Related papers: Decoding Network Codes by Message Passing
Graph kernels have recently emerged as a promising approach for tackling the graph similarity and learning tasks at the same time. In this paper, we propose a general framework for designing graph kernels. The proposed framework capitalizes…
A single-source network is said to be \textit{memory-free} if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the incoming symbols (received at their incoming…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
We consider a communication network with a single source that has a set of messages and two terminals where each terminal is interested in an arbitrary subset of messages at the source. A tight capacity region for this problem is…
Motivated by signal processing, we present a new class of channel codes, called signal codes, for continuous-alphabet channels. Signal codes are lattice codes whose encoding is done by convolving an integer information sequence with a fixed…
We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $<u, v>$, along with a…
In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter…
In random-access networks, such as the IEEE 802.11 network, different users may transmit their packets simultaneously, resulting in packet collisions. Traditionally, the collided packets are simply discarded. To improve performance,…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a…
In this paper, we incorporate a graph filter deconvolution step into the classical geometric convolutional neural network pipeline. More precisely, under the assumption that the graph domain plays a role in the generation of the observed…
Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social…
We describe message-passing and decimation approaches for lossy source coding using low-density generator matrix (LDGM) codes. In particular, this paper addresses the problem of encoding a Bernoulli(0.5) source: for randomly generated LDGM…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
We investigate the problem of decoding a bar code from a signal measured with a hand-held laser-based scanner. Rather than formulating the inverse problem as one of binary image reconstruction, we instead incorporate the symbology of the…
Under the emerging network coding paradigm, intermediate nodes in the network are allowed not only to store and forward packets but also to process and mix different data flows. We propose a low-complexity cryptographic scheme that exploits…
In this paper, convolutional network coding is formulated by means of matrix power series representation of the local encoding kernel (LEK) matrices and global encoding kernel (GEK) matrices to establish its theoretical fundamentals for…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…