Approximate Sum-Capacity of the Y-channel

TL;DR

This paper analyzes the sum-capacity of the Y-channel, a network with three users exchanging information via a relay, providing approximate capacity bounds and extending results to K-user scenarios.

Contribution

It introduces new genie-aided bounds for the Y-channel and demonstrates that a simple time-sharing strategy achieves near-optimal sum-capacity within a constant gap.

Findings

Sum-capacity characterized within 2 bits for all channel conditions.

A time-sharing scheme achieves the capacity bounds within a constant gap.

Extension of the approach to K-user case with a gap of 2log(K-1) bits.

Abstract

A network where three users want to establish multiple unicasts between each other via a relay is considered. This network is called the Y-channel and resembles an elemental ingredient of future wireless networks. The sum-capacity of this network is studied. A characterization of the sum-capacity within an additive gap of 2 bits, and a multiplicative gap of 4, for all values of channel gains and transmit powers is obtained. Contrary to similar setups where the cut-set bounds can be achieved within a constant gap, they can not be achieved in our case, where they are dominated by our new genie-aided bounds. Furthermore, it is shown that a time-sharing strategy, in which at each time two users exchange information using coding strategies of the bi-directional relay channel, achieves the upper bounds to within a constant gap. This result is further extended to the K-user case, where it is shown that the same scheme achieves the sum-capacity within 2log(K-1) bits.