Secrecy Capacity of Colored Gaussian Noise Channels with Feedback

TL;DR

This paper demonstrates that for Gaussian channels with feedback, a modified Schalkwijk-Kailath scheme can achieve the same capacity even with an eavesdropper, establishing the secrecy capacity as equal to the feedback capacity.

Contribution

It introduces a coding scheme that achieves the same capacity with an eavesdropper as without, extending to quantized feedback in AWGN channels.

Findings

Secrecy capacity equals feedback capacity in Gaussian channels with feedback.

The proposed scheme achieves positive secrecy rates with quantized feedback.

Secrecy rate approaches channel capacity as quantization noise diminishes.

Abstract

In this paper, the k-th order autoregressive moving average (ARMA(k)) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that a variant of the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.