Related papers: Communication Requirements for Generating Correlat…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
The generalization of Shannon's theory to include messages with given autocorrelations is presented. The analytical calculation of the channel capacity is based on the transfer matrix method of the effective 1D Hamiltonian. This bridge…
A notion of directed information between two continuous-time processes is proposed. A key component in the definition is taking an infimum over all possible partitions of the time interval, which plays a role no less significant than the…
We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…
Common randomness (CR), as a resource, is not commonly exploited in existing practical communication systems. In the CR generation framework, both the sender and receiver aim to generate a common random variable observable to both, ideally…
In the problem of channel resolvability, where a given output probability distribution via a channel is approximated by transforming the uniform random numbers, characterizing the asymptotically minimum rate of the size of the random…
Optimal transport has numerous applications, particularly in machine learning tasks involving generative models. In practice, the transportation process often encounters an information bottleneck, typically arising from the conversion of a…
Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on…
We explore the duality between the simulation and extraction of secret correlations in light of a similar well-known operational duality between the two notions of common information due to Wyner, and G\'acs and K\"orner. For the inverse…
We derive sequential necessary and sufficient conditions for any channel input conditional distribution ${\cal P}_{0,n}\triangleq\{P_{X_t|X^{t-1},Y^{t-1}}:~t=0,\ldots,n\}$ to maximize the finite-time horizon directed information defined by…
Given two channels that convey information about the same random variable, we introduce two measures of the unique information of one channel with respect to the other. The two quantities are based on the notion of generalized weighted Le…
In this paper we provide an achievable rate region for the discrete memoryless multiple access channel with correlated state information known non-causally at the encoders using a random binning technique. This result is a generalization of…
One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
We study and solve the problem of classical channel simulation with quantum side information at the receiver. This is a generalization of both the classical reverse Shannon theorem, and the classical-quantum Slepian-Wolf problem. The…
The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The…
We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount…
A dealer aims to share a secret with participants so that only predefined subsets can reconstruct it, while others learn nothing. The dealer and participants access correlated randomness and communicate over a one-way, public, rate-limited…
Using the concept of discrete noiseless channels, it was shown by Shannon in A Mathematical Theory of Communication that the ultimate performance of an encoder for a constrained system is limited by the combinatorial capacity of the system…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…