arXiv subjects

Amos Lapidoth

Publications and source records attributed to Amos Lapidoth.

63 records · Page 4Linked to original sources

arXiv2007

Sending a Bivariate Gaussian Source over a Gaussian MAC with Feedback

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.

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arXiv2006

Carbon Copying Onto Dirty Paper

A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multi-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we establish the capacity when there are two receivers. When there are many receivers, we show that the transmitter side information provides a vanishingly small benefit. When the interference is large and independent across the users, we show that time sharing is optimal. For the Gaussian case we present a coding scheme and establish its optimality in the high signal-to-interference-plus-noise limit when there are two receivers. When the interference is large and independent across users we show that time-sharing is again optimal. Connections to the problem of robust dirty paper coding are also discussed.

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arXiv2006

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 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.

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arXiv2006

Sending a Bi-Variate Gaussian Source over a Gaussian MAC

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.

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arXiv2006

On the Capacity of Fading MIMO Broadcast Channels with Imperfect Transmitter Side-Information

A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signal-to-noise (SNR) throughput is greatly reduced if, rather than knowing the fading realization \emph{precisely}, the trasmitter only knows the fading realization \emph{approximately}. The results are general and are not limited to memoryless Gaussian fading.

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arXiv2006

On the Low SNR Capacity of Peak-Limited Non-Coherent Fading Channels with Memory

The capacity of non-coherent stationary Gaussian fading channels with memory under a peak-power constraint is studied in the asymptotic weak-signal regime. It is assumed that the fading law is known to both transmitter and receiver but that neither is cognizant of the fading realization. A connection is demonstrated between the asymptotic behavior of channel capacity in this regime and the asymptotic behavior of the prediction error incurred in predicting the fading process from very noisy observations of its past. This connection can be viewed as the low signal-to-noise ratio (SNR) analog of recent results by Lapidoth & Moser and by Lapidoth demonstrating connections between the high SNR capacity growth and the noiseless or almost-noiseless prediction error. We distinguish between two families of fading laws: the ``slowly forgetting'' and the ``quickly forgetting''. For channels in the former category the low SNR capacity is achieved by IID inputs, whereas in the latter such inputs are typically sub-optimal. Instead, the asymptotic capacity can be approached by inputs with IID phase but block-constant magnitude.

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arXiv2005

Monotonicity Results for Coherent MIMO Rician Channels

The dependence of the Gaussian input information rate on the line-of-sight (LOS) matrix in multiple-input multiple-output coherent Rician fading channels is explored. It is proved that the outage probability and the mutual information induced by a multivariate circularly symmetric Gaussian input with any covariance matrix are monotonic in the LOS matrix D, or more precisely, monotonic in D'D in the sense of the Loewner partial order. Conversely, it is also demonstrated that this ordering on the LOS matrices is a necessary condition for the uniform monotonicity over all input covariance matrices. This result is subsequently applied to prove the monotonicity of the isotropic Gaussian input information rate and channel capacity in the singular values of the LOS matrix. Extensions to multiple-access channels are also discussed.

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arXiv2005

Duality Bounds on the Cut-Off Rate with Applications to Ricean Fading

We propose a technique to derive upper bounds on Gallager's cost-constrained random coding exponent function. Applying this technique to the non-coherent peak-power or average-power limited discrete time memoryless Ricean fading channel, we obtain the high signal-to-noise ratio (SNR) expansion of this channel's cut-off rate. At high SNR the gap between channel capacity and the cut-off rate approaches a finite limit. This limit is approximately 0.26 nats per channel-use for zero specular component (Rayleigh) fading and approaches 0.39 nats per channel-use for very large specular components. We also compute the asymptotic cut-off rate of a Rayleigh fading channel when the receiver has access to some partial side information concerning the fading. It is demonstrated that the cut-off rate does not utilize the side information as efficiently as capacity, and that the high SNR gap between the two increases to infinity as the imperfect side information becomes more and more precise.

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arXiv2004

On the High-SNR Capacity of Non-Coherent Networks

We obtain the first term in the high signal-to-noise ratio (SNR) expansion of the capacity of fading networks where the transmitters and receivers--while fully cognizant of the fading \emph{law}--have no access to the fading \emph{realization}. This term is an integer multiple of $\log \log \textnormal{SNR}$ with the coefficient having a simple combinatorial characterization.

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