In this paper, we study the two transmitter multiple-access channel (MAC) with noncausal side information at one (single-sided) or both (two-sided) of the encoders in the presence of an external wiretapper (WT) and under individual and collective secrecy constraints. Our work consists of four parts. First, we consider the discrete memoryless (DM-MAC-WT) case of the model and derive inner and outer bounds on the secrecy capacity region under both of the secrecy constraints. Second, the results are extended to the Gaussian memoryless case [Gaussian multiple-access channel WT (GMAC-WT)] in detail and are used to illustrate numerically that the secrecy rate region is enlarged by increasing the power of the interference signal which is known noncausally at the encoder. Third, we analyze the strong interference regime as an important regime in GMAC with side information and show that under collective secrecy constraint, we can achieve the secrecy capacity region of the single-sided channel asymptotically for a special case in which the signal and noise powers satisfy specific constraints. To the best of our knowledge, this capacity region is the first one obtained for GMAC-WT. Finally, we show that our results include previous works as its special cases for both the single-sided and two-sided channel models.
In this paper, we study the two transmitter multiple-access channel (MAC) with noncausal side information at one (single-sided) or both (two-sided) of the encoders in the presence of an external wiretapper (WT) and under individual and collective secrecy constraints. Our work consists of four parts. First, we consider the discrete memoryless (DM-MAC-WT) case of the model and derive inner and outer bounds on the secrecy capacity region under both of the secrecy constraints. Second, the results are extended to the Gaussian memoryless case [Gaussian multiple-access channel WT (GMAC-WT)] in detail and are used to illustrate numerically that the secrecy rate region is enlarged by increasing the power of the interference signal which is known noncausally at the encoder. Third, we analyze the strong interference regime as an important regime in GMAC with side information and show that under collective secrecy constraint, we can achieve the secrecy capacity region of the single-sided channel asymptotically for a special case in which the signal and noise powers satisfy specific constraints. To the best of our knowledge, this capacity region is the first one obtained for GMAC-WT. Finally, we show that our results include previous works as its special cases for both the single-sided and two-sided channel models.
We consider the Gaussian multiple access wire-tap channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define a suitable security measure for this multi-access environment. We derive an outer bound for the rate region such that secrecy to some pre-determined degree can be maintained. We also find, using Gaussian codebooks, an achievable such secrecy region. Gaussian codewords are shown to achieve the sum capacity outer bound, and the achievable region coincides with the outer bound for Gaussian codewords, giving the capacity region when inputs are constrained to be Gaussian. We present numerical results showing the new rate region and compare it with that of the Gaussian multiple-access channel (GMAC) with no secrecy constraints
We consider a 2-user Gaussian Multiple-Access Wiretap channel (GMAC-WT), with the Eavesdropper (E) having access to signal from only one (say, T2) of the two transmitters. We characterize the capacity region of this channel approximately within. 5 bits, where the approximation is in terms of only T1's rate or the sum-rate depending on the relative strength of the eavesdropper's channel. However, the approximation is. 5 bits independent of channel coefficients or operating Signal-to-Noise Ratios (SNR). To prove this approximate result we propose two different coding schemes, namely, the power adaptation and the time sharing coding schemes and derive their corresponding achievable rate regions. Both of them use Gaussian input distribution. To establish the approximate capacity, we first derive supersets to the capacity region and then show that corresponding to each rate pair at the boundary of these supersets there exists an achievable rate pair in one of the aforementioned achievable rate regions which are within 1/2 bits to the former pair. In comparison to a very recent result (Xie and Ulukus, ISIT 2013) on a GMAC-WT showing the requirement of interference alignment (IA) to achieve even the degrees of freedom performance, the result of this paper is surprising: our channel model is an interesting variation of the GMAC-WT for which IA is not necessary and Gaussian signalling is sufficient to achieve the entire capacity region within. 5 bits.
In this paper, we study the problem of secret communication over a multiple-access channel with a common message. Here, we assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. We call this setting as Multiple-Access Wiretap Channel with Common message (MAWC-CM). For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a special case called the switch channel. As well, for a Gaussian version of MAWC-CM, we derive inner and outer bounds on the secrecy capacity region. Providing numerical results for the Gaussian case, we illustrate the comparison between the derived achievable rate region and the outer bound for the considered model and the capacity region of compound multiple access channel.
In this paper, some new results on the multiple-access wiretap channel (MAC-WT) are provided. Specifically, first, we investigate the degraded MAC-WT, where two users transmit their corresponding confidential messages (no common message) to a legitimate receiver via a multiple-access channel (MAC), while a wiretapper wishes to obtain the messages via a physically degraded wiretap channel. The secrecy capacity region of this model is determined for both the discrete memoryless and Gaussian cases. For the Gaussian case, we find that this secrecy capacity region is exactly the same as the achievable secrecy rate region provided by Tekin and Yener, i.e., Tekin–Yener’s achievable region is exactly the secrecy capacity region of the degraded Gaussian MAC-WT. Second, we study a special Gaussian MAC-WT, and find the power control for two kinds of optimal points (max-min point and single user point) on the secrecy rate region of this special Gaussian model.
In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner (termed here noncausal side information) or causal manner (termed here causal side information). Inner and outer bounds are derived on the capacity-equivocation regions for the noncausal and causal manners, and the secrecy capacities for both manners are described and bounded, which provide the best transmission rate with perfect secrecy. Moreover, for the case that the side information is available at the transmitter in a memoryless manner (termed here memoryless side information), both the capacity-equivocation region and the secrecy capacity are determined. The results of this paper extend the previous work on wiretap channel with noncausal side information by providing an outer bound on the capacity-equivocation region. In addition, we find that the memoryless side information can not help to obtain the same secrecy capacity as that of the causal case, and this is different from the well known fact that the memoryless manner can achieve the capacity of the channel with causal side information.
We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper. We define two suitable secrecy measures, termed individual and collective, to reflect the confidence in the system for this multi-access environment. We determine achievable rates such that secrecy to some pre-determined degree can be maintained, using Gaussian codebooks. We also find outer bounds for the case when the eavesdropper receives a degraded version of the intended receiver's signal. In the degraded case, Gaussian codewords are shown to achieve the sum capacity for collective constraints. In addition, a TDMA scheme is shown to also achieve sum capacity for both sets of constraints. Numerical results showing the new rate region are presented and compared with the capacity region of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. We then find the secrecy sum-rate maximizing power allocations for the transmitters, and show that a cooperative jamming scheme can be used to increase achievable rates in this scenario.