Related papers: Gilbert-Varshamov Bound for Codes in $L_1$ Metric …
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Given a $q$-ary frequency hopping sequence set of length $n$ and size $M$ with Hamming correlation $H$, one can obtain a $q$-ary (nonlinear) cyclic code of length $n$ and size $nM$ with Hamming distance $n-H$. Thus, every upper bound on the…
Consider a pair of correlated Gaussian sources (X1,X2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear…
Increasingly, visual signals such as images, videos and point clouds are being captured solely for the purpose of automated analysis by computer vision models. Applications include traffic monitoring, robotics, autonomous driving, smart…
In this article we present a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces). The lower bounds we derive via the linear programming (LP) techniques of…
In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (delta,s,n)-nets of low discrepancy. It…
We consider lossy compression of a binary symmetric source by means of a low-density generator-matrix code. We derive two lower bounds on the rate distortion function which are valid for any low-density generator-matrix code with a given…
Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…
In this note we report two versions of Gilbert-Varshamov type existential bounds for asymmetric quantum error-correcting codes.
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are…
In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving…
As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often…
We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. Generalized…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
This paper considers coding for so-called partially stuck (defect) memory cells. Such memory cells can only store partial information as some of their levels cannot be used fully due to, e.g., wearout. First, we present new constructions…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…
We initiate the study of what we term ``fast good codes'' with ``fast good duals.'' Specifically, we consider the task of constructing a rate 1/2 binary linear code such that both it and its dual are asymptotically good (in fact, have…