Related papers: Thresholds of Random Quasi-Abelian Codes
The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We…
We study the problem of transmission of information over classical and classical-quantum channels in the one-shot regime where the underlying codes are constrained to be group codes. In the achievability part, we introduce a new input…
Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However,…
We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solve the problem for Cartesian powers of arbitrary graphs. In detail, let $G$ be a connected graph on $k$…
In this paper we give an explicit bound on the distance to chisquare for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge this is the first explicit…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the…
Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
In this paper we examine isotropic Gaussian random fields defined on $\mathbb R^N$ satisfying certain conditions. Specifically, we investigate the type of a critical point situated within a small vicinity of another critical point, with…
While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…
It is well known that a random q-ary code of rate \Omega(\epsilon^2) is list decodable up to radius (1 - 1/q - \epsilon) with list sizes on the order of 1/\epsilon^2, with probability 1 - o(1). However, until recently, a similar statement…
Assume that $p > 1$ and $p - 1 \le \alpha \le p$ are real numbers and $\Omega$ is a non-empty open subset of ${\mathbb R}^n$, $n \ge 2$. We consider the inequality $$ {\rm div} \, A (x, D u) + b (x) |D u|^\alpha \ge 0, $$ where $D =…
Standard upper and lower bounds on the capacity of relay channels are cut-set (CS), decode-forward (DF), and quantize-forward (QF) rates. For real additive white Gaussian noise (AWGN) multicast relay channels with one source node and one…
We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+\delta$. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) case, we prove that…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student $t$ 95% confidence intervals based on a modest number of replicates were seen to be very effective and…
The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem the optimum mean codeword length of variable-length codes has already been determined. On the…
The maximum likelihood threshold of a statistical model is the minimum number of datapoints required to fit the model via maximum likelihood estimation. In this paper we determine the maximum likelihood thresholds of generic linear…