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Entropy 2017, 19(2), 59; doi:10.3390/e19020059

On the Binary Input Gaussian Wiretap Channel with/without Output Quantization

1
Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, 611756 Chengdu, China
2
Institute of Digital Signal Processing, University of Duisburg-Essen, 47057 Duisburg, Germany
3
Center for Telecommunications, University of Johannesburg, Auckland Park 2006, South Africa
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 8 November 2016 / Revised: 7 January 2017 / Accepted: 30 January 2017 / Published: 4 February 2017
(This article belongs to the Section Information Theory)
View Full-Text   |   Download PDF [472 KB, uploaded 4 February 2017]   |  

Abstract

In this paper, we investigate the effect of output quantization on the secrecy capacity of the binary-input Gaussian wiretap channel. As a result, a closed-form expression with infinite summation terms of the secrecy capacity of the binary-input Gaussian wiretap channel is derived for the case when both the legitimate receiver and the eavesdropper have unquantized outputs. In particular, computable tight upper and lower bounds on the secrecy capacity are obtained. Theoretically, we prove that when the legitimate receiver has unquantized outputs while the eavesdropper has binary quantized outputs, the secrecy capacity is larger than that when both the legitimate receiver and the eavesdropper have unquantized outputs or both have binary quantized outputs. Further, numerical results show that in the low signal-to-noise ratio (SNR) (of the main channel) region, the secrecy capacity of the binary input Gaussian wiretap channel when both the legitimate receiver and the eavesdropper have unquantized outputs is larger than the capacity when both the legitimate receiver and the eavesdropper have binary quantized outputs; as the SNR increases, the secrecy capacity when both the legitimate receiver and the eavesdropper have binary quantized outputs tends to overtake. View Full-Text
Keywords: binary input Gaussian wiretap channel; information theoretic security; secrecy capacity; binary output quantization binary input Gaussian wiretap channel; information theoretic security; secrecy capacity; binary output quantization
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Qi, C.; Chen, Y.; Vinck, A.J.H. On the Binary Input Gaussian Wiretap Channel with/without Output Quantization. Entropy 2017, 19, 59.

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