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.
Highlights
The capacity of the Gaussian channel with binary inputs is a important metric on the performance of practical communication systems
We give the numerical comparison of the secrecy capacity CSS, CHH, (CHS )lower, and (CSH )lower
Recall that γ1, γ2 are the signal-to-noise ratio (SNR) of the legitimate channel and the wiretap channel, respectively
Summary
The capacity of the Gaussian channel with binary inputs is a important metric on the performance of practical communication systems. The closed-form expression of the secrecy capacity of the Gaussian wiretap channel with continuous input signal was given in [9]. Two constraints are imposed on the Gaussian wiretap channel: the input signal is binary; the output is restricted to the binary quantized output and the unquantized output. In the binary-input Gaussian wiretap channel (BI-GWC), since the legitimate receiver and the wiretapper can have either binary quantized outputs or unquantized outputs, there are four cases under consideration: 2. It is known that the quantized output leads to a lower channel capacity than the unquantized output does for the binary input Gaussian channel [10]. The problem is whether quantized output would still lead to a lower secrecy capacity.
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