Related papers: More on Combinatorial Batch Codes
In this paper, we propose a new coding scheme and establish new bounds on the capacity region for the multi-sender unicast index-coding problem. We revisit existing partitioned Distributed Composite Coding (DCC) proposed by Sadeghi et al.…
The concept of spatial coupling is among the most significant breakthroughs in coding theory over the past decade. The excellent waterfall and error floor performance of spatially coupled codes has positioned them as promising coding…
Inspired by the "generalized t-designs" defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835--4842], we define a new class of combinatorial designs which simultaneously provide a generalization…
The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and…
Generally, combinatorial design concerns with the arrangement of a finite set of elements into patterns (subsets, words, arrays) according to specified rules. The usefulness of this design method is that the number of input combination can…
This article investigates integer sequences that partition the sequence into blocks of various lengths - irregular arrays. The main result of the article is explicit formulas for numbering of irregular arrays. A generalization of Cantor…
A combinatorial theory for type $R_I$ orthogonal polynomials is given. The ingredients include weighted generalized Motzkin paths, moments, continued fractions, determinants, and histories. Several explicit examples in the Askey scheme are…
The subspace channel was introduced by Koetter and Kschischang as an adequate model for the communication channel from the source node to a sink node of a multicast network that performs random linear network coding. So far, attention has…
For the additive white Gaussian noise channel with average power constraint, sparse superposition codes, proposed by Barron and Joseph in 2010, achieve the capacity. While the codewords of the original sparse superposition codes are made…
We give a modern computational introduction to the S,K combinators invented by Moses Sch\"onfinkel in 1920, and present a variety of new results and ideas about combinators. We explore the spectrum of behavior obtained with small combinator…
Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…
The ${\mathbb B}_n^{(k)}$ poly-Bernoulli numbers --- a natural generalization of classical Bernoulli numbers ($B_n={\mathbb B}_n^{(1)}$) --- were introduced by Kaneko in 1997. When the parameter $k$ is negative then ${\mathbb B}_n^{(k)}$ is…
In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. In this paper, the metric used is the so-called…
We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of…
Polycyclic codes are a generalization of cyclic and constacyclic codes. Even though they have been known since 1972 and received some attention more recently, there have not been many studies on polycyclic codes. This paper presents an…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
Recently a powerful class of rate-compatible serially concatenated convolutional codes (SCCCs) have been proposed based on minimizing analytical upper bounds on the error probability in the error floor region. Here this class of codes is…
Results of testing the fast CASCIE (Code for Accelerating Structures - Coupled Integral Equations) code developed as an analytical-numerical tool for studying the properties of inhomogeneous structured waveguides are presented. We have used…
Schreier sets have been an object of study since first introduced in 1930 by Jozef Schreier to construct a counterexample to a conjecture of Banach. In 1974 George Andrews found interesting connections between these sets and Fibonacci…
We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the…