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Information Theory and Applications Workshop (ITA)

Secrecy Capacity Region of Parallel Broadcast Channels

Yingbin Liang, H. Vincent Poor, Shlomo Shitz Shamai

Published Jan 1, 2007• 14 citations
Publisher

Abstract

The parallel broadcast channel with confidential messages (BCC) is investigated, where a source node transmits to two receivers (receivers 1 and 2) over multiple independent subchannels. The source node has common information for both receivers, and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The secrecy capacity region of the parallel BCC is established. It is shown that independent input distribution for each subchannel is optimal. It is also shown that the secrecy capacity region of the parallel BCC can be larger than the sum of the secrecy capacity regions of the subchannels. The secrecy capacity region is further derived for the parallel BCC with degraded subchannels. Applications of these results to the fading BCC are also discussed.

DOI
10.1109/ita.2007.4357587

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•Mar 27, 2014•0 citations
The parallel broadcast channel with confidential messages (BCC) is investigated, where a source node transmits to two receivers (receivers 1 and 2) over multiple independent subchannels. The source node has common information for both receivers, and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The secrecy capacity region of the parallel BCC is established. It is shown that independent input distribution for each subchannel is optimal. It is also shown that the secrecy capacity region of the parallel BCC can be larger than the sum of the secrecy capacity regions of the subchannels. The secrecy capacity region is further derived for the parallel BCC with degraded subchannels. Applications of these results to the fading BCC are also discussed.
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. This result is then specialized to give 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. Both the ergodic and outage performances are studied.
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.
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.
We consider a broadcast communication system over parallel sub-channels where the transmitter sends three messages: a common message to two users, and two confidential messages to each user which need to be kept secret from the other user. We assume partial channel state information at the transmitter (CSIT), stemming from noisy channel estimation. The first contribution of this paper is the characterization of the secrecy capacity region boundary as the solution of weighted sum-rate problems, with suitable weights. Partial CSIT is addressed by adding a margin to the estimated channel gains. The second paper contribution is the solution of this problem in an almost closed-form, where only two single real parameters must be optimized, e.g., through dichotomic searches. On the one hand, the considered problem generalizes existing literature where only two out of the three messages are transmitted. On the other hand, the solution finds also practical applications into the resource allocation of orthogonal frequency division multiplexing (OFDM) systems with both secrecy and fairness constraints.
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.
We consider a broadcast communication system over parallel sub-channels where the transmitter sends a common message to two users, and two confidential messages to each user which need to be kept secret from the other user. Assuming perfect channel state information at the transmitter, the characterization of the boundary for the secrecy capacity region turns into solving a power allocation optimization problem. We derive the power allocation algorithm reaching the boundary of the secrecy capacity region under an average total power constraint. Numerical simulations are presented in comparison to existing power allocation schemes, showing the merit of the proposed algorithm.