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arXiv:cs/0701024 · Allerton Conference on Communication, Control, and Computing

Secure Communication over Fading Channels

Yingbin Liang, H. Vincent Poor, Shamai, Shlomo

Published Jan 4, 2007• 69 citations
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Abstract

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.

DOI
10.48550/arxiv.cs/0701024

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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 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.
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 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 wire-tap channel is investigated, where the source-to-destination channel and the source-to-wire-tapper channel are corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information is assumed to be known at both the transmitter and the receiver. The parallel wire-tap channel with independent subchannels is first studied, which serves as an information-theoretic model for the fading wire-tap channel. The secrecy capacity of the parallel wire-tap channel is established. This result is then specialized to give the secrecy capacity of the fading wire-tap channel, which is achieved with the source node dynamically changing the power allocation according to the channel state realization. An optimal source power allocation is obtained to achieve the secrecy capacity.
In this work, we examine the secrecy capacity region of the block-fading broadcast channel with confidential messages (BCC) when the transmitter has limited knowledge of the channel. In particular, we consider a two-user communication system where the transmitter has one common message to be transmitted to both users and one confidential message intended to only one of them. The confidential message has to be kept secret from the other user to whom the information is not intended. The transmitter is not aware of the channel state information (CSI) of neither channel and is only provided by limited CSI feedback sent at the beginning of each fading block. Assuming an error-free feedback link, we characterize the secrecy capacity region of this channel and show that even with a 1-bit CSI feedback, a positive secrecy rate can still be achieved. Then, we look at the case where the feedback link is not error- free and is rather a binary erasure channel (BEC). In the latter case, we provide an achievable secrecy rate region and show that as long as the erasure event is not a probability 1 event, the transmitter can still transmit the confidential information with a positive secrecy rate.
We consider the fading broadcast channel from a secrecy point of view. In this channel, each user views the other user as an eavesdropper, and wants to keep its information as secret from the other user as possible. First, we consider a more general channel model which consists of L independent sub-channels, where in each sub-channel, one of the users' channel is less noisy with respect to the other user. Since the user which has the less noisy observation can be different in each sub-channel, the overall channel is not less noisy for any one of the users. We establish the secrecy capacity region of this channel for the case where the transmitter sends a common message to both users and an individual confidential message to each user. This channel model encompasses the sub-class of channels, where in each sub-channel, one of the users' observation is degraded with respect to the other user. The parallel Gaussian broadcast channel belongs to this sub-class. In the Gaussian case, we identify the optimum input distribution, which is Gaussian, and the optimum power allocation corresponding to each point on the boundary of the secrecy capacity region. Finally, noting that the fading Gaussian broadcast channel is equivalent to a parallel Gaussian broadcast channel from an ergodic capacity perspective, we explicitly evaluate the ergodic secrecy capacity region of the fading broadcast channel.