相关论文: Common Randomness Generation from Sources with Cou…

The nonlocal behavior of quantum mechanics can be used to generate guaranteed fresh randomness from an untrusted device that consists of two nonsignalling components; since the generation process requires some initial fresh randomness to…

A subset of a group invariably generates the group if it generates even when we replace the elements by any of their conjugates. In a 2016 paper, Pemantle, Peres and Rivin show that the probability that four randomly selected elements…

The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav & Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are…

This paper discusses and analyzes various models of binary correlated sources, which may be relevant in several distributed communication scenarios. These models are statistically characterized in terms of joint Probability Mass Function…

The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We solve the problem for three particular channels. Our…

The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…

The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits…

Shannon's theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly, and in the presence of various resources that are all classes of non-signalling correlations:…

We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission…

Let $ X_1, \ldots, X_n $ be independent random variables taking values in the alphabet $ \{0, 1, \ldots, r\} $, and $ S_n = \sum_{i = 1}^n X_i $. The Shepp--Olkin theorem states that, in the binary case ($ r = 1 $), the Shannon entropy of $…

This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit…

We define the common randomness assisted capacity of an arbitrarily varying channel (AVWC) when the Eavesdropper is kept ignorant about the common randomness. We prove a multi-letter capacity formula for this model. We prove that, if enough…

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

Shannon entropy is not the only entropy that is relevant to machine-learning datasets, nor possibly even the most important one. Traditional entropies such as Shannon entropy capture information represented by elements' frequencies but not…

We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of…

We investigate the problem of common randomness (CR) generation from discrete correlated sources aided by one-way communication over single-user multiple-input multiple-output (MIMO) slow fading channels with additive white Gaussian noise…

This paper introduces and studies a new uncertainty measure, the cumulative residual interval entropy (CRIE). Defined as the cumulative residual entropy of a doubly truncated (interval) continuous random variable, this measure has several…

We study common randomness generation problems where $n$ players aim to generate same sequences of random coin flips where some subsets of the players share an independent common coin which can be tossed multiple times, and there is a…

We ask whether demographic identity, signaled by a name alone, systematically reshapes the generative distribution of a language model. Measuring full-vocabulary Shannon entropy at temperature zero across six open-weight base models and…