This paper analyzes the maximal achievable rate for a given blocklength and error probability over multiple-antenna ambient backscatter channel. The result consists of finite channel coding achievability bound converse legacy system with alphabet constraints multiple-input-multiple-output based on Neyman-Pearson test, Berry-Esseen theorem, Mellin transform. Then, we derive closed-form expressio...

The inductive size bias coupling technique and Stein’s method yield a Berry-Esseen theorem for the number of urns having occupancy d ≥ 2 when n balls are uniformly distributed over m urns. In particular, there exists a constant C depending only on d such that sup z∈R |P (Wn,m ≤ z)− P (Z ≤ z)| ≤ C σn,m 1 + ( n m )3 for all n ≥ d and m ≥ 2, where Wn,m and σ 2 n,m are the standardized count and va...

We establish fundamental limits on estimation accuracy for the noisy 20 questions problem with measurement-dependent noise and introduce optimal non-adaptive procedures that achieve these limits. The minimal achievable resolution is defined as absolute difference between estimated true locations of a target over unit cube, given finite number queries constrained by excess-resolution probability...

Suppose that X1, . . . ,Xn are independent, identically-distributed random variables of mean zero and variance one. Assume that E|X1| ≤ δ4. We observe that there exist many choices of coefficients θ1, . . . , θn ∈ R with ∑ j θ 2 j = 1 for which sup α,β∈R α<β ∣∣∣∣∣ P  α ≤ n ∑ j=1 θjXj ≤ β   − 1 √ 2π ∫ β α e−t 2/2dt ∣∣∣∣∣ ≤ Cδ 4 n , (1) where C > 0 is a universal constant. Inequality (1) shou...

We propose an estimator for the singular vectors of high-dimensional low-rank matrices corrupted by additive subgaussian noise, where noise matrix is allowed to have dependence within rows and heteroskedasticity between them. prove finite-sample $\ell _{2,\infty }$ bounds a Berry-Esseen theorem individual entries estimator...

Let ${(g{n}){n\\geq 1}}$ be a sequence of independent and identically distributed (i.i.d.) ${d\\times d}$ real random matrices. For ${n\\geq 1}$ set ${G_n = g_n \\ldots g_1}$. Given any starting point ${x=\\mathbb R v\\in\\mathbb{P}^{d-1}}$, consider the Markov chain ${X_n^x \\mathbb G_n v }$ on projective space ${\\mathbb P^{d-1}}$ define norm cocycle by ${\\sigma(G_n, x)= \\log (|G_n v|/|v|)}...

as n → ∞. This is a deep extension of Hardy-Ramanujan Theorem (see [13]). In addition, the central limit theorem holds in a more general setting for additive functions. A formal treatment and proofs can be found in e.g. Durrett [7]. In terms of rate of convergence to the Gaussian distribution, i.e. Berry-Esseen bounds, Rényi and Turán [18] obtained the sharp rate of convergenceO(1/ √ log logn)....

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical ...

Preface The reliable transmission of information bearing signals over a noisy communication channel is at the heart of what we call communication. Information theory—founded by Claude E. Shannon in 1948—provides a mathematical framework for the theory of communication; it describes the fundamental limits to how efficiently one can encode information and still be able to recover it with negligib...