Related papers: Degenerate flag varieties in network coding
We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, metric, normal vector, exponential map, geodesic, parallel…
In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known.…
Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the…
Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed, and there have been efforts to use sparse models for regularizing blind…
We present the first empirical evaluation of techniques for encoding distributions of quantitative edge values within adjacency matrices. In many real-world networks, edges represent not a single value but a set of measurements. While…
A matching $M$ in a graph $G$ is $r$-degenerate if the subgraph of $G$ induced by the set of vertices incident with an edge in $M$ is $r$-degenerate. Goddard, Hedetniemi, Hedetniemi, and Laskar (Generalized subgraph-restricted matchings in…
We present a general theory to obtain good linear network codes utilizing the osculating nature of algebraic varieties. In particular, we obtain from the osculating spaces of Veronese varieties explicit families of equidimensional vector…
We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code…
This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous…
In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity order or the transmission rate…
Differential linear network coding (DLNC) is a precoding scheme for information transmission over random linear networks. By using differential encoding and decoding, the conventional approach of lifting, required for inherent channel…
We investigate techniques for designing modulation/coding schemes for the wireless two-way relaying channel. The relay is assumed to have perfect channel state information, but the transmitters are assumed to have no channel state…
We study algebraic, combinatorial and geometric aspects of weighted PBW-type degenerations of (partial) flag varieties in type $A$. These degenerations are labeled by degree functions lying in an explicitly defined polyhedral cone, which…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Neural networks are powerful functions with widespread use, but the theoretical behaviour of these functions is not fully understood. Creating deep neural networks by stacking many layers has achieved exceptional performance in many…
A Mustafin degeneration is a degeneration of a flag variety induced by a vertex configuration in the Bruhat-Tits building of the projective linear group over a field with a non-archimedean discrete valuation. In the case where the flag type…
Classification for degraded images having various levels of degradation is very important in practical applications. This paper proposes a convolutional neural network to classify degraded images by using a restoration network and an…
In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…
Following the historical track in pursuing $T$-equivariant flat toric degenerations of flag varieties and spherical varieties, we explain how powerful tools in algebraic geometry and representation theory, such as canonical bases,…
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then,…