# 2009 Research Summary

## Multiway Interactions Involving More than Two Users

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Krish Eswaran and Michael Gastpar

National Science Foundation 0326503

The advent of portable wireless devices enables a kind of conferencing reminiscent of conference calls, in which each user in a group is interested in sending and receiving data to and from all members of the group. For example, members of an emergency response team, each equipped with a wireless enabled device, may want to transmit and receive data to and from all other responders at a disaster site.

For the case of two users, a well-known information-theoretic model has been studied: the additive white Gaussian two-way channel. In this model, the two users' signals add and then are corrupted by additive white Gaussian noise.

Note that because each user can both generate channel inputs and observe channel outputs, there is the potential for interaction between the two users. However, it turns out that in this setting, there exist rate-optimal strategies that do not require either user's channel inputs to depend on the observations of previous channel outputs. Thus, interaction is unnecessary for optimal communication in the two user setting [1].

We consider a generalization of the additive Gaussian two-way channel to K users. While one might expect there to exist rate-optimal strategies that ignore interaction, we demonstrate that interaction can strictly improve the rate over non-feedback strategies when K > 2. Furthermore, for a special case of this model in which all users observe the same channel output, we provide an interactive strategy that is sum-rate optimal.

Ongoing work is looking at interactive strategies for general K user multiway chanels and how the rate improvements these interactive strategies provide trade off with the decoding error probability.

- [1]
- C. E. Shannon, “Two-Way Communication Channels,”
*Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability,*J. Neyman, ed., Vol. 1, 1961, pp. 611–644.