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We investigate the problem of common randomness (CR) generation from discrete correlated sources aided by one-way communication over single-user multiple-input multiple-output (MIMO) slow fading channels with additive white Gaussian noise (AWGN) and arbitrary state distribution. MIMO slow fading channels are indispensable in many scenarios in modern wireless communication. We completely solve the MIMO slow fading case by providing first an outage formulation of its channel capacity that holds for arbitrary state distribution. For this purpose, we provide an achievable rate for a specific MIMO compound Gaussian channel. Second, we establish the outage CR capacity over the MIMO slow fading channel using our result on its outage transmission capacity. Index TermsCommon randomness, outage capacity, MIMO slow fading channels, MIMO compound Gaussian channels I. INTRODUCTIONThe availability of common randomness (CR) as a resource plays a key role in distributed computational settings [1]. It allows to design correlated communication protocols that perform faster and more efficiently than without correlation. We study the problem of CR generation in the basic two-party communication setting in which Alice and Bob aim to agree on a common random variable with high probability by observing i.i.d samples of correlated discrete sources and while communicating as little as possible. Under additional secrecy constraints, the generated CR can be used as secret keys, as shown in the fundamental two papers [2] [3]. In our work, however, we will not impose any secrecy requirements. Furthermore, the resource CR is highly relevant in the identification scheme, an approach in communications developed by Ahlswede and Dueck [4]. In the identification framework, the decoder is not interested in knowing what the received message is. He rather wants to know if a specific message of special interest to him has been sent or not. It turns out that in contrast to transmission, CR may allow a significant increase in the identification capacity [5]- [7]. The identification scheme presents practical applications in several machine-to-machine and human-to-machine systems [8], the tactile internet [9], digital watermarking [10] [11] and industry 4.0 [12]. In addition, it is worth mentioning that identification codes [14] can be used in autonomous driving, as described in [13]. The latter is a typical use case for ultra reliable low-latency communication.CR generation from discrete correlated sources was initially introduced in [6], where the communication was over discrete noiseless channels with limited capacity. A single-letter characterization of the CR capacity for this model was established in [6]. CR capacity refers to the maximum rate of CR that Alice and Bob can generate using the resources available in the model. The results on CR capacity were later extended to Gaussian channels in [15]. Recently, the CR generation problem over single input single output (SISO) slow fading channels has been studied in [16]. In such a scenario, the channe...

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