Related papers: Upper bound on list-decoding radius of binary code…
In this paper, new techniques are presented to either simplify or improve most existing upper bounds on the maximum-likelihood (ML) decoding performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly,…
In this work, we study the problem of list decoding of insertions and deletions. We present a Johnson-type upper bound on the maximum list size. The bound is meaningful only when insertions occur. Our bound implies that there are binary…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
Lossy data compression lies at the heart of modern communication and storage systems. Shannon's rate-distortion theory provides the fundamental limit on how much a source can be compressed at a given fidelity, but it assumes infinitely long…
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…
In this paper, we are interested in the problem of scattering by strictly convex obstacles in the plane. We provide an upper bound for the number $N(r,\gamma)$ of resonances in the box $\{r \le \Re(\lambda) \le r + 1$; $\Im(\lambda) \ge -…
We compute the code parameters for binary linear codes obtained by greedy constructing the parity check matrix. Then we show that these codes improve the Gilbert-Varshamov (GV) bound on the code size and rate. This result counter proves the…
This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…
Gap Hamming Distance is a well-studied problem in communication complexity, in which Alice and Bob have to decide whether the Hamming distance between their respective n-bit inputs is less than n/2-sqrt(n) or greater than n/2+sqrt(n). We…
We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to…
In this article we improve the dimension and minimum distance bound of the the Hermitian Lifted Codes LRCs construction from L\'opez, Malmskog, Matthews, Pi\~nero and Wooters (L\'opez et. al.) via elementary univariarte polynomial division.…
We use $p$-rank bounds on partial ovoids and the classical bounds on Ramsey numbers to obtain upper bounds on the size of partial $m$-ovoids in finite classical polar spaces. These bounds imply non-existence of $m$-ovoids for new infinite…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…
We give an improved upper bound for the Gr\"unbaum--Hadwiger--Ramos problem: Let $d,n,k \in \mathbb{N}$ such that $d \geq 2^n(1+2^{k-1})$. Given $2^{n+1}$ masses on $\mathbb{R}^d$, there exist $k$ hyperplanes in $\mathbb{R}^d$ that…
For non-binary codes the Elias bound is a good upper bound for the asymptotic information rate at low relative minimum distance, where as the Plotkin bound is better at high relative minimum distance. In this work, we obtain a hybrid of…
We thoroughly study a novel but basic combinatorial matrix completion problem: Given a binary incomplete matrix, fill in the missing entries so that every pair of rows in the resulting matrix has a Hamming distance within a specified range.…
Explicit non-asymptotic upper bounds on the sizes of multiple-deletion correcting codes are presented. In particular, the largest single-deletion correcting code for $q$-ary alphabet and string length $n$ is shown to be of size at most…
Coding Theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. Such codes over rings had important applications and many interesting mathematical…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…