Related papers: Degenerate flag varieties in network coding
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…
In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding…
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving…
Systems that employ network coding for content distribution convey to the receivers linear combinations of the source packets. If we assume randomized network coding, during this process the network nodes collect random subspaces of the…
We present RL-VAE, a graph-to-graph variational autoencoder that uses reinforcement learning to decode molecular graphs from latent embeddings. Methods have been described previously for graph-to-graph autoencoding, but these approaches…
Let $\Fl_\lambda$ be a generalized flag variety of a simple Lie group $G$ embedded into the projectivization of an irreducible $G$-module $V_\lambda$. We define a flat degeneration $\Fl_\lambda^a$, which is a ${\mathbb G}^M_a$ variety.…
We restrict a degenerate quadratic form $f$ over a finite field of odd characteristic to subspaces. Thus, a quotient space related to $f$ is introduced. Then we get a non-degenerate quadratic form induced by $f$ over the quotient space.…
We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
Increasing network utilization is often considered as the holy grail of communications. In this article, the concept of sub-rate coding and decoding in the framework of linear network coding (LNC) is discussed for single-source…
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear…
AI systems frequently exhibit and amplify social biases, leading to harmful consequences in critical areas. This study introduces a novel encoder-decoder approach that leverages model gradients to learn a feature neuron encoding societal…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Schubert calculus provides algebraic tools to solve enumerative problems. There have been several applied problems in systems theory, linear algebra and physics which were studied by means of Schubert calculus. The method is most powerful…
This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random…
We present a new deep unfolding network for analysis-sparsity-based Compressed Sensing. The proposed network coined Decoding Network (DECONET) jointly learns a decoder that reconstructs vectors from their incomplete, noisy measurements and…
While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform…
Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links and multicast…
We conceptualize in the paper the linear degenerate symplectic flag varieties as symmetric degenerations within the framework of type $A$ equioriented quivers. First, in the larger context of symmetric degenerations, we give a…
This paper considers the problem of network coding for multiple unicast connections in networks represented by directed acyclic graphs. The concept of interference alignment, traditionally used in interference networks, is extended to…