In this paper, we investigate secret communications over a two-user semi-deterministic broadcast channel, in which user 1's channel is deterministic, while user 2's channel is a discrete memoryless channel. The transmitter has two independent confidential messages, each of which is intended for one of the receivers, but is kept completely secret from the other. We first establish the secrecy capacity region of the semi-deterministic broadcast channel. Next, as a special case, we consider both channels are deterministic and compare the secrecy capacity region with the well-known general capacity region of the deterministic broadcast channel without secrecy constraint. Our result illustrates the fundamental loss of the transmission rates due to keeping the messages secret as well as the tradeoff between the communication rate and the perfect secrecy requirement.
In this paper, we investigate secret communications over a two-user semi-deterministic broadcast channel, in which user 1's channel is deterministic, while user 2's channel is a discrete memoryless channel. The transmitter has two independent confidential messages, each of which is intended for one of the receivers, but is kept completely secret from the other. We first establish the secrecy capacity region of the semi-deterministic broadcast channel. Next, as a special case, we consider both channels are deterministic and compare the secrecy capacity region with the well-known general capacity region of the deterministic broadcast channel without secrecy constraint. Our result illustrates the fundamental loss of the transmission rates due to keeping the messages secret as well as the tradeoff between the communication rate and the perfect secrecy requirement.
In this study, we obtain an outer bound on the secrecy capacity region of a two-user semi-deterministic discrete memoryless broadcast channel with considering side-information available at the transmitter, where, the sender contain two independent confidential messages, each one is deliberated for one of the receivers but is kept entirely secret from the other. Further, we compare obtained outer bound via the specified secrecy capacity outer bound of the semi-deterministic broadcast channel without side information and without secrecy constraint; specifically, the side information impact on the outer bound is explained.
In this paper, we study secure communications over a two-user semi-deterministic broadcast channel, i.e., one of the receivers is connected to the transmitter through a deterministic channel. We consider the case where the deterministic receiver is also the eavesdropper for the other receiver's message. We derive the secrecy capacity region by showing that superposition encoding plus Gel'fand-Pinsker encoding is optimal. We find that due to the deterministic component of the channel, Gel'fand-Pinsker binning alone is enough to achieve perfect secrecy. We also compare our scheme with the capacity-achieving scheme of Marton for the semi-deterministic broadcast channel where there is no secrecy constraint.
This paper studies capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. Both inner and outer bounds are proposed to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszar and Korner's rate equivocation region for broadcast channels with a single confidential message, Liu 's achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand-Pinsker's achievable rate region for general broadcast channels. The proposed outer bounds, together with the inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including the less noisy, deterministic, and semideterministic broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.
This paper studies the problem of secure communication over the broadcast channel with receiver-side information under the lens of individual secrecy constraints, that is, the transmitter wants to send two independent messages to two receivers, which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) is characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a rectangle with missing corners; a phenomenon occurring due to the coupling between user's rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper's channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper's channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage rate from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate, making secrecy more affordable but still acceptable to the end user.
The broadcast channel (BC) with one confidential message and where the decoders cooperate via a one-sided link is considered. A pair of messages is transmitted, one message for each user. The message to the cooperative user is confidential and is kept secret from the cooperation-aided user. The secrecy level is measured by the equivocation rate. An inner bound on the secrecy-capacity region of the BC is derived. The inner bound is achieved by double-binning the codebook of the secret message. The inner bound is tight for the semi-deterministic (SD) and physically degraded (PD) cases. The secrecy results are compared to those of the corresponding BCs without a secrecy constraint. A cooperative Blackwell channel example illustrates the impact of secrecy on the rate regions.
In this paper, we derive information-theoretic performance limits for secure and reliable communications over the general two-user discrete memoryless broadcast channel with side-information at the transmitter. The sender wishes to broadcast two independent messages to two receivers, under the constraint that each message should be kept confidential from the unintended receiver. Furthermore, the encoder has side-information - for example, fading in the wireless medium, interference caused by neighboring nodes in the network, etc. - provided to it in a noncausal manner, i.e., before the process of transmission. We derive an inner bound on the capacity region of this channel, by employing an extension of Marton's coding technique used for the classical two-user broadcast channel, in conjunction with a stochastic encoder to satisfy confidentiality constraints. Based on previously known results, we discuss a procedure to present a schematic of the achievable rate region. The rate-penalties for dealing with side-information and confidentiality constraints make the achievable region for this channel strictly smaller than the rate regions of those channels where one or both of these constraints are relaxed.