相关论文: Linear Fractional Network Coding and Representable…
Models for noncoherent error control in random linear network coding (RLNC) and store and forward (SAF) have been recently proposed. In this paper, we model different types of random network communications as the transmission of flats of…
It is known that there exists a network, called as the M-network, which is not scalar linearly solvable but has a vector linear solution for message dimension two. Recently, a generalization of this result has been presented where it has…
This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same…
We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an…
Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from cyclic permutation matrices. When $L$ is a prime with primitive root $2$, it was…
We study matroidal networks introduced by Dougherty et al. We prove the converse of the following theorem: If a network is scalar-linearly solvable over some finite field, then the network is a matroidal network associated with a…
We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
Fiber network modeling can be used for studying mechanical properties of paper. The individual fibers and the bonds in-between constitute a detailed representation of the material. However, detailed microscale fiber network models must be…
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…
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
It is known that there exists a multiple-unicast network which has a rate $1$ linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co-finite set of primes. In this paper, we show…
It is well known that linear rank-metric codes give rise to q-polymatroids. Analogously to matroid theory one may ask whether a given q-polymatroid is representable by a rank-metric code. We provide an answer by presenting an example of a…
A $q$-matroid is the analogue of a matroid which arises by replacing the finite ground set of a matroid with a finite-dimensional vector space over a finite field. These $q$-matroids are motivated by coding theory as the representable…
This paper presents the first implementation of a two-way relay network based on the principle of physical-layer network coding. To date, only a simplified version of physical-layer network coding (PNC) method, called analog network coding…
Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
The connection between index coding and matroid theory have been well studied in the recent past. El Rouayheb et al. established a connection between multilinear representation of matroids and wireless index coding. Muralidharan and Rajan…
Direct application of network coding at the physical layer - physical layer network coding (PNC) - is a promising technique for two-way relay wireless networks. In a two-way relay network, relay nodes are used to relay two-way information…
Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…