Multiple Access Outerbounds and the Inseparability of Parallel Interference Channels

TL;DR

This paper demonstrates that, unlike other multi-carrier channels, parallel Gaussian interference channels cannot generally be separated into independent subchannels for capacity achievement, highlighting the need for joint encoding.

Contribution

It provides a counter-example showing the inseparability of parallel interference channels and introduces new outerbounds on their capacity.

Findings

Separate encoding is insufficient for capacity in parallel interference channels.

Joint encoding across carriers can significantly increase capacity.

New outerbounds on 3-user interference channel capacity are proposed.

Abstract

It is known that the capacity of parallel (multi-carrier) Gaussian point-to-point, multiple access and broadcast channels can be achieved by separate encoding for each subchannel (carrier) subject to a power allocation across carriers. In this paper we show that such a separation does not apply to parallel Gaussian interference channels in general. A counter-example is provided in the form of a 3 user interference channel where separate encoding can only achieve a sum capacity of $\log({SNR})+o(\log({SNR}))$ per carrier while the actual capacity, achieved only by joint-encoding across carriers, is $3/2\log({SNR}))+o(\log({SNR}))$ per carrier. As a byproduct of our analysis, we propose a class of multiple-access-outerbounds on the capacity of the 3 user interference channel.