Multiple Access Channel Simulation

We study the problem of simulating a two-user multiple-access channel (MAC) over a multiple access network of noiseless links. Two encoders observe independent and identically distributed (i.i.d.) copies of a source random variable each, while a decoder observes i.i.d. copies of a side-information random variable. There are rate-limited noiseless communication links between each encoder and the decoder, and there is independent pairwise shared randomness between all the three possible pairs of nodes. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the two sources and the side information. We are interested in the rate tuples which permit this simulation. This setting can be thought of as a multi-terminal generalization of the point-to-point channel simulation problem studied by Bennett et al. (2002) and Cuff (2013). When the pairwise shared randomness between the encoders is absent, the setting reduces to a special case of MAC simulation using another MAC studied by Haddadpour et al.~(2013). We establish that the presence of encoder shared randomness can strictly improve the communication rate requirements. We first show that the inner bound derived from Haddadpour et al.~(2013) is tight when the sources at the encoders are conditionally independent given the side-information at the decoder. This result recovers the existing results on point-to-point channel simulation and function computation over such multi-terminal networks. We then explicitly compute the communication rate regions for an example both with and without the encoder shared randomness and demonstrate that its presence strictly reduces the communication rates. Inner and outer bounds for the general case are also obtained.