Related papers: Sharp moment-entropy inequalities and capacity bou…
We study the amplitude-constrained additive white Gaussian noise channel. It is well known that the capacity-achieving input distribution for this channel is discrete and supported on finitely many points. The best known bounds show that…
One of the basic tenets in information theory, the data processing inequality states that output divergence does not exceed the input divergence for any channel. For channels without input constraints, various estimates on the amount of…
Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space.…
We consider the problem of reliable communication over multiple-access channels (MAC) where the channel is driven by an independent and identically distributed state process and the encoders and the decoder are provided with various degrees…
In some applications, the variance of additive measurement noise depends on the signal that we aim to measure. For instance, additive Gaussian signal-dependent noise (AGSDN) channel models are used in molecular and optical communication.…
We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for…
We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 years to determine the capacities of…
Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume $M_\avg^*(n,\epsilon)$ of length-$n$ codes subject to an average decoding error…
This paper studies the relaying strategies and the approximate capacity of the classic three-node Gaussian relay channel, but where the noises at the relay and at the destination are correlated. It is shown that the capacity of such a relay…
The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented.…
We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the…
We investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown…
We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…
The data-processing inequality ensures quantum channels reduce state distinguishability, with contraction coefficients quantifying optimal bounds. However, these can be overly optimistic and not representative of the usual behavior. We…
We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error correction, through the lens of distributional robustness. We assume that the distribution of the source or of the additive…
The first terms of the low-signal-energy asymptotics for the mutual information in the discrete-time Poisson channel are derived and compared to an asymptotic expression of the capacity. In the presence of non-zero additive noise (either…
Consider a binary additive noise channel with noiseless feedback. When the noise is a stationary and ergodic process $\mathbf{Z}$, the capacity is $1-\mathbb{H}(\mathbf{Z})$ ($\mathbb{H}(\cdot)$ denoting the entropy rate). It is shown…
We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…
We investigate the role of convexity in R\'enyi entropy power inequalities. After proving that a general R\'enyi entropy power inequality in the style of Bobkov-Chistyakov (2015) fails when the R\'enyi parameter $r\in(0,1)$, we show that…
This paper studies the high-power capacity scaling of additive noise channels whose noise arises from the first-hitting location of a multidimensional drift-diffusion process on an absorbing hyperplane. By identifying the underlying…