The Degraded Gaussian Diamond-Wiretap Channel

TL;DR

This paper derives bounds on the secrecy capacity of the degraded Gaussian diamond-wiretap channel, analyzing the impact of eavesdroppers and randomness availability at the source and relays.

Contribution

It provides new upper and lower bounds on the secrecy capacity, considering different randomness scenarios and relay cooperation strategies.

Findings

Bounds coincide in certain channel parameter ranges

Correlation between relay signals affects capacity bounds

Different coding schemes improve secrecy capacity under various conditions

Abstract

In this paper, we present nontrivial upper and lower bounds on the secrecy capacity of the degraded Gaussian diamond-wiretap channel and identify several ranges of channel parameters where these bounds coincide with useful intuitions. Furthermore, we investigate the effect of the presence of an eavesdropper on the capacity. We consider the following two scenarios regarding the availability of randomness: 1) a common randomness is available at the source and the two relays and 2) a randomness is available only at the source and there is no available randomness at the relays. We obtain the upper bound by taking into account the correlation between the two relay signals and the availability of randomness at each encoder. For the lower bound, we propose two types of coding schemes: 1) a decode-and-forward scheme where the relays cooperatively transmit the message and the fictitious message and 2) a partial DF scheme incorporated with multicoding in which each relay sends an independent partial message and the whole or partial fictitious message using dependent codewords.