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The causal cognitive interference channel

Shraga I. Bross, Yossef Steinberg, Stephan Tinguely

Published Jan 1, 2010• 6 citations
Publisher

Abstract

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.

DOI
10.3929/ethz-a-006000764

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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.
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 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.
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.
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.
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.
In this paper, capacity limits are explored for the Cognitive Radio Channel (CRC) with confidential messages. As an idealized information theoretic model for the cognitive radio, this channel includes two transmitters which send independent messages to their corresponding receivers such that one transmitter, i.e., the cognitive transmitter, has access non-causally to the message of the other transmitter, i.e., the primary transmitter. The message designated to each receiver is required to be kept confidential with respect to the other receiver. The secrecy level for each message is evaluated using the equivocation rate. Novel inner and outer bounds for the capacity-equivocation region are established. It is shown that these bounds coincide for some special cases. Specifically, the capacity-equivocation region is derived for a class of less-noisy CRCs and also a class of semi-deterministic CRCs. For the case where only the message of the cognitive transmitter is required to be kept confidential, the capacity-equivocation region is also established for the Gaussian CRC with weak interference.