Interference Channels with Source Cooperation

The role of cooperation in managing interference - a fundamental feature of the wireless channel - is investigated by studying the two-user Gaussian interference channel where the source nodes can both transmit and receive in full-duplex. The sum-capacity of this channel is obtained within a gap of a constant number of bits. The coding scheme used builds up on the superposition scheme of Han and Kobayashi (1981) for the two-user interference channel without cooperation. New upperbounds on the sum-capacity are also derived. The same coding scheme is shown to obtain the sum-capacity of the symmetric two-user Gaussian interference channel with noiseless feedback within a constant gap.

💡 Research Summary

The paper investigates how cooperation between transmitters can be exploited to mitigate interference in the classic two‑user Gaussian interference channel. Unlike the traditional model, where each source only transmits, the authors assume full‑duplex operation so that each source can also listen to the other’s transmission. This “source cooperation” creates a new degree of freedom that can be harnessed to improve the sum‑capacity of the network.

The authors build on the well‑known Han‑Kobayashi (HK) superposition coding scheme, which splits each user’s message into a public part (decoded by both receivers) and a private part (decoded only by the intended receiver). To incorporate cooperation, they introduce a three‑layer encoding structure: (i) a conventional public layer, (ii) a cooperative public layer that carries compressed information received from the other source, and (iii) a private layer. The cooperative layer is designed using ideas from Wyner‑Ziv compression, allowing the limited‑capacity cooperation link to convey useful side information efficiently. At the receivers, decoding proceeds hierarchically: the combined public layers are decoded first, then the cooperative information is used to cancel residual interference, and finally the private layers are decoded.

On the converse side, the paper derives new upper bounds on the sum‑capacity. In addition to the classic cut‑set bound, a genie‑aided technique is employed: a hypothetical genie provides a receiver with extra side information (e.g., the other user’s private message or part of the cooperative layer). By varying the genie’s assistance, the bound smoothly interpolates between the no‑cooperation case (standard interference channel) and the infinite‑cooperation case (full cooperation). The authors prove that the gap between their achievable sum‑rate and these upper bounds is bounded by a constant number of bits (no more than five), independent of the signal‑to‑noise ratio (SNR) or channel gains. Consequently, the proposed scheme is “capacity‑optimal to within a constant gap.”

A further contribution is the analysis of the symmetric Gaussian interference channel with noiseless feedback. The authors show that perfect feedback from each receiver to its own transmitter provides the same informational advantage as a full‑duplex cooperation link. By applying the same three‑layer coding strategy, they achieve the sum‑capacity of the feedback channel within the same constant‑gap bound. This result underscores that feedback can be viewed as a special case of source cooperation.

Numerical simulations complement the theoretical findings. Across a range of SNRs and interference strengths, the cooperative scheme consistently outperforms the original HK scheme. The most pronounced gains appear when the cooperation link capacity is moderate (approximately 2–4 bits per channel use), where the extra side information significantly reduces the effective interference seen by each receiver. In the feedback scenario, similar improvements are observed, confirming the theoretical equivalence between feedback and cooperation.

In summary, the paper makes four key contributions: (1) it introduces a full‑duplex source‑cooperation model for the two‑user Gaussian interference channel; (2) it designs a three‑layer superposition coding scheme that integrates compressed cooperative information with the classic HK framework; (3) it derives novel constant‑gap upper bounds, proving that the achievable sum‑rate is within a few bits of capacity for any channel parameters; and (4) it extends the analysis to the noiseless‑feedback setting, showing that the same scheme attains the sum‑capacity within a constant gap. These results provide both a deeper theoretical understanding of cooperation in interference‑limited networks and practical guidelines for designing future cooperative or feedback‑enabled wireless systems.