Related papers: Generalized Forms of the Kraft Inequality for Fini…
In this short paper, we shall provide a dynamical systems' proof of the famous Kraft-McMillan inequality and its converse. Kraft-McMillan inequality is a basic result in information theory which gives a necessary and sufficient condition…
We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless…
The Ingleton inequality is a classical linear information inequality that holds for representable matroids but fails to be universally valid for entropic vectors. Understanding the extent to which this inequality can be violated has been a…
We derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well known Shannon lower bound in a variety of instances of rate-distortion…
Previous work by the authors on parity-preserving fixed-length constrained encoders is extended to the variable-length case. Parity-preserving variable-length encoders are formally defined, and, to this end, Kraft conditions are developed…
We introduce a refinement to the convex split lemma by replacing the max mutual information with the collision mutual information, transforming the inequality into an equality. This refinement yields tighter achievability bounds for quantum…
In this paper we consider the use of variable length non prefix-free codes for coding constrained sequences of symbols. We suppose to have a Markov source where some state transitions are impossible, i.e. the stochastic matrix associated…
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the…
We investigate the problem of estimating simultaneously multiple parameters encoded in the shape of the modes on which the light is expanded. For this, we generalize the mode-encoded parameter estimation theory as introduced in Ref.[1] to a…
A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential,…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
We establish a new spectral inequality for the quantified estimation of the $H^s$-norm, $s\ge 0$ of a finite linear combination of eigenfunctions in a domain in terms of its $H^s$-norm in a strictly open subset of the whole domain. The…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…
The notion of weighted quantum entropy is reviewed and considered for bipartite and noncomposite quantum systems. The known for the weighted entropy information inequality (subadditivity condition) is extended to the case of indivisible…
In this paper, we present a generalized Bell inequality for mixed states. The distinct characteristic is that the inequality has variable bound depending on the decomposition of the density matrix. The inequality has been shown to be more…
Quantum optics bridges esoteric notions of entanglement and superposition with practical applications like metrology and communication. Throughout, there is an interplay between information theoretic concepts such as entropy and physical…
A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with…
Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to…
We study the following semi-deterministic setting of the joint source-channel coding problem: a deterministic source sequence (a.k.a. individual sequence) is transmitted via a memoryless channel, using delay-limited encoder and decoder,…