相关论文: Structural Properties of Index Coding Capacity Usi…
This letter investigates the role of index coding in the capacity of AWGN broadcast channels with receiver message side information. We first show that index coding is unnecessary where there are two receivers; multiplexing coding and…
We investigate the possibility of proving upper bounds on Hadwiger's number of a graph with partial information, mirroring several known upper bounds for the chromatic number. For each such bound we determine whether the corresponding bound…
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…
For every $q\in \mathbb N$ let $\textrm{FO}_q$ denote the class of sentences of first-order logic FO of quantifier rank at most $q$. If a graph property can be defined in $\textrm{FO}_q$, then it can be decided in time $O(n^q)$. Thus,…
A large body of work has investigated the properties of graph neural networks and identified several limitations, particularly pertaining to their expressive power. Their inability to count certain patterns (e.g., cycles) in a graph lies at…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
We consider the communication channel given by a fiber optical transmission line. We develop a method to perturbatively calculate the information capacity of a nonlinear channel, given the corresponding evolution equation. Using this…
We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all…
Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large…
Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible…
Fractional repetition (FR) codes is a family of codes for distributed storage systems that allow for uncoded exact repairs having the minimum repair bandwidth. However, in contrast to minimum bandwidth regenerating (MBR) codes, where a…
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply shows that in order to achieve capacity…
The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes -- a purely combinatorial one and two geometric ones. It is shown, that most…
According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…
The concept of graph compositions is related to several number theoretic concepts, including partitions of positive integers and the cardinality of the power set of finite sets. This paper examines graph compositions where the total number…
Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become…
A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. A dominating set is connected if the subgraph induced by its vertices is connected. The connected domatic partition problem asks for…
Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…