[Paper Review] Independent signaling achieves the capacity region of the Gaussian interference channel with common information to within one bit

Chinmay S. Vaze, Mahesh K. Varanasi|arXiv (Cornell University)|Feb 29, 2012

Wireless Communication Security Techniques14 references4 citations

TL;DR

This paper establishes the capacity region of the Gaussian interference channel with common information (IC-CI) within one bit, using an explicit inner and outer bound. Surprisingly, the optimal rate region is achieved via independent signaling—despite available transmitter cooperation through shared common messages—demonstrating that such cooperation does not improve performance, and that the common message enables a substantial, potentially unbounded, rate gain via full utilization of signal-level dimensions.

ABSTRACT

The interference channel with common information (IC-CI) consists of two transmit-receive pairs that communicate over a common noisy medium. Each transmitter has an individual message for its paired receiver, and additionally, both transmitters have a common message to deliver to both receivers. In this paper, through explicit inner and outer bounds on the capacity region, we establish the capacity region of the Gaussian IC-CI to within a bounded gap of one bit, independently of the values of all channel parameters. Using this constant-gap characterization, the generalized degrees of freedom (GDoF) region is determined. It is shown that the introduction of the common message leads to an increase in the GDoF over that achievable over the Gaussian interference channel without a common message, and hence to an unbounded improvement in the achievable rate. A surprising feature of the capacity-within-one-bit result is that most of the available benefit (i.e., to within one bit of capacity) due to the common message is achieved through a simple and explicit coding scheme that involves independent signaling at the two transmitters so that, in effect, this scheme forgoes the opportunity for transmitter cooperation that is inherently available due to shared knowledge of the common message at both transmitters.

Motivation & Objective

• To characterize the capacity region of the Gaussian interference channel with common information (IC-CI) under general channel conditions.
• To determine whether transmitter cooperation—enabled by shared knowledge of the common message—can improve achievable rates in IC-CI.
• To quantify the generalized degrees of freedom (GDoF) region and assess the impact of the common message on spectral efficiency.
• To close the gap between known inner and outer bounds on the IC-CI capacity region, achieving a constant gap of one bit regardless of channel parameters.

Proposed method

• Derives explicit inner and outer bounds on the capacity region of the Gaussian IC-CI using information-theoretic techniques.
• Proposes a simple coding scheme based on independent signaling at transmitters, where each transmitter sends its individual and common messages without coordination, despite shared knowledge of the common message.
• Uses rate-splitting and superposition coding principles to construct the inner bound, with messages split into public and private sub-messages.
• Applies joint typicality decoding at receivers to extract intended messages from the superimposed signals.
• Characterizes the generalized degrees of freedom (GDoF) region by analyzing the asymptotic behavior of the rate region under high SNR.
• Establishes a universal gap of one bit between the inner and outer bounds, independent of channel parameters such as SNR and INR.

Experimental results

Research questions

• RQ1 Can the capacity region of the Gaussian IC-CI be characterized within a bounded gap, independent of channel parameters?
• RQ2 Does transmitter cooperation, enabled by shared knowledge of the common message, provide a rate gain in the IC-CI?
• RQ3 How does the presence of a common message affect the generalized degrees of freedom (GDoF) compared to the standard IC without common information?
• RQ4 Is there a simple coding scheme that achieves the capacity region to within one bit, even without exploiting transmitter cooperation?
• RQ5 To what extent does the common message enable full utilization of the physical layer's signal-level dimensions in interference-limited networks?

Key findings

• The capacity region of the Gaussian IC-CI is characterized within one bit of the true capacity, with the gap independent of all channel parameters such as SNR and INR.
• The optimal rate region is achieved by a simple independent signaling scheme, which forgoes transmitter cooperation despite its availability due to shared knowledge of the common message.
• The generalized degrees of freedom (GDoF) region is fully characterized, showing that the common message enables an unbounded improvement in spectral efficiency over the standard IC without common information.
• The GDoF per user increases due to the common message, indicating that the common message allows full exploitation of the physical layer's signal-level dimensions.
• The inner bound based on independent signaling matches the outer bound to within one bit, proving that cooperation between transmitters is not necessary to achieve near-capacity performance.
• The DoF gain is explained by the fact that common message transmission allows receivers to fully utilize the interference channel's spatial and power dimensions, which are underused when only individual messages are sent.