Related papers: Rate-distance tradeoff for codes above graph capac…
The capacity of a graph is defined as the rate of exponential grow of independent sets in the strong powers of the graph. In strong power, an edge connects two sequences if at each position letters are equal or adjacent. We consider a…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
For a graph $G$, its $k$-th graph power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$. We consider the problem of deriving upper bounds on the Shannon capacity of graph powers by using spectral…
Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed $\rho$-capacity, that generalizes the Shannon capacity of a graph. We derive upper and lower bounds on the $\rho$-capacity of arbitrary…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several…
We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
We prove an upper bound on the Shannon capacity of a graph via a linear programming variation. We show that our bound can outperform both the Lov\'asz theta number and the Haemers minimum rank bound. As a by-product, we also obtain a new…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
The edge-connectivity of a graph is the minimum number of edges whose deletion disconnects the graph. Let $\Delta(G)$ the maximum degree of a graph $G$ and let $\rho(G)$ be the spectral radius of $G$. In this article we present a lower…
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.…
The Shannon capacity of a graph is a fundamental quantity in zero-error information theory measuring the rate of growth of independent sets in graph powers. Despite being well-studied, this quantity continues to hold several mysteries.…
We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if the vertex codes have minimum distance $\ge 3$, the overall…
This paper presents general bounds on the highest achievable rate for list-decodable insertion-deletion codes. In particular, we give novel outer and inner bounds for the highest achievable communication rate of any insertion-deletion code…
For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth power of G in terms of the order of G and…
An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment and…
We improve the best known upper bound on the number of edges in a unit-distance graph on $n$ vertices for each $n\in\{16,\ldots,30\}$. When $n\leq 21$, our bounds match the best known lower bounds, and we fully enumerate the densest…
Given a linear ordering of the vertices of a graph, the cutwidth of a vertex $v$ with respect to this ordering is the number of edges from any vertex before $v$ (including $v$) to any vertex after $v$ in this ordering. The cutwidth of an…