相关论文: On Critical Index Coding Problems
The capacity of symmetric instance of the multiple unicast index coding problem with neighboring antidotes (side-information) with number of messages equal to the number of receivers was given by Maleki \textit{et al.} In this paper, we…
This paper investigates secure storage codes over graphs, where multiple independent source symbols are encoded and stored at graph nodes subject to edge-wise correctness and security constraints. For each edge, a specified subset of source…
Packets originated from an information source in the network can be highly correlated. These packets are often routed through different paths, and compressing them requires to process them individually. Traditional universal compression…
The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source,…
We describe a rational approach to reduce the computational and communication complexities of lossless point-to-point compression for computation with side information. The traditional method relies on building a characteristic graph with…
We say a hypergraph $\mathcal{H}$ contains a graph $G$ as trace if there exists a vertex subset $S \subseteq V(\mathcal{H})$ such that $|S| = V(G)$ and $\{e \cap S \mid e \in E(\mathcal{H})\}$ contains $G$ as a subgraph. We use…
We identify the common underlying form of the capacity expression that is applicable to both cases where causal or non-causal side information is made available to the transmitter. Using this common form we find that for the single user…
An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability…
A signed bipartite (simple) graph $(G, \sigma)$ is said to be $C_{-4}$-critical if it admits no homomorphism to $C_{-4}$ (a negative 4-cycle) but every proper subgraph of it does. In this work, first of all we show that the notion of…
The cyclic code is a subclass of linear codes and has applications in consumer electronics, data storage systems and communication systems due to the efficient encoding and decoding algorithms. In 2013, Ding, et al. presented nine open…
We consider a graphical approach to index coding. While cycles have been shown to provide coding gain, only disjoint cycles and cliques (a specific type of overlapping cycles) have been exploited in existing literature. In this paper, we…
Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
Confirming a conjecture of Gy\'arf\'as, we prove that, for all natural numbers $k$ and $r$, the vertices of every $r$-edge-coloured complete $k$-uniform hypergraph can be partitioned into a bounded number (independent of the size of the…
The recently proposed set-up of source coding with a side information "vending machine" allows the decoder to select actions in order to control the quality of the side information. The actions can depend on the message received from the…
Gallai asked in 1984 if any $k$-critical graph on $n$ vertices contains at least $n$ distinct $(k-1)$-critical subgraphs. The answer is trivial for $k\leq 3$. Improving a result of Stiebitz, Abbott and Zhou proved in 1995 that for all…
In this paper we study acyclic colouring in the random subgraph $\mathit{G}$ of the complete graph $\mathit{K}_n$ on $\mathit{n}$ vertices where each edge is present with probability $\mathit{p}$; independent of the other edges. We show…
Given an undirected graph $G$ and integers $c$ and $k$, the Maximum Edge-Colorable Subgraph problem asks whether we can delete at most $k$ edges in $G$ to obtain a graph that has a proper edge coloring with at most $c$ colors. We show that…
This paper studies the problem of information theoretic secure communication when a source has private messages to transmit to $m$ destinations, in the presence of a passive adversary who eavesdrops an unknown set of $k$ edges. The…
We study experiment design for unique identification of the causal graph of a simple SCM, where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic…