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In this paper, we would like to study the common randomness (CR) capacity ofintertwined two-way channels, namely those whose marginal channel transitionprobabilities depends also on the signal they transmit. We bring a few specialsettings and provide constructive schemes with which the two nodes can agreeupon a common randomness. We then provide an outer bound on the CR capacity ofintertwined receiver-decomposable (RD) two-way channel and will provide a boundon the cardinality of the available auxiliary variables. We will also show thisouter bound is bounded above by Venkatesan-Anantharam CR capacity which makesit tight for decomposing two-way setting.

On the Common Randomness Capacity of a Special Class of Two-way Channels