Shraga I. Bross

The Gaussian MAC with conferencing encoders

We derive the capacity region of the Gaussian version of Willemspsilas two-user MAC with conferencing encoders. This setting differs from the classical MAC in that, prior to each transmission block, the two transmitters can communicate with each other over noise-free bit-pipes of given capacities. The derivation requires a new technique for proving the optimality of Gaussian input distributions in certain mutual information maximizations under a Markov constraint. We also consider a Costa-type extension of the Gaussian MAC with conferencing encoders. In this extension, the channel can be described as a two-user MAC with Gaussian noise and Gaussian interference where the interference is known non-causally to the encoders but not to the decoder. We show that as in Costas setting the interference sequence can be perfectly canceled, i.e., that the capacity region without interference can be achieved.

Superimposed Coded and Uncoded Transmissions of a Gaussian Source over the Gaussian Channel

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 channels capacity), this transmission scheme is asymptotically optimal (as the quantizers 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

Broadcasting Correlated Gaussians

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.

An improved achievable region for the discrete memoryless two-user multiple-access channel with noiseless feedback

An achievable region for the two-user discrete memoryless multiple-access channel (DMMAC) with noiseless feedback is proposed. The proposed region includes the Cover-Leung region, with the inclusion being, for some channels, strict. This inner bound is demonstrated for the ideal two-user Poisson multiple-access channel with noiseless feedback, in which case it is shown to improve on the Cover-Leung rate-sum.

Achievable Rates for the Discrete Memoryless Relay Channel With Partial Feedback Configurations

Achievable rates over the discrete memoryless relay channel with partial feedback configurations are proposed. Specifically, we consider partial feedback from the receiver to the sender as well as partial feedback from the relay to the sender. These achievable rates are calculated for the general Gaussian and the Z relay channels and are shown to improve on the known one-way achievable rates

The state-dependent multiple-access channel with states available at a cribbing encoder

The two-user discrete memoryless state-dependent multiple-access channel (MAC) models a scenario in which two encoders transmit independent messages to a single receiver via a MAC whose channel law is governed by an i.i.d. state random variable. In the cooperative state-dependent MAC model it is further assumed that Message 1 is shared by both encoders whereas Message 2 is known only to Encoder 2 — the cognitive transmitter. The capacity of the cooperative state-dependent MAC where the realization of the state sequence is known non-causally to the cognitive encoder was derived by Somekh-Baruch et. al. In this work we dispense with the assumption that Message 1 is shared by both encoders. Instead, we study the case in which Encoder 2 cribs causally from Encoder 1. We determine the capacity region for the case where the cribbing is strictly causal.

Broadcasting correlated Gaussians

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.

On the Relay Channel With Receiver–Transmitter Feedback

An achievable rate for the discrete memoryless relay channel with receiver-transmitter feedback is proposed based on block-Markov superposition encoding. The achievable rate can also be extended to Gaussian channels. A second achievable rate for the Gaussian relay channel based on a Schalkwijk-Kailath type scheme is presented. For some channels both achievable rates strictly improve upon all previously known achievable rates. For the discrete memoryless relay channel also a converse result is provided.

The Poisson channel with side information

The continuous-time, peak-limited, infinite-bandwidth Poisson channel with spurious counts is considered. It is shown that if the times at which the spurious counts occur are known noncausally to the transmitter but not to the receiver, then the capacity is equal to that of the Poisson channel with no spurious counts. Knowing the times at which the spurious counts occur only causally at the transmitter does not increase capacity.

Dirty-Paper Coding for the Gaussian Multiaccess Channel With Conferencing

We derive the capacity region of the two-user dirty-paper Gaussian multiaccess channel (MAC) with conferencing encoders. In this MAC, prior to each transmission block, the transmitters can hold a conference in which they can communicate with each other over error-free bit pipes of given capacities. The received signal suffers not only from additive Gaussian noise but also from additive interference, which is known noncausally to the transmitters but not to the receiver. The additive interference is modeled as Gaussian or uniform over a sphere. We show that the interference can be perfectly mitigated, i.e., that the capacity region without interference can also be achieved in its presence. This holds irrespective of whether the transmitters learn the interference before or after the conference. It follows as a corollary that also for the MAC with degraded message sets, the interference can be perfectly mitigated if it is known noncausally to the transmitters. To derive our results, we generalize Costas single-user writing-on-dirty-paper achievability result to channels with dependent interference and not-necessarily Gaussian noise.