonstrate that the memory resources dedicated to storing channel information play an important role in achieving a high CR generation rate. Specifically, we demonstrate, through an experimental testbed with Ettus N210 USRPs Software Defined Radios (SDRs) (from which we make datasets publicly available), how allocating higher memory resources for storing accurate RSSI channel information at the terminals (transceivers) increases the achievable CR generation rate.
With rapid advances made in quantum computing, information theoretic security is of paramount importance for Internet of Things (IoT), particularly for low-powered devices like sensors and actuators, where there is generally little to no room for complex security features. Common Randomness (CR) can be considered as a resource, that can be used for adding information theoretic security to the IoT systems. The most desired CR is a lengthy CR with uniform distribution. In this study, we design and implement channel reciprocity based CR using a Software Defined Radio (SDR). Furthermore, we also implement Quantum Entanglement (QE) assisted CR generation scheme and compare it against the classical channel reciprocity based scheme. The evaluation of both CR generation schemes has been carried out on the basis of National Institute for Statistical Tests (NIST) and bit discrepancy results. We show that QE assisted CR generation is more efficient compared to channel reciprocity based CR, in terms of generating uniformly distributed CR, if the latter is observing slow fading channel.