Related papers: Improved Condensers for Chor-Goldreich Sources
In this paper we give improved constructions of several central objects in the literature of randomness extraction and tamper-resilient cryptography. Our main results are: (1) An explicit seeded non-malleable extractor with error $\epsilon$…
We derive a lower bound on the differential entropy of a log-concave random variable $X$ in terms of the $p$-th absolute moment of $X$. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds…
We introduce two variants of the information spectrum relative entropy defined by Tomamichel and Hayashi which have the particular advantage of satisfying the data-processing inequality, i.e. monotonicity under quantum operations. This…
Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as device independent randomness amplification and expansion. Furthermore they are also a useful tool in quantum Shannon…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
Estimating the support size of a distribution is a well-studied problem in statistics. Motivated by the fact that this problem is highly non-robust (as small perturbations in the distributions can drastically affect the support size) and…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
This paper investigates the existence of minimal $p$-encoders for convolutional codes over $\mathbb{Z}_{p^r}$, where $p$ is a prime. This addresses a conjecture from \cite{k}, which posits that every such code admits a minimal $p$-encoder,…
This paper provides an extensive study of the behavior of the best achievable rate (and other related fundamental limits) in variable-length lossless compression. In the non-asymptotic regime, the fundamental limits of fixed-to-variable…
Conformal risk control (CRC) provides distribution-free guarantees for controlling the expected loss at a user-specified level. Existing theory typically assumes that the loss decreases monotonically with a tuning parameter that governs the…
In this paper, source coding or data compression is viewed as a measurement problem. Given a measurement device with fewer states than the observable of a stochastic source, how can one capture the essential information? We propose modeling…
This paper considers the joint compression of a pair of correlated sources, where the encoder is allowed to access only one of the sources. The objective is to recover both sources under separate distortion constraints for each source while…
Decoy-state QKD with phase-randomized weak coherent pulses is typically analyzed assuming independent, precisely prepared intensities. Real sources, however, can exhibit correlated intensity drift across rounds, potentially leaking…
In this paper, we revisit the sequential source coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our…
For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N>>1 spins with the remainder is logarithmic in N with a prefactor fixed by the central charge of the associated conformal field theory. We…
For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…
A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{Z}_p \setminus \{0\}$ can be ordered so that all partial sums are distinct. Although this conjecture was recently proved for sufficiently large primes by Pham and…
In terms of the Dirac representation of sample mean and the weak convergence of empirical distributions that holds almost surely, we construct a new proof for a strong law of large numbers of Kolmogorov's type with i.i.d. random variables…
Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…