Convexity of the Capacity of One-Bit Quantized Additive White Gaussian Noise Channels

Bibliographic Details
Title:	Convexity of the Capacity of One-Bit Quantized Additive White Gaussian Noise Channels
Authors:	Sungmin Lee, Moonsik Min
Source:	Mathematics, Vol 10, Iss 22, p 4343 (2022)
Publisher Information:	MDPI AG, 2022.
Publication Year:	2022
Collection:	LCC:Mathematics
Subject Terms:	convexity, entropy, mutual information, channel capacity, Mathematics, QA1-939
More Details:	In this study, the maximum error-free transmission rate of an additive white Gaussian noise channel with a symmetric analog-to-digital converter (ADC) was derived as a composite function of the binary entropy function, Gaussian Q-function, and the square root function, assuming that the composite function was convex on the set of all non-negative real numbers. However, because mathematically proving this convexity near zero is difficult, studies in this field have only presented numerical results for small values in the domain. Because the low-signal-to-noise (SNR) regime is considered to be a major application area for one-bit ADCs in wireless communication, deriving a concrete proof of the convexity of the composite function on small SNR values (non-negative values near zero) is important. Therefore, this study proposes a novel proof for convexity, which is satisfied for all non-negative values, based on the continuity of the involved functions.
Document Type:	article
File Description:	electronic resource
Language:	English
ISSN:	10224343 2227-7390
Relation:	https://www.mdpi.com/2227-7390/10/22/4343; https://doaj.org/toc/2227-7390
DOI:	10.3390/math10224343
Access URL:	https://doaj.org/article/e3685ad549e64f338864b2da66b54dfe
Accession Number:	edsdoj.3685ad549e64f338864b2da66b54dfe
Database:	Directory of Open Access Journals

More Details
ISSN:	10224343 22277390
DOI:	10.3390/math10224343
Published in:	Mathematics
Language:	English