Related papers: Smoothing of binary codes, uniform distributions, …
In this work we improve the quantum communication rates of various quantum channels of interest using permutation-invariant quantum codes. We focus in particular on parametrized families of quantum channels and aim to improve bounds on…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity…
The {\em discrepancy} of a matrix $M \in \mathbb{R}^{d \times n}$ is given by $\mathrm{DISC}(M) := \min_{\boldsymbol{x} \in \{-1,1\}^n} \|M\boldsymbol{x}\|_\infty$. An outstanding conjecture, attributed to Koml\'os, stipulates that…
We perform a smoothed analysis of the GCC-condition number C(A) of the linear programming feasibility problem \exists x\in\R^{m+1} Ax < 0. Suppose that \bar{A} is any matrix with rows \bar{a_i} of euclidean norm 1 and, independently for all…
Inverse probability problems whose generative models are given by strictly nonlinear Gaussian random fields show the all-or-nothing behavior: There exists a critical rate at which Bayesian inference exhibits a phase transition. Below this…
A polar coding scheme is introduced in this paper for the wire-tap channel. It is shown that the provided scheme achieves the entire rate-equivocation region for the case of symmetric and degraded wire-tap channel, where the weak notion of…
The question whether RM codes are capacity-achieving is a long-standing open problem in coding theory that was recently answered in the affirmative for transmission over erasure channels [1], [2]. Remarkably, the proof does not rely on…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
In this paper, the sphere bound (SB) is revisited within a general bounding framework based on nested Gallager regions. The equivalence is revealed between the SB proposed by Herzberg and Poltyrev and the SB proposed by Kasami et al.,…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…
We characterize the streaming space complexity of every symmetric norm $l$ (a norm on $\mathbb{R}^n$ invariant under sign-flips and coordinate-permutations), by relating this space complexity to the measure-concentration characteristics of…
This paper is concerned with the systematic Bernoulli generator matrix~(BGM) codes, which have been proved to be capacity-achieving over binary-input output-symmetric~(BIOS) channels in terms of bit-error rate~(BER). We prove that the…
One major challenge for living cells is the measurement and prediction of signals corrupted by noise. In general, cells need to make decisions based on their compressed representation of noisy, time-varying signals. Strategies for signal…
We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…
We study the problem of achieving average consensus between a group of agents over a network with erasure links. In the context of consensus problems, the unreliability of communication links between nodes has been traditionally modeled by…
We investigate linear network coding in the context of robust function computation, where a sink node is tasked with computing a target function of messages generated at multiple source nodes. In a previous work, a new distance measure was…
We consider the problem of reliable communication over non-binary insertion/deletion channels where symbols are randomly deleted from or inserted in the transmitted sequence and all symbols are corrupted by additive white Gaussian noise. To…
This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with…
The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and…