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arXiv:1411.0294 · IEEE Information Theory Workshop (ITW)

Capacity region continuity of the compound broadcast channel with confidential messages

Andrea Grigorescu, Holger Boche, Rafael F. Schaefer, H. Vincent Poor

Published Apr 1, 2015• 2 citations
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Abstract

The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.

DOI
10.1109/itw.2015.7133119

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The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.
The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.
The broadcast channel with confidential messages (BCC) consists of one transmitter and two receivers, where the transmitter sends a common message to both receivers and, at the same time, a confidential message to one receiver which has to be kept secret from the other one. In this paper, this communication scenario is studied for compound channels, where it is only known to the transmitter and receivers that the actual channel realization is fixed and from a prespecified set of channels. The information theoretic criterion of strong secrecy is analyzed in detail and its impact on the decoding performance of the non-legitimate receiver is characterized. In particular, it is shown that regardless of the computational capabilities and the applied decoding strategy of the non-legitimate receiver, his decoding error always tends to one. This gives a valuable signal processing implication of the strong secrecy criterion and identifies desirable properties of an optimal code design. Further, an achievable strong secrecy rate region is derived and a multiletter outer bound is given. Both together yield a multiletter expression of the strong secrecy capacity region of the compound BCC.
Abstract — We study the compound multi-input multi-output (MIMO) broadcast channel with confidential messages (BCC), where one transmitter sends a common message to two receivers and two confidential messages respectively to each receiver. The channel state may take one of a finite set of states, and the transmitter knows the state set but does not know the realization of the state. We study achievable rates with perfect secrecy in the high SNR regime by characterizing an achievable secrecy degree of freedom (s.d.o.f.) region for two models, the Gaussian MIMO-BCC and the ergodic fading multi-input single-output (MISO)-BCC without a common message. We show that by exploiting an additional temporal dimension due to state variation in the ergodic fading model, the achievable s.d.o.f. region can be significantly improved compared to the Gaussian model with a constant state, although at the price of a larger delay. I.
We study the compound multi-input multi-output (MIMO) broadcast channel with confidential messages (BCC), where one transmitter sends a common message to two receivers and two confidential messages respectively to each receiver. The channel state may take one of a finite set of states, and the transmitter knows the state set but does not know the realization of the state. We study achievable rates with perfect secrecy in the high SNR regime by characterizing an achievable secrecy degree of freedom (s.d.o.f.) region for two models, the Gaussian MIMO-BCC and the ergodic fading multi-input single-output (MISO)-BCC without a common message. We show that by exploiting an additional temporal dimension due to state variation in the ergodic fading model, the achievable s.d.o.f. region can be significantly improved compared to the Gaussian model with a constant state, although at the price of a larger delay.
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 secrecy capacity region is first 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 Gaussian case of the Csiszar-Korner BCC model. The secrecy capacity results are then applied to give the ergodic secrecy capacity region for the fading BCC.