Related papers: Asymmetric numeral systems
Quantum key distribution protocols based on equiangular spherical codes are introduced and their behavior under the intercept/resend attack investigated. Such protocols offer a greater range of secure noise tolerance and speed options than…
Locating bugs is challenging but one of the most important activities in software development and maintenance phase because there are no certain rules to identify all types of bugs. Existing automatic bug localization tools use various…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
In 2002, Russell and Wang proposed a definition of entropically security that was developed within the framework of secret key cryptography. An entropically-secure system is unconditionally secure, that is, unbreakable, regardless of the…
Random number generation plays a vital role in cryptographic systems and computational applications, where uniformity, unpredictability, and robustness are essential. This paper presents the Entropy Mixing Network (EMN), a novel hybrid…
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
It is possible to interpret text as numbers (and vice versa) if one interpret letters and other characters as digits and assume that they have an inherent immutable ordering. This is demonstrated by the conventional digit set of the…
Multipath interference is an ubiquitous phenomenon in modern communication systems. The conventional way to compensate for this effect is to equalize the channel by estimating its impulse response by transmitting a set of training symbols.…
This paper considers rateless network error correction codes for reliable multicast in the presence of adversarial errors. Most existing network error correction codes are designed for a given network capacity and maximum number of errors…
The security of any cryptosystem relies on the secrecy of the system's secret keys. Yet, recent experimental work demonstrates that tens of thousands of devices on the Internet use RSA and DSA secrets drawn from a small pool of candidate…
In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if…
Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…
The container methods are powerful tools to bound the number of independent sets of graphs and hypergraphs, and they have been extremely influential in the area of extremal and probabilistic combinatorics. We will focus on more specialized…
Subword tokenization is a key part of many NLP pipelines. However, little is known about why some tokenizer and hyperparameter combinations lead to better downstream model performance than others. We propose that good tokenizers lead to…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…
In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions,…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…