相关论文: Pseudocodewords of Tanner graphs
In this paper we present various lower bound results on collective tree spanners and on spanners of bounded treewidth. A graph $G$ is said to admit a system of $\mu$ collective additive tree $c$-spanners if there is a system $\cal{T}$$(G)$…
Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call ``diffusion codes'', defined by placing each edge connecting…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
In this paper, we investigate the manner in which interpretable sub-word speech units emerge within a convolutional neural network model trained to associate raw speech waveforms with semantically related natural image scenes. We show how…
In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine $\F_{q^r}$-rational points of the Norm-Trace curve. In particular, we investigate…
The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix…
Traditional communication theory focuses on minimizing transmit power. However, communication links are increasingly operating at shorter ranges where transmit power can be significantly smaller than the power consumed in decoding. This…
Every rational number p/q defines a rational base numeration system in which every integer has a unique finite representation, up to leading zeroes. This work is a contribution to the study of the set of the representations of integers.…
In the literature, several different identification problems in graphs have been studied, the most widely studied such problems are the ones based on dominating sets as a tool of identification. Hereby, the objective is to separate any two…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…
There is a long line of research in the literature dedicated to word-representable graphs, which generalize several important classes of graphs. However, not much is known about word-representability of split graphs, another important class…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
Contagions (e.g. virus, gossip) spread over the nodes in propagation graphs. We can use the temporal and textual data of the nodes to compute the edge weights and then generate subgraphs with highly relevant nodes. This is beneficial to…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
The connection between dependency trees and spanning trees is exploited by the NLP community to train and to decode graph-based dependency parsers. However, the NLP literature has missed an important difference between the two structures:…
Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g.\ in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics…
Most multi-dimensional (more than two dimensions) lattice partitions only form additive quotient groups and lack multiplication operations. This prevents us from constructing lattice codes based on multi-dimensional lattice partitions…
We study the set of all decompositions (clusterings) of a graph through its characterization as a set of lifted multicuts. This leads us to practically relevant insights related to the definition of a class of decompositions by must-join…