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IEEE Conference on Communications and Network Security

Gaussian fading channel with secrecy outside a bounded range

Shaofeng Zou, Yingbin Liang, Shlomo Shitz Shamai

Published Oct 1, 2017• 1 citation
Publisher

Abstract

The Gaussian fading channel is studied, in which the channel from the transmitter to the receiver is corrupted by a multiplicative fading coefficient H and an additive Gaussian random noise. It is assumed that the channel is experiencing block fading, and the transmitter does not know the channel state information (CSI). The receiver is assumed to have full knowledge of the CSI. If the channel state is better, then more information is required to be decoded by the receiver, and if the channel state is worse, more information is required to be secure from the receiver. Furthermore, the information intended to be decoded by the receiver with a better state (e.g., |H| ≥ |h0|) is required to be secure from the receiver if it has a state worse than |h0| by Δ (i.e., |H| ≤ |h0| — Δ), which is referred to as secrecy outside a bounded range. A (layered) broadcast approach is studied for this problem, which views the fading channel as a degraded broadcast channel with a number of receivers each experiencing a different fading coefficient. The achievable scheme designates one superposition layer to each message with binning employed to protect all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can be shared with its upper-layer messages to enlarge the rate region. The achievable secrecy rate region via the broadcast approach is characterized. The developed scheme can adapt the transmission rate to the actual unknown channel state without exploiting the CSI at the transmitter.

DOI
10.1109/cns.2017.8228688

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The Gaussian fading channel is studied, in which the channel from the transmitter to the receiver is corrupted by a multiplicative fading coefficient H and an additive Gaussian random noise. It is assumed that the channel is experiencing block fading, and the transmitter does not know the channel state information (CSI). The receiver is assumed to have full knowledge of the CSI. If the channel state is better, then more information is required to be decoded by the receiver, and if the channel state is worse, more information is required to be secure from the receiver. Furthermore, the information intended to be decoded by the receiver with a better state (e.g., |H| ≥ |h0|) is required to be secure from the receiver if it has a state worse than |h0| by Δ (i.e., |H| ≤ |h0| — Δ), which is referred to as secrecy outside a bounded range. A (layered) broadcast approach is studied for this problem, which views the fading channel as a degraded broadcast channel with a number of receivers each experiencing a different fading coefficient. The achievable scheme designates one superposition layer to each message with binning employed to protect all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can be shared with its upper-layer messages to enlarge the rate region. The achievable secrecy rate region via the broadcast approach is characterized. The developed scheme can adapt the transmission rate to the actual unknown channel state without exploiting the CSI at the transmitter.
A K-receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends K messages respectively to K receivers, and the channel quality gradually degrades from receiver K to receiver 1. Each receiver k is required to decode messages W1, …, Wk, for 1 ≤ k ≤ K. Furthermore, each message Wkshould be kept secure from receivers with two-level worse channel quality, i.e., receivers 1, …, k − 2. The secrecy capacity region is fully characterized. The achievable scheme designates one superposition layer to each message with random binning employed for each layer for protecting all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can potentially be shared with its immediate upper-layer message to enlarge the rate region. More importantly, an induction approach is developed to perform Fourier-Motzkin elimination over 2K variables among Θ(K2) bounds to obtain a close-form achievable rate region. A converse proof is developed that matches the achievable rate region, which involves recursive construction of the rate bounds.
A three-receiver degraded broadcast channel with secrecy outside of a bounded range is studied, in which the channel quality gradually degrades from receiver 3 to receiver 1. The transmitter has three messages intended for the receivers with receiver 3 decoding all messages, receiver 2 decoding the first two messages, and receiver 1 decoding only the first message. Furthermore, the third message should be kept secure from receiver 1. The discrete memoryless channel is studied and the secrecy capacity region is characterized. The achievable scheme is based on superposition coding and random binning, in which one superposition layer and random binning together provide secrecy. The converse proof is derived based on the insight obtained from the achievable scheme so that manipulations of terms yield tight rate bounds.
A four-receiver degraded broadcast channel with secrecy outside a bounded range is studied, over which a transmitter sends four messages to four receivers. In the model considered, the channel quality gradually degrades from receiver 4 to receiver 1, and receiver k is required to decode the first k messages for k = 1, …, 4. Furthermore, message 3 is required to be secured from receiver 1, and message 4 is required to be secured from receivers 1 and 2. The secrecy capacity region is established. The achievable scheme includes not only superposition, binning and embedded coding used in previous studies, but also rate splitting and sharing particularly designed for this model, which is shown to be critical to further enlarge the achievable region and enable the development of the converse proof.
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.