Multiple Access Channel Simulation

We study the problem of simulating a multiple access channel over a 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 and independent pairwise shared randomness resources between each encoder and the decoder. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the observed random variables. 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). General inner and outer bounds on the rate region are derived. For the special case when the sources at the encoders are conditionally independent given the side-information at the decoder, we completely characterize the rate region. Our bounds recover the existing results on deterministic function computation over such multi-terminal networks. We then show through an example that an additional independent source of shared randomness between the encoders that is not available to the decoder strictly improves the communication rates.