We establish 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: 1) common randomness is available at the source and the two relays and 2) randomness is available only at the source, and there is no randomness at the relays. Our upper bounds are established by taking into account the correlation between the two relay signals and the available randomness at the encoders, which generalize the techniques recently developed for the case without secrecy constraint. For the lower bounds, we propose two types of coding schemes: 1) decode-and-forward schemes where the relays cooperatively transmit the message and the fictitious message and 2) partial decode-and-forward schemes incorporated with multicoding in which each relay sends an independent partial message and the whole or partial fictitious message using dependent codewords.
We establish 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: 1) common randomness is available at the source and the two relays and 2) randomness is available only at the source, and there is no randomness at the relays. Our upper bounds are established by taking into account the correlation between the two relay signals and the available randomness at the encoders, which generalize the techniques recently developed for the case without secrecy constraint. For the lower bounds, we propose two types of coding schemes: 1) decode-and-forward schemes where the relays cooperatively transmit the message and the fictitious message and 2) partial decode-and-forward schemes incorporated with multicoding in which each relay sends an independent partial message and the whole or partial fictitious message using dependent codewords.
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.
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.
We study the degraded multi-receiver wiretap channel with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The legitimate users and the eavesdropper satisfy a certain degradation order. In this paper, we study this channel model for the scenario where the transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. First, we obtain an inner bound for the capacity region of the discrete memoryless channel by using an achievable scheme that uses superposition coding and binning. Next, we obtain an outer bound for the capacity region of the degraded discrete memoryless channel. We show that this outer bound partially matches the inner bound. Consequently, we provide a partial characterization of the capacity region of the degraded discrete memoryless channel. Finally, we consider the degraded Gaussian multi-input multi-output (MIMO) wiretap channel with public and confidential messages. We show that, to evaluate both the inner and outer bounds for the Gaussian MIMO case, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Since the inner and outer bounds provided earlier for the degraded discrete memoryless channel partially match, these sufficiency results provide a partial characterization of the capacity region of the degraded Gaussian MIMO channel.
The secrecy capacity of relay channels with orthogonal components is studied in the presence of an additional passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multiantenna point-to-point channel with a multiantenna eavesdropper. The outer bounds are shown to be tight for two subclasses of channels. The first subclass is one in which the source and relay are clustered, and the eavesdropper receives signals only on the channel from the source and the relay to the destination, for which the PDF strategy is optimal. The second is a subclass in which the source does not transmit to the relay, for which a noise-forwarding strategy is optimal.
Secrecy capacity is analyzed in a Gaussian two-way relay wiretap channel (TRWC), where two legitimate source nodes wish to exchange their messages through a relay in the presence of an eavesdropper. We assume that all intended nodes operate in full-duplex mode and there is no direct path between two sources. In the Gaussian TRWC, we propose an achievable coding scheme composed of superposed lattice codes with both structured and random codebooks. A jamming strategy is further introduced at the two sources as well as at the relay to maximize the achievable secrecy rate regions, where each node allocates part of its power to jam the eavesdropper. Our result indicates that positive achievable secrecy rates are maintained even for the reversely degraded scenario. In addition, assuming two sources with equal power constraint, it is shown that the scheme asymptotically achieves within 1/2 bit from the cut-set bound based on the channel with no secrecy constraints, as the downlink phase is in the high signal-to-noise ratio regime.
We study the multi-receiver wiretap channel with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless multi-receiver wiretap channel as well as its Gaussian multi-input multi-output (MIMO) instance. First, we consider the degraded discrete memoryless channel, and obtain an inner bound for the capacity region by using an achievable scheme that uses superposition coding and binning. Next, we obtain an outer bound, and show that this outer bound partially matches the inner bound, providing a partial characterization for the capacity region of the degraded channel model. Second, we obtain an inner bound for the general, not necessarily degraded, discrete memoryless channel by using Marton's inner bound, superposition coding, rate-splitting and binning. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Since the inner and outer bounds partially match, these sufficiency results provide a partial characterization of the capacity region of the degraded Gaussian MIMO channel. Finally, we provide an inner bound for the capacity region of the general, not necessarily degraded, Gaussian MIMO multi-receiver wiretap channel.