Related papers: The Asymptotic Generalized Poor-Verdu Bound Achiev…
A recent asymptotic expansion for the positive zeros $x=j_{\nu,m}$ ($m=1,2,3,\ldots$) of the Bessel function of the first kind $J_{\nu}(x)$ is studied, where the order $\nu$ is positive. Unlike previous well-known expansions in the…
We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing…
We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss $\ell$ can control the test error under all Moreau…
We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…
This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel.…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…
We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…
Feedback holds a pivotal role in practical communication schemes, even though it does not enhance channel capacity. Its main attribute includes adaptability in transmission that allows for a higher rate of convergence of the error…
Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the…
We study variable-length feedback (VLF) codes with noiseless feedback for discrete memoryless channels. We present a novel non-asymptotic bound, which analyzes the average error probability and average decoding time of our modified…
This paper shows that the probability that the error exponent of a given code randomly generated from a pairwise independent ensemble being smaller than a lower bound on the typical random-coding exponent tends to zero as the codeword…
In this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the Barnes $G$-function. Using these representations, we obtain explicit and numerically computable error…
We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
For a sequence of independent identically distributed random variables having a distribution function with an unknown parameter from a set $\Theta \subset \mathbf{R}^d$, we prove an analogue of the lower bound of Bahadur asymptotic…
We investigate the maximum coding rate for a given average blocklength and error probability over a K-user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback…
We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…