This paper considers a state dependent channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem at hand is to effectively "amplify" the channel state sequence at Bob while "masking" it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage, and the paper is aimed at characterizing the tradeoff-region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter enumerates the state sequence using two indices, and transmits one of the indices over the channel to facilitate the amplification process. For the case when Bob observes a "stronger" channel than Eve, the achievable coding scheme is enhanced with secure refinement. The optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the degraded binary and the degraded Gaussian channels. For the degraded Gaussian model, extremal corner points of the trade-off region are characterized. In addition, the gap between the outer bound and achievable rate-regions is determined, where it is shown that the gap is less than half a bit for a wide set of channel parameters.
This paper considers a state dependent channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem at hand is to effectively "amplify" the channel state sequence at Bob while "masking" it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage, and the paper is aimed at characterizing the tradeoff-region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter enumerates the state sequence using two indices, and transmits one of the indices over the channel to facilitate the amplification process. For the case when Bob observes a "stronger" channel than Eve, the achievable coding scheme is enhanced with secure refinement. The optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the degraded binary and the degraded Gaussian channels. For the degraded Gaussian model, extremal corner points of the trade-off region are characterized. In addition, the gap between the outer bound and achievable rate-regions is determined, where it is shown that the gap is less than half a bit for a wide set of channel parameters.
This paper considers a state dependent broadcast channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem is to effectively convey (“amplify”) the channel state sequence to Bob while “masking” it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage. This can be viewed as a secrecy problem, where we desire that the channel state itself be minimally leaked to Eve while being communicated to Bob. This paper is aimed at characterizing the tradeoff region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter transmits a partial state information over the channel to facilitate the amplification process. For the case when Bob observes a stronger signal than Eve, the achievable coding scheme is enhanced with secure refinement. Outer bounds on the tradeoff region are also derived, and used in characterizing some special case results. In particular, the optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the reversely degraded discrete memoryless channel, the degraded binary, and the degraded Gaussian channels. In addition, for the degraded Gaussian model, the extremal corner points of the tradeoff region are characterized, and the gap between the outer bound and achievable rate-regions is shown to be less than half a bit for a wide set of channel parameters.
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 investigates the problem of source-channel coding for secure transmission with arbitrarily correlated side informations at both receivers. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the problems of secure source coding with (uncoded) side information at the decoders and the wiretap channel. A general outer bound on the rate-distortion-equivocation region, as well as an inner bound based on a pure digital scheme, is derived for arbitrary channels and side informations. In some special cases of interest, it is proved that this digital scheme is optimal and that separation holds. However, it is also shown through a simple counterexample with a binary source that a pure analog scheme can outperform the digital one while being optimal. According to these observations and assuming matched bandwidth, a novel hybrid digital/analog scheme that aims to gather the advantages of both digital and analog ones is then presented. In the quadratic Gaussian setup when side information is only present at the eavesdropper, this strategy is proved to be optimal. Furthermore, it outperforms both digital and analog schemes and cannot be achieved via time-sharing. Through an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.
Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. This problem of secret communication and secret-key generation when two resources are available-correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources is studied. The goal is to characterize the fundamental tradeoff between the rates of the secret message and secret key. An achievable solution and proof of its optimality for the parallel channels and sources case when each subchannel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper) is presented. This includes the case of jointly Gaussian sources and an additive Gaussian channel, for which the secrecy region is evaluated.
This paper studies the problem of secure communication over broadcast channels under the lens of individual secrecy constraints (i.e., information leakage from each message to an eavesdropper is made vanishing). It is known that, for the communication over the degraded broadcast channels, the stronger receiver is able to decode the message of the weaker receiver. In the individual secrecy setting, the message for the weaker receiver can be further utilized to secure the partial message that is intended to the stronger receiver. With such a coding spirit, it is shown that more secret bits can be conveyed to the stronger receiver. In particular, for the corresponding Gaussian model, a constant gap (i.e., 0.5 bits within the individual secrecy capacity region) result is obtained. Overall, when compared with the joint secrecy constraint, the results allow for trading-off secrecy level and throughput in the system.
This paper studies the problem of secure communications over broadcast channels under theindividualsecrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant ofeachmessage (i.e., the information leakage rate fromeachmessage to the eavesdropper is made vanishing). Building upon Carleial–Hellman’s secrecy coding, Wyner’s secrecy coding, and the framework of Marton’s coding together with techniques, such as rate splitting and indirect decoding, an achievable individual secrecy rate region is established with the characterization of capacity regions for some special cases. In particular, the individual secrecy capacity region for the linear deterministic model is fully characterized, and for the Gaussian model, a constant gap (i.e., 0.5 b within the individual secrecy capacity region) result is obtained. To illustrate the impact of different secrecy constraints on the corresponding capacity regions, comparisons are made with those satisfying joint secrecy and without secrecy constraints. Overall, when compared with the joint secrecy constraint, the results allow for trading off secrecy level and throughput in the system.