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International Conference on Computer and Knowledge Engineering

Semi-deterministic Broadcast Channel With Side Information: A Secrecy Capacity Outer Bound

Saeid Pakravan, Ghosheh Abed Hodtani

Published Oct 29, 2020• 2 citations
Publisher

Abstract

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.

DOI
10.1109/iccke50421.2020.9303628

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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 article, a broadcast channel in the degraded state with two legitimate receivers in the attendance of an eavesdropper has been studied, where, the sender demands to forward two independent confidential messages that ought to be kept as secret as feasible of the eavesdropper to the legitimate receivers. In the studied system, it has been supposed that the non-causal channel state information has been considered at the transmitter side and every one of receivers has the message forwarded via source demanded via the further one. The model studied in this paper is further generalized into the formerly considered broadcast channel with confidential messages and considering side information in the receiver. It has been supplied an outer bound by considering confidentially conditions for proposed system.
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.
This paper studies the individual secrecy capacity region of the broadcast channel with receiver side information. First, an achievable rate region is established for the discrete memoryless case by employing superposition coding. Further, it is extended to the corresponding Gaussian case, where the individual secrecy capacity region is characterized in case of a weak or strong eavesdropper (compared to two legitimate receivers). For the case left, inner and outer bounds are established and the individual secrecy capacity region is characterized for the low and high SNR regimes. Note that the last case is distinctive due to the individual secrecy constraint, in the sense that positive rate pair is still possible although the eavesdropper may have the advantage against at least one of the legitimate receivers over the channel, unlike the situation if the joint secrecy constraint is imposed.
We study secure communication in which two confidential messages are transmitted over a broadcast channel to two legitimate receivers, while keeping an eavesdropper ignorant. Each legitimate receiver is interested in decoding one confidential message, while having the other one as side information. In order to measure the secrecy of the communication, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide an achievable rate region and a matching multi-letter outer bound presenting a multi-letter description for the capacity region. We further investigate the class of more capable channels and provide a single-letter converse establishing the secrecy capacity region, not only for more capable channels but less noisy and degraded channels as well. Our results indicate that the secrecy capacity for individual secrecy is higher than the one for joint secrecy, as one message can be used as a secret key for the other one.
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.
This paper studies the secrecy capacity of a class of degraded broadcast channels in the presence of an external eavesdropper, where a transmitter aims to deliver two independent confidential messages to two legitimate receivers. The transmitter is assumed to have non-causal access to the channel state information (CSI), and each legitimate receiver possesses prior knowledge of the other receiver's message, referred to as receiver message side information (RMSI). We consider two distinct scenarios: complementary RMSI, where each receiver knows only the other's message, and non-complementary RMSI, where the side information does not perfectly align. For both scenarios, we derive novel inner bounds on the achievable secrecy rate region and present tight outer bounds, establishing the secrecy capacity region for the considered degraded channel settings. Unlike prior works, which primarily address general broadcast settings without secrecy constraints or omit key interactions between RMSI and CSI, our results provide a complete characterization of the secure communication limits under these conditions. Moreover, we extend our analysis to the Gaussian degraded broadcast channel, highlighting the pivotal role of CSI in enhancing secure transmission performance. Our findings demonstrate that the combination of RMSI and CSI can be strategically leveraged to expand the secrecy capacity region, thus offering new insights into secure multiuser communication system design.