Related papers: Vector Network Coding Based on Subspace Codes Outp…
Subspace codes form the appropriate mathematical setting for investigating the Koetter-Kschischang model of fault-tolerant network coding. The Main Problem of Subspace Coding asks for the determination of a subspace code of maximum size…
In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…
A linear Fractional Network Coding (FNC) solution over $\mathbb{F}_q$ is a linear network coding solution over $\mathbb{F}_q$ in which the message dimensions need not necessarily be the same and need not be the same as the edge vector…
Circular-shift linear network coding (LNC) is a class of vector LNC with local encoding kernels selected from cyclic permutation matrices, so that it has low coding complexities. However, it is insufficient to exactly achieve the capacity…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
The recent introduction of vector coded caching has revealed that multi-rank transmissions in the presence of receiver-side cache content can dramatically ameliorate the file-size bottleneck of coded caching and substantially boost…
We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized network coding operations on the source packets. We propose a channel model for the…
It is known that there exists a network which does not have a scalar linear solution over any finite field but has a vector linear solution when message dimension is $2$ [3]. It is not known whether this result can be generalized for an…
This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…
An index coding problem arises when there is a single source with a number of messages and multiple receivers each wanting a subset of messages and knowing a different set of messages a priori. The noiseless Index Coding Problem is to…
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…
In this work, we study the problem of index coding from graph homomorphism perspective. We show that the minimum broadcast rate of an index coding problem for different variations of the problem such as non-linear, scalar, and vector index…
An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding…
Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we…
A class of network codes have been proposed in the literature where the symbols transmitted on network edges are binary vectors and the coding operation performed in network nodes consists of the application of (possibly several)…
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible.…
We consider a two-unicast-$Z$ network over a directed acyclic graph of unit capacitated edges; the two-unicast-$Z$ network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted…
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…
We present a heuristic for designing vector non-linear network codes for non-multicast networks, which we call quasi-linear network codes. The method presented has two phases: finding an approximate linear network code over the reals, and…