Harnessing Interference with an Out-of-Band Relay: An Approximate Capacity Result

Abstract

Abstract-This work studies the Gaussian interference channel (IC) with an out-of-band relay (OBR) from an informationtheoretical perspective. The relay works in bands orthogonal to the IC. The focus is on a symmetric channel model, in order to understand the fundamental impact of the OBR on the signal interaction of the IC, in the simplest possible setting. We classify the interference links as extremely strong, very strong, strong, moderate, weak, and very weak. We find that interference is useful to improve the achievable rates when it is extremely strong or very strong. Specifically, when interference is extremely strong, the channel acts as if there are two disjoint OBRs helping each source-destination pair. For strong interference, separate encoding, i.e., transmitting independent messages thorough the IC and OBR, is optimal, while for moderate interference, separate encoding is close to optimal. For weak or very weak interference, we show that the OBR can help improve the rates for common messages and further reduce the interference. It is shown that our strategy achieves the symmetric capacity to within 1.14625 bits per channel use for all channel parameters.

Symmetric Capacity of the Gaussian Interference Channel With an Out-of-Band Relay to Within 1.15 Bits

“…E. Case 5: 2 3 n d > n c ≥ 1 2 n d This is the case with weak interference. The signal interaction in the IC is shown in Figure 9.…”

“…Without the relay, the sum rate optimal transmission strategy for the IC is to use the signal spaces A 1 and B 1 to transmit common information, which is to be decoded at both destinations, and use the signal spaces A 4 and B 4 to transmit private information, which is to be decoded at the intended destinations. The condition 2 3 n d > n c ≥ 1 2 n d guarantees that the bits from signal spaces A 1 , A 4 , B 1 , B 4 are aligned at the receivers such that they do not interfere with each other. The remaining signal spaces A 2 , A 3 , B 2 , B 3 are left unused, since the information bits transmitted using these signal spaces cause interference at the receivers.…”

“…Relation to the deterministic model: This condition corresponds to the case of weak or very weak interference, i.e., 2 3 n d > n c , in the deterministic model. For these two cases, the summary for the deterministic model in Remark 11 and Remark 12 suggests us to utilize the relay to decode the common messages in the most efficient manner, i.e., the sources should use the signal spaces of the relay in common as much as possible.…”