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.

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.

We study the transmission of a memoryless bivariate Gaussian source over an average-power-constrained one-to-two Gaussian broadcast channel. The transmitter observes the source and describes it to the two receivers by means of an average-power-constrained signal. Each receiver observes the transmitted signal corrupted by a different additive white Gaussian noise and wishes to estimate the source component intended for it: Receiver 1 wishes to estimate the first source component and Receiver 2 wishes to estimate the second. Our interest is in the pairs of expected squared-error distortions that are simultaneously achievable at the two receivers. We prove that an uncoded transmission scheme that sends a linear combination of the source components achieves the optimal power-versus-distortion trade-off whenever the signal-to-noise ratio is below a certain threshold. The threshold is a function of the source correlation and the distortion at the receiver with the weaker noise.

We study the power-versus-distortion tradeoff for the transmission of a memoryless bivariate Gaussian source over a two-to-one Gaussian multiple-access channel with perfect causal feedback. In this problem, each of two separate transmitters observes a different component of a memoryless bivariate Gaussian source as well as the feedback from the channel output of the previous time-instants. Based on the observed source sequence and the feedback, each transmitter then describes its source component to the common receiver via an average-power constrained Gaussian multiple-access channel. From the resulting channel output, the receiver wishes to reconstruct each source component with the least possible expected squared-error distortion. We study the set of distortion pairs that can be achieved by the receiver on the two source components. We present sufficient conditions and necessary conditions for the achievability of a distortion pair. These conditions are expressed in terms of the source correlation and of the signal-to-noise ratio (SNR) of the channel. In several cases the necessary conditions and sufficient conditions are shown to agree. In particular, we show that if the channel SNR is below a certain threshold, then an uncoded transmission scheme that ignores the feedback is optimal. Thus, below this SNR-threshold, feedback is useless. We also derive the optimal high-SNR asymptotics.

We study the power-versus-distortion tradeoff for the distributed transmission of a memoryless bivariate Gaussian source over a two-to-one average-power limited Gaussian multiple-access channel. In this problem, each of two separate transmitters observes a different component of a memoryless bivariate Gaussian source. The two transmitters then describe their source component to a common receiver via an average-power constrained Gaussian multiple-access channel. From the output of the multiple-access channel, the receiver wishes to reconstruct each source component with the least possible expected squared-error distortion. Our interest is in characterizing the distortion pairs that are simultaneously achievable on the two source components. We focus on the ¿equal bandwidth¿ case, where the source rate in source-symbols per second is equal to the channel rate in channel-uses per second. We present sufficient conditions and necessary conditions for the achievability of a distortion pair. These conditions are expressed as a function of the channel signal-to-noise ratio (SNR) and of the source correlation. In several cases, the necessary conditions and sufficient conditions are shown to agree. In particular, we show that if the channel SNR is below a certain threshold, then an uncoded transmission scheme is optimal. Moreover, we introduce a ¿source-channel vector-quantizer¿ scheme which is asymptotically optimal as the SNR tends to infinity.

We consider a one-to-two Gaussian broadcasting problem where the transmitter observes a memoryless bi-variate Gaussian source and each receiver wishes to estimate one of the source components. The transmitter describes the source pair by means of an average-power-constrained signal and each receiver observes this signal corrupted by a different additive white Gaussian noise. From its respective observation, Receiver 1 wishes to estimate the first source component and Receiver 2 wishes to estimate the second. We seek to characterize the pairs of expected squared-error distortions that are simultaneously achievable at the two receivers. Our result is that below a certain SNR-threshold an ldquouncoded schemerdquo that sends a linear combination of the source components is optimal. We present a lower bound on this threshold in terms of the source correlation and the distortion at the receiver with weaker channel noise.

We consider the problem of transmitting a bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with feedback. Each of the transmitters observes one of the source components and tries to describe it to the common receiver. We are interested in the minimal mean squared error at which the receiver can reconstruct each of the source components. In the "symmetric case" we show that, below a certain signal-to-noise ratio threshold which is determined by the source correlation, feedback is useless and the minimal distortion is achieved by uncoded transmission. For the general case we give necessary conditions for the achievability of a distortion pair.

We propose to send a Gaussian source over an average-power limited additive white Gaussian noise channel by transmitting a linear combination of the source sequence and the result of its quantization using a high dimensional Gaussian vector quantizer. We show that, irrespective of the rate of the vector quantizer (assumed to be fixed and smaller than the channel's capacity), this transmission scheme is asymptotically optimal (as the quantizer's dimension tends to infinity) under the mean squared-error fidelity criterion. This generalizes the classical result of Goblick about the optimality of scaled uncoded transmission, which corresponds to choosing the rate of the vector quantizer as zero, and the classical source-channel separation approach, which corresponds to choosing the rate of the vector quantizer arbitrarily close to the capacity of the channel

We consider a problem where a memoryless bi-variate Gaussian source is to be transmitted over an additive white Gaussian multiple-access channel with two transmitting terminals and one receiving terminal. The first transmitter only sees the first source component and the second transmitter only sees the second source component. We are interested in the pair of mean squared-error distortions at which the receiving terminal can reproduce each of the source components. It is demonstrated that in the symmetric case, below a certain signal-to-noise ratio (SNR) threshold, which is determined by the source correlation, uncoded communication is optimal. For SNRs above this threshold we present outer and inner bounds on the achievable distortions