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IEEE Convention of Electrical and Electronics Engineers in Israel

The noisy feedback interference channel with secrecy

Shraga I. Bross, Yossef Steinberg, Stephan Tinguely

Published Nov 1, 2010• 0 citations
Publisher

Abstract

We study the interference channel with one-sided generalized feedback and secrecy requirements. In our model Message 1 which is known just to Encoder 1 should be decoded by both receivers. Message 2 - known only to Encoder 2 - should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an achievable rate-equivocation region for this model and an outer bound for the “noisy cribbing” regime that coincides with the inner bound the gap being in the Markov conditions satisfied by one of the auxiliary random variables.

DOI
10.1109/eeei.2010.5662125

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We study the interference channel with one-sided generalized feedback and secrecy requirements. In our model Message 1 which is known just to Encoder 1 should be decoded by both receivers. Message 2 - known only to Encoder 2 - should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an achievable rate-equivocation region for this model and an outer bound for the “noisy cribbing” regime that coincides with the inner bound the gap being in the Markov conditions satisfied by one of the auxiliary random variables.
We study the interference channel with one-sided generalized feedback and secrecy requirements. In our model, Message 1 that is known just to Encoder 1 should be decoded by both receivers. Message 2—known only to Encoder 2—should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an achievable rate-equivocation region for this model and an outer bound for the “noisy cribbing” regime without secrecy, the gap being the Markov conditions satisfied by one of the auxiliary random variables. Furthermore, we consider a simplified causal cognitive interference model: the interference channel with a cribbing encoder. We derive an inner bound on the rate region for this model and prove that when the interference channel is degraded conditionally on the input of Encoder 1, our inner bound is tight.
We study the interference channel with one-sided generalized feedback and secrecy requirement. In our model Message 1 that is known just to Encoder 1 should be decoded by both receivers. Message 2-known only to Encoder 2-should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an outer bound on the capacity-equivocation region for this model that is valid for the ”noisy cribbing” regime. The gap between this upper bound and the inner bound reported before is just in the Markov conditions satisfied by one of the auxiliary random variables. Furthermore, we consider a simplified causal cognitive interference model: the interference channel with a cribbing encoder. We show that when, conditioned on the input of Encoder 1, the interference channel is degraded our outer bound is tight thereby establishing the capacity-equivocation region for this case.
The (non-causal) cognitive interference channel, studied recently by Liang et. al., is a model for a classical two-user discrete memoryless interference channel, over which two transmitters send a pair of independent messages. It is assumed that the first message is shared by both encoders, whereas the second message is known only to Encoder 2-the cognitive transmitter. Receiver 2 needs to decode both messages, and Receiver 1 should decode only the first message while Message 2 should be kept as secret as possible from Receiver 1. The level of secrecy is measured by the equivocation rate. For this model the capacity-equivocation region has been derived by Liang et. al. In this work we dispense of the assumption that Message 1 is shared a-priori by both encoders. Instead, we study the case in which Encoder 2 observes causally a feedback output of the channel and derive an achievable rate-equivocation region for this model. For a simplified model in which Encoder 2 cribs causally from Encoder 1 we establish the capacity-equivocation region for a degraded interference channel.
The (non-causal) cognitive interference channel, studied recently by Liang et.al., is a model for a classical twouser discrete memoryless interference channel, over which two transmitters send a pair of independent messages.It is assumed that the first message is shared by both encoders, whereas the second message in known only to Encoder 2 -the cognitive transmitter.Receiver 2 needs to decode both messages, and Receiver 1 should decode only the first message while Message 2 should be kept as secret as possible from Receiver 1.The level of secrecy is measured by the equivocation rate.For this model the capacity-equivocation region has been derived by Liang et.al..In this work we dispense of the assumption that Message 1 is shared a-priori by both encoders.Instead, we study the case in which Encoder 2 cribs causally from Encoder 1.We derive an achievable rate-equivocation region for this model and establish the capacity-equivocation region for a degraded interference channel.
Like the conventional two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at two receivers. It is assumed that there is a common message (message 1) known to both transmitters, and an additional independent message (message 2) known only to the cognitive transmitter (transmitter 2). The cognitive receiver (receiver 2) needs to decode messages 1 and 2, while the non cognitive receiver (receiver 1) should decode only message 1. Furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. The level of secrecy is measured by the equivocation rate. In this paper, a single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is obtained. The capacity-equivocation region for the Gaussian cognitive interference channel is also obtained explicitly. Moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, the capacity region for the two-user cognitive interference channel is obtained, by providing a converse theorem.
The cognitive interference channel with confidential messages is studied. Similarly to the classical two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at the two receivers. It is assumed that there is a common message source (message 1) known to both transmitters, and an additional independent message source (message 2) known only to the cognitive transmitter (transmitter 2). The cognitive receiver (receiver 2) needs to decode both messages, while the non-cognitive receiver (receiver 1) should decode only the common message. Furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. The level of secrecy is measured by the equivocation rate. A single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is established and is further explicitly derived for the Gaussian case. Moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, establishes a new capacity theorem for a class of interference channels, by providing a converse theorem.