Unachievability of network coding capacity

Authors:
Randall Dougherty;Chris Freiling;Kenneth Zeger
Affiliations:
Center for Communications Research, San Diego, CA;Department of Mathematics, California State University, San Bernardino, CA;Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA
Venue:
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Year:
2006

Citing 6
Cited 6

Network coding

Network coding
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)

A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
Network information flow

IEEE Transactions on Information Theory
Linear network coding

IEEE Transactions on Information Theory
Insufficiency of linear coding in network information flow

IEEE Transactions on Information Theory
Network routing capacity

IEEE Transactions on Information Theory

Network coding theory: single sources

Communications and Information Theory
Partial content distribution on high performance networks

Proceedings of the 16th international symposium on High performance distributed computing
Network coding applications

Foundations and Trends® in Networking
A constant bound on throughput improvement of multicast network coding in undirected networks

IEEE Transactions on Information Theory
SER performance analysis for physical layer network coding over AWGN channels

GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
On the security performance of physical-layer network coding

ICC'09 Proceedings of the 2009 IEEE international conference on Communications

Quantified Score

Hi-index	0.06

Visualization

Abstract

The coding capacity of a network is the supremum of ratios k/n for which there exists a fractional (k, n) coding solution, where k is the source message dimension and n is the maximum edge dimension. The coding capacity is referred to as routing capacity in the case when only routing is allowed. A network is said to achieve its capacity if there is some fractional (k, n) solution for which k/n equals the capacity. The routing capacity is known to be achievable for arbitrary networks.We give an example of a network whose coding capacity (which is 1) cannot be achieved by a network code. We do this by constructing two networks, one of which is solvable if and only if the alphabet size is odd, and the other of which is solvable if and only if the alphabet size is a power of 2. No linearity assumptions are made.