Related papers: Optimal Scalar Linear Index Codes for One-Sided Ne…
A variant of the index coding problem (ICP), the embedded index coding problem (EICP) was introduced in [A. Porter and M. Wootters, "Embedded index coding," ITW, Sweden, 2019] which was motivated by its application in distributed computing…
Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric…
In this paper, we propose a new coding scheme and establish new bounds on the capacity region for the multi-sender unicast index-coding problem. We revisit existing partitioned Distributed Composite Coding (DCC) proposed by Sadeghi et al.…
It has been known that the insufficiency of linear coding in achieving the optimal rate of the general index coding problem is rooted in its rate's dependency on the field size. However, this dependency has been described only through the…
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…
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a…
In index coding, a server broadcasts multiple messages to their respective receivers, each with some side information that can be utilized to reduce the amount of communication from the server. Distributed index coding is an extension of…
Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em…
In the traditional index coding problem, a server employs coding to send messages to $n$ clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the…
This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side…
In this paper, we investigate the necessity of finite blocklength codes in distributed transmission of independent message sets over channels with feedback. Previously, it was shown that finite effective length codes are necessary in…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and…
This work introduces a hypergraph formulation that generalizes the classical paradigm of Bar-Yossef et al. to the multi-sender index coding (MSIC) setting. Central to the model is a 4-regular side-information hypergraph G, a new adjacency…
Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this…
Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrix-variable optimization problems. Based on the optimal structures…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
In the pliable variant of index coding, receivers are allowed to decode any new message not known a priori. Optimal code design for this variant involves identifying each receiver's choice of a new message that minimises the overall…
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…
This paper investigates the linear precoder design that maximizes the average mutual information of multiple-input multiple-output channels with finite-alphabet inputs and statistical channel state information known at the transmitter. This…