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Japan Journal of Applied Mathematics

A new treatment of communication processes with Gaussian channels

Masanori Ohya, Noboru Watanabe

Published Jun 1, 1986• 24 citations
Publisher
DOI
10.1007/bf03167097

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In order to discuss the efficiency of information transmission of the Gaussian communication processes consistently, we introduced an entropy type functional and a mutual entropy type functional in reference [16]. In that study, we used the set of Gaussian input measures with covariance operators of trace one. In this paper, we refine the formulation and modify the entropy type complexity and the mutual entropy type complexity to be able to study the efficiency of information transmission for more general input Gaussian measures and Gaussian channels.
New applications in modern communications are demanding robust and ultra-reliable low latency information exchange such as machine-to-machine and human-to-machine communications. For many of these applications, the identification approach of Ahlswede and Dueck is much more efficient than the classical message transmission scheme proposed by Shannon. Previous studies concentrate mainly on identification over discrete channels. For discrete channels, it was proved that identification is robust under channels uncertainty. Furthermore, optimal identification schemes that are secure and robust against jamming attacks have been considered. However, no results for continuous channels have yet been established. That is why we focus on the continuous case: the Gaussian channel for its known practical relevance. We deal with secure identification over Gaussian channels. Provable secure communication is of a high interest for future communication systems. A key technique for implementing secure communication is the physical layer security based on information theoretic security. We model this with the wiretap channel. In particular, we provide a suitable coding scheme for the Gaussian wiretap channel (GWC) and determine the corresponding secure identification capacity. We also consider Multiple-Input Multiple-Output (MIMO) Gaussian channels and provide an efficient signal-processing scheme. This scheme allows a separation of signal-processing and Gaussian coding.