An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Information flow decomposition for network coding
IEEE Transactions on Information Theory
Network coding for routability improvement in VLSI
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
A doubly distributed genetic algorithm for network coding
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Foundations and Trends® in Networking
On network coding in wireless ad-hoc networks
International Journal of Ad Hoc and Ubiquitous Computing
Improving FPGA routability using network coding
Proceedings of the 18th ACM Great Lakes symposium on VLSI
An overview of network coding for dynamically changing networks
International Journal of Autonomous and Adaptive Communications Systems
Network coding: a computational perspective
IEEE Transactions on Information Theory
Communicating the sum of sources in a 3-sources/3-terminals network
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Design of efficient robust network codes for multicast connections
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
On-chip bidirectional wiring for heavily pipelined systems using network coding
ICCD'09 Proceedings of the 2009 IEEE international conference on Computer design
Protecting network coded packets in coalition networks
WONS'10 Proceedings of the 7th international conference on Wireless on-demand network systems and services
A population based incremental learning for delay constrained network coding resource minimization
EvoApplications'11 Proceedings of the 2011 international conference on Applications of evolutionary computation - Volume Part II
An effective genetic algorithm for network coding
Computers and Operations Research
Entropy-based efficiency enhancement techniques for evolutionary algorithms
Information Sciences: an International Journal
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In the multicast network coding problem, a source s needs to deliver h packets to a set of k terminals over an underlying communication network G. The nodes of the multicast network can be broadly categorized into two groups. The first group incudes encoding nodes, i.e., nodes that generate new packets by combining data received from two or more incoming links. The second group includes forwarding nodes that can only duplicate and forward the incoming packets. Encoding nodes are, in general, more expensive due to the need to equip them with encoding capabilities. In addition, encoding nodes incur delay and increase the overall complexity of the network.Accordingly, in this paper, we study the design of multicast coding networks with a limited number of encoding nodes. We prove that in a directed acyclic coding network, the number of encoding nodes required to achieve the capacity of the network is bounded by h3 k2. Namely, we present (efficiently constructible) network codes that achieve capacity in which the total number of encoding nodes is independent of the size of the network and is bounded by h3k2. We show that the number of encoding nodes may depend both on h and k by presenting acyclic coding networks that require Ω (h2k) encoding nodes. In the general case of coding networks with cycles, we show that the number of encoding nodes is limited by the size of the minimum feedback link set, i.e., the minimum number of links that must be removed from the network in order to eliminate cycles. We prove that the number of encoding nodes is bounded by (2B + 1) h3k2, where Bis the minimum size of a feedback link set. Finally, we observe that determining or even crudely approximating the minimum number of required encoding nodes is an NP-hard problem.