Capacity Bounds for the Gaussian Interference Channel (0801.1306v1)

Abstract: The capacity region of the two-user Gaussian Interference Channel (IC) is studied. Three classes of channels are considered: weak, one-sided, and mixed Gaussian IC. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The sum capacity for a certain range of channel parameters is derived. For this range, it is proved that using Gaussian codebooks and treating interference as noise is optimal. It is shown that when Gaussian codebooks are used, the full Han-Kobayashi achievable rate region can be obtained by using the naive Han-Kobayashi achievable scheme over three frequency bands (equivalently, three subspaces). For the one-sided Gaussian IC, an alternative proof for the Sato's outer bound is presented. We derive the full Han-Kobayashi achievable rate region when Gaussian codebooks are utilized. For the mixed Gaussian IC, a new outer bound is obtained that outperforms previously known outer bounds. For this case, the sum capacity for the entire range of channel parameters is derived. It is proved that the full Han-Kobayashi achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of channel parameters.

• The paper presents novel outer bounds and optimal conditions for weak and mixed Gaussian interference channels using Gaussian codebooks.
• It demonstrates that frequency partitioning simplifies the Han-Kobayashi achievable rate region, reducing computational complexity.
• The study reveals capacity equivalence between one-sided and mixed channels, offering practical insights for interference-limited network design.

Capacity Bounds for the Gaussian Interference Channel

The paper by Motahari and Khandani explores the sophisticated analysis of the two-user Gaussian Interference Channel (IC), tackling a crucial problem in information theory. The paper is structured around three specific classes of ICs, namely weak, one-sided, and mixed Gaussian ICs. The authors present novel outer bounds and address the sum capacity, alongside evaluating the Han-Kobayashi (HK) achievable rate region within these contexts.

Weak Gaussian Interference Channel

For weak Gaussian ICs, the authors provide a new outer bound that improves upon previously established results by Kramer and others. They define the sum capacity for a segment of channel parameters and prove that using Gaussian codebooks with interference treated as noise is optimal in this range. A key insight here is the reduction of computational complexity in characterizing the HK achievable region by employing a straightforward frequency partitioning strategy, demonstrating optimality with three subspaces.

One-sided Gaussian Interference Channel

The analysis of the one-sided Gaussian IC is distinguished into strong and weak interference scenarios. For the weak case, an alternative proof is provided for Sato's outer bound, showing how such channels relate to the degraded Gaussian broadcast channel. The authors offer a comprehensive characterization of the HK achievable region, maintaining Gaussian codebook assumptions.

Mixed Gaussian Interference Channel

For mixed Gaussian ICs, the paper derives a new outer bound and establishes the sum capacity over the entire parameter range, outperforming other known bounds. The paper illustrates that the full HK achievable region corresponds to the one-sided Gaussian IC for specific channel configurations. This equivalence is pivotal as it suggests a surprising facet of the capacity region employing both common and private messages.

Implications and Future Directions

The implications of these findings are noteworthy both in theory and practice. By reducing the complexity of HK region characterization, the research advances our understanding of interference channels and enhances the efficiency of communication strategies in Gaussian settings. The results introduce opportunities for practical applications in networks where interference is a predominant factor, suggesting pathways to improve transmission rates and spectral efficiency.

Future work may explore further relaxation or extension of these bounds to other types of interference channels or multi-user scenarios. Moreover, exploring the impact of varying degrees of channel knowledge or advanced modulation schemes could broaden the applicability of these results. The interplay between computational complexity and achievable gains will likely continue to be a fertile area for exploration in the ongoing development of network information theory.

This paper delineates strong numerical results and makes bold claims without unrealistic sensationalism, marking it as a substantive contribution to the domain of communication channels.