相关论文: Degenerate flag varieties in network coding

We introduce loop spaces (in the sense of derived algebraic geometry) into the representation theory of reductive groups. In particular, we apply the theory developed in our previous paper arXiv:1002.3636 to flag varieties, and obtain new…

In this paper, we show how to construct a factor graph from a network code. This provides a systematic framework for decoding using message passing algorithms. The proposed message passing decoder exploits knowledge of the underlying…

A root systems in Carroll spaces with degenerate metric are defined. It is shown that their Cartan matrices and reflection groups are affine. With the help of the geometric consideration the root system structure of affine algebras is…

We establish an explicit combinatorial/homological characterization of supports for linear degenerations of flag varieties. For such purpose, we introduce the concept of an excessive multisegment. It provides a new class of combinatorial…

The theory of flag algebras, introduced by Razborov in 2007, has opened the way to a systematic approach to the development of computer-assisted proofs in extremal combinatorics. It makes it possible to derive bounds for parameters in…

We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated…

Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multi-level space-time codes for flat fading channels have been designed from sets…

In this paper an interpolation-based decoding algorithm to decode Gabidulin codes, transmitted through a finely restricted channel, is proposed. The algorithm is able to decode rank errors beyond half the minimum distance by one unit. Also…

In this paper, we present a general framework to scale graph autoencoders (AE) and graph variational autoencoders (VAE). This framework leverages graph degeneracy concepts to train models only from a dense subset of nodes instead of using…

Random linear network coding (RLNC) in theory achieves the max-flow capacity of multicast networks, at the cost of high decoding complexity. To improve the performance-complexity tradeoff, we consider the design of sparse network codes. A…

The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…

The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…

Subspace codes and rank-metric codes can be used to correct errors and erasures in network, with linear network coding. Subspace codes were introduced by Koetter and Kschischang to correct errors and erasures in networks where topology is…

We consider the decoding problem or the problem of finding low weight codewords for rank metric codes. We show how additional information about the codeword we want to find under the form of certain linear combinations of the entries of the…

Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local…

This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric. The new decoder is an adaption of the Hamming-metric decoder by Metzner and Kapturowski (1990) and guarantees to…

This article is about a decoding algorithm for error-correcting subspace codes. A version of this algorithm was previously described by Rosenthal, Silberstein and Trautmann. The decoding algorithm requires the code to be defined as the…

Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "push to the top"…

We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…

Neural networks can be thought of as applying a transformation to an input dataset. The way in which they change the topology of such a dataset often holds practical significance for many tasks, particularly those demanding non-homeomorphic…