NDLI: The I-MMSE approach on the weak Gaussian Z-interference channel and the type I Gaussian Broadcast-Z-interference channel

Content Provider	IEEE Xplore Digital Library
Author	Bustin, R. Shamai, S.
Copyright Year	2010
Description	Author affiliation: Dept. Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel (Bustin, R.; Shamai, S.)
Abstract	A fundamental relationship between Estimation Theory and Information Theory for Gaussian channels was derived by Guo, Shamai and Verdú (first presented in ISIT 2008); in particular, it was shown that for the MIMO standard Gaussian channel, the mutual information and the minimum mean-square error (MMSE) are related. This fundamental relationship and its generalizations, referred to as the I-MMSE relationships, have already been shown to be useful in several aspects of Information Theory. An inherent property of the MMSE, is the “single crossing point” property: as a function of snr, the MMSE of the Gaussian input distribution and the MMSE of an arbitrary input distribution intersect at most once. In this work we will use this property and its recent extensions to the MIMO scenario. In this paper we take a look at two variations of the interference channel: the Gaussian Z-interference channel and the type I Gaussian Broadcast-Z-interference channel. We use the I-MMSE approach to derive outer bounds on the capacity region of these channels. The Z-interference problem is a simplified case of the more general interference channel, for which the capacity region is unknown, in general. The Gaussian Z-interference channel in its standard form is given by: $Y_{1}$ = $X_{1}$ + $√aX_{2}$ + $N_{1}$ $Y_{2}$ = $X_{2}$ + $N_{2}$ where Ni and N2 are standard Gaussian and may be considered independent. We consider a power constraints $P_{i},$ i ϵ {1, 2}, on both inputs. For a ϵ (0, 1), that is, weak interference, there is no known single letter expression for the capacity region. The best known general outer bound is due to Sato. Using Ahlswede's limiting expression for the capacity region, we re-derive Sato's outer bound directly from the limiting expression using the I-MMSE approach and show why this outer bound can not be tight in general. As an additional example of the usage of the I-MMSE approach, we examine the type I Gaussian Broadcast-Z-interference channel, recently presented by Shang and Poor. For this channel we show that the I-MMSE approach can derive equivalent, more natural and insightful, outer bound for the weak interference case.
Starting Page	000291
Ending Page	000295
File Size	388122
Page Count	5
File Format	PDF
ISBN	9781424486816
e-ISBN	9781424486823
DOI	10.1109/EEEI.2010.5661978
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-11-17
Publisher Place	Israel
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Interference channels MIMO Upper bound Limiting Mutual information
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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