This paper considers the Broadcast Channel with Confidential Message (BCCM) where the sender attempts to send altogether a common message to two receivers and a confidential message to one of them. The achievable rate regions are derived for the power-constrained Gaussian BCCM with finite input alphabet using various transmission strategies. Namely, time sharing, superposition modulation and superposition coding are used as broadcast strategies. For superposition modulation and superposition coding, the maximal achievable rate regions are obtained by maximizing over both constellation symbol positions and the joint probability distribution. The maximization of the secrecy rate for wiretap channels is also studied as a particular case of the BCCM problem. We compare the considered transmission strategies in terms of percentage gains in achievable rates. We concentrate on the impact of the finite alphabet constraint on achievable rates, and show that this constraint may change well known results obtained in the Gaussian case. We show also that the secrecy constraint can change the shape of the achievable rate region in superposition modulation used in some standards when symbols are equiprobable. On a more practical side, it is shown that a performance close to the optimum can be obtained by strategies with reduced complexity.
This paper considers the Broadcast Channel with Confidential Message (BCCM) where the sender attempts to send altogether a common message to two receivers and a confidential message to one of them. The achievable rate regions are derived for the power-constrained Gaussian BCCM with finite input alphabet using various transmission strategies. Namely, time sharing, superposition modulation and superposition coding are used as broadcast strategies. For superposition modulation and superposition coding, the maximal achievable rate regions are obtained by maximizing over both constellation symbol positions and the joint probability distribution. The maximization of the secrecy rate for wiretap channels is also studied as a particular case of the BCCM problem. We compare the considered transmission strategies in terms of percentage gains in achievable rates. We concentrate on the impact of the finite alphabet constraint on achievable rates, and show that this constraint may change well known results obtained in the Gaussian case. We show also that the secrecy constraint can change the shape of the achievable rate region in superposition modulation used in some standards when symbols are equiprobable. On a more practical side, it is shown that a performance close to the optimum can be obtained by strategies with reduced complexity.
This paper investigates the maximization of the secrecy-achievable rate region for the Gaussian broadcast channel with confidential message (BCCM) using finite input constellations. The maximization is done jointly over symbol positions and their joint probabilities. The secrecy-achievable rate regions are given for various broadcast strategies which differ in their complexity of implementation. We compare these strategies in terms of improvement in achievable rates and we study the impact of finite input alphabet on the secrecy-achievable rates. It is shown that finite alphabet constraints may change well known results holding in the Gaussian case.
This paper investigates the maximization of the secrecy-achievable rate region for the Gaussian broadcast channel with confidential message (BCCM) using finite input constel-lations. The maximization is done jointly over symbol posi-tions and their joint probabilities. The secrecy-achievable rate regions are given for various broadcast strategies which differ in their complexity of implementation. We compare these strategies in terms of improvement in achievable rates and we study the impact of finite input alphabet on the secrecy-achievable rates. It is shown that finite alphabet constraints may change well known results holding in the Gaussian case. Index Terms — Secrecy-achievable rate region, information-theoretic security, finite-input alphabet.
We investigate the effects of an additional relay node on the secrecy of broadcast channels by considering the model of relay broadcast channels with confidential messages. We show that this additional relay node can increase the achievable secrecy rate region of the broadcast channels with confidential messages. More specifically, first, we investigate the discrete memoryless relay broadcast channels with two confidential messages and one common message. Three inner bounds (with respect to decode-forward, generalized noise-forward and compress-forward strategies) and an outer bound on the capacity-equivocation region are provided. Removing the secrecy constraint, this outer bound can also be served as a new outer bound for the relay broadcast channel. Second, we investigate the discrete memoryless relay broadcast channels with two confidential messages (no common message). Inner and outer bounds on the capacity-equivocation region are provided. Then, we study the Gaussian case, and find that with the help of the relay node, the achievable secrecy rate region of the Gaussian broadcast channels with two confidential messages is enhanced. Finally, we investigate the discrete memoryless relay broadcast channels with one confidential message and one common message. This work generalizes Lai-Gamals work on the relay-eavesdropper channel by considering an additional common message for both the legitimate receiver and the eavesdropper. Inner and outer bounds on the capacity-equivocation region are provided, and the results are further explained via a Gaussian example. Compared with Csiszár-Körner’s work on broadcast channels with confidential messages (BCC), we find that with the help of the relay node, the secrecy capacity region of the Gaussian BCC is enhanced.
The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.
In this paper, we first consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-taper also receives the transmitted signal. We assume that the signals are transmitted over additive white Gaussian noise channels. We characterize the secrecy capacity region of this channel. Our achievable coding scheme is based on superposition coding and the random binning. We refer to this scheme as secret superposition coding. The converse proof combines the converse proof for the conventional Gaussian broadcast channel and the perfect secrecy constraint. This capacity region matches the capacity region of the broadcast channel without security constraint. It also matches the secrecy capacity of the wire-tap channel. Based on the rate characterization of the secure Gaussian broadcast channel, we then use a multilevel coding approach for the slowly fading wire-tap. We assume that the transmitter only knows the eavesdropper's channel. In this approach, source node sends secure layered coding and the receiver viewed as a continuum ordered users. We derive optimum power allocation for the layers which maximizes the total average rate.
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.