State-Dependent Interference Channel With Correlated States

Sun, Yunhao; Duan, Ruchen; Liang, Y. T.; Shamai, Shlomo

doi:10.1109/tit.2019.2899392

Cited by 1 publication

(1 citation statement)

References 30 publications

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“…The problem of Gaussian interference channel has been the subject of numerous outstanding prior works, paving the way to the current point and moving beyond. A subset of these works, reported in [1] to [39], are briefly discussed in this section. A more complete and detailed literature survey will be provided in subsequent revisions of this article Reference [1] discusses degraded Gaussian interference channel (degraded means one of the two receivers is a degraded version of the other one) and presents multiple bounds and achievable rate regions.…”

Section: Literature Surveymentioning

confidence: 99%

Capacity Region of Two-users Weak Gaussian Interference Channel

Khandani

2020

Preprint

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Capacity region of two-users (2-users) weak Gaussian Interference Channel (GIC) has been solved only in some special cases. The problem is complex since knowledge of input distributions is needed in order to express the underlying mutual information terms in closed forms, which in turn should be optimized over selection of input distributions and the associated power and bandwidth allocation. In addition, the optimum solution may require dividing the available resources (time, bandwidth and power) among several 2-users GIC (called "constituent 2-users GIC", or simply "constituent regions", hereafter) and apply time-sharing among them to form their upper concave envelope, and thereby enlarge the capacity region. The current article, in most parts, focuses on a single constituent 2-users GIC, meaning that the constraints on resources are all satisfied with equality. This does not result in any loss of generality because a similar solution technique is applicable to any constituent 2-users GICs. This article shows that, by relying on a different, intuitively straightforward, interpretation of the underlying optimization problem, one can determine the encoding/decoding strategies in the process of computing the optimum solution (for a single constituent 2-users GIC). This is based on gradually moving along the boundary of the capacity region in infinitesimal steps, where the solution for the end point in each step is constructed and optimized relying on the solution at the step's starting point. This approach enables proving Gaussian distribution is optimum over the entire boundary, and also allows finding simple closed form solutions describing different parts of the capacity region. The solution for each constituent 2-users GIC coincides with the optimum solution to the well known Han-Kobayashi (HK) system of constraints with i.i.d. (scalar) Gaussian inputs. Although the article is focused on 2-users weak Gaussian interference channel, the proof for optimality of Gaussian distribution is independent of the values of cross gains, and thereby is universally applicable to strong, mixed and Z interference channels, as well as to GIC with more than two users. In addition, the procedure for the construction of boundary is applicable for arbitrary cross gain values, by re-deriving various conditions that have been established in this article assuming a < 1 and b < 1. Note:The current arXiv submission differs from the earlier one (submitted on November 25th, 2020) in: (i) An Introduction section and a brief literature survey are added. (ii) The proof for the upper bound (presented in Appendix A) is made more clear. (iii) Section 3.1.4, which provided an alternative proof for part of what is presented in Appendix A, is removed. Sections 1.4/1.5 are revised.

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Section: Literature Surveymentioning

confidence: 99%

Capacity Region of Two-users Weak Gaussian Interference Channel

Khandani

2020

Preprint

View full text Add to dashboard Cite

show abstract

State-Dependent Interference Channel With Correlated States

Cited by 1 publication

References 30 publications

Capacity Region of Two-users Weak Gaussian Interference Channel

Capacity Region of Two-users Weak Gaussian Interference Channel

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