Related papers: Permute & Add Network Codes via Group Algebras
Multiplex networks allow us to study a variety of complex systems where nodes connect to each other in multiple ways, for example friend, family, and co-worker relations in social networks. Link prediction is the branch of network analysis…
We present a heuristic for designing vector non-linear network codes for non-multicast networks, which we call quasi-linear network codes. The method presented has two phases: finding an approximate linear network code over the reals, and…
Network embedding is a highly effective method to learn low-dimensional node vector representations with original network structures being well preserved. However, existing network embedding algorithms are mostly developed for a single…
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…
Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…
Combinatorial generalization - the ability to understand and produce novel combinations of already familiar elements - is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body…
Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links and multicast…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
Network coding is famous for significantly improving the throughput of networks. The successful decoding of the network coded data relies on some side information of the original data. In that framework, independent data flows are usually…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
While there are continuous efforts to introduce new communication systems and standards, it is legitimate to ask the question: how can one send additional bits by minimally changing the systems that are already operating? This is of a…
This paper presents a joint typicality framework for encoding and decoding nested linear codes for multi-user networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…
Random linear network code has to sacrifice part of bandwidth to transfer the coding vectors, thus a head of size k log|T| is appended to each packet. We present a distributed random network coding approach based on the Chinese remainder…
A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
This paper considers distributed coding for multi-source single-sink data collection wireless networks. A unified framework for network coding and channel coding, termed "generalized adaptive network coded cooperation" (GANCC), is proposed.…