相关论文: Entropy of a bit-shift channel
A surrogate data analysis is presented, which is based on the fluctuations of the ``entropy'' $S$ defined in the natural time-domain [Phys. Rev. E {\bf 68}, 031106, 2003]. This entropy is not a static one as, for example, the Shannon…
A mathematical interpretation of the usual definition of entropy (for a discrete probability distribution or a trace 1 positive operator) is given. This formulation makes some properties of entropy immediate.
The indirect source-coding problem in which a Bernoulli process is compressed in a lossy manner from its noisy observations is considered. These noisy observations are obtained by passing the source sequence through a The indirect…
The exponential growth of data transmission and processing speeds in modern digital infrastructure requires entropy sources capable of producing large volumes of true randomness for information security. Chaotic emissions from semiconductor…
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of…
In this paper we analyse and improve integer discrete flows for lossless compression. Integer discrete flows are a recently proposed class of models that learn invertible transformations for integer-valued random variables. Their discrete…
Spiking activity from populations of neurons display causal interactions and memory effects. Therefore, they are expected to show some degree of irreversibility in time. Motivated by the spike train statistics, in this paper we build a…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\rho$-th moment of the number of performed…
By defining information entropy in terms of probabilities densities $|\Psi|^2$ ($\Psi$ is a wave function in the coordinate representation) it is explicitly shown how a loss of quantum information occurs in a transition from a quantum to a…
We propose an operational definition of the entropy of cosmological perturbations based on a truncation of the hierarchy of Green functions. The value of the entropy is unambiguous despite gauge invariance and the renormalization procedure.…
We consider the task of deriving a key with high HILL entropy from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was $\eps$ indistinguishable from having min-entropy was via…
A word-valued source $\mathbf{Y} = Y_1,Y_2,...$ is discrete random process that is formed by sequentially encoding the symbols of a random process $\mathbf{X} = X_1,X_2,...$ with codewords from a codebook $\mathscr{C}$. These processes…
We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change…
Large alphabet source coding is a basic and well-studied problem in data compression. It has many applications such as compression of natural language text, speech and images. The classic perception of most commonly used methods is that a…
Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the…
Our understanding of information in systems has been based on the foundation of memoryless processes. Extensions to stable Markov and auto-regressive processes are classical. Berger proved a source coding theorem for the marginally unstable…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based…
The notion of a 1-vertex transfer matrix for multi-dimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex…