17 research outputs found
On the Impact of a Single Edge on the Network Coding Capacity
In this paper, we study the effect of a single link on the capacity of a
network of error-free bit pipes. More precisely, we study the change in network
capacity that results when we remove a single link of capacity . In a
recent result, we proved that if all the sources are directly available to a
single super-source node, then removing a link of capacity cannot
change the capacity region of the network by more than in each
dimension. In this paper, we extend this result to the case of multi-source,
multi-sink networks for some special network topologies.Comment: Originally presented at ITA 2011 in San Diego, CA. The arXiv version
contains an updated proof of Theorem
Can Negligible Cooperation Increase Network Capacity? The Average-Error Case
In communication networks, cooperative strategies are coding schemes where
network nodes work together to improve network performance metrics such as
sum-rate. This work studies encoder cooperation in the setting of a discrete
multiple access channel with two encoders and a single decoder. A node in the
network that is connected to both encoders via rate-limited links, referred to
as the cooperation facilitator (CF), enables the cooperation strategy.
Previously, the authors presented a class of multiple access channels where the
average-error sum-capacity has an infinite derivative in the limit where CF
output link capacities approach zero. The authors also demonstrated that for
some channels, the maximal-error sum-capacity is not continuous at the point
where the output link capacities of the CF equal zero. This work shows that the
the average-error sum-capacity is continuous when CF output link capacities
converge to zero; that is, the infinite derivative of the average-error
sum-capacity is not a result of its discontinuity as in the maximal-error case.Comment: 20 pages, 1 figure. To be submitted to ISIT '1
Can Negligible Cooperation Increase Network Reliability?
In network cooperation strategies, nodes work together with the aim of
increasing transmission rates or reliability. This paper demonstrates that
enabling cooperation between the transmitters of a two-user multiple access
channel, via a cooperation facilitator that has access to both messages, always
results in a network whose maximal- and average-error sum-capacities are the
same---even when those capacities differ in the absence of cooperation and the
information shared with the encoders is negligible. From this result, it
follows that if a multiple access channel with no transmitter cooperation has
different maximal- and average-error sum-capacities, then the maximal-error
sum-capacity of the network consisting of this channel and a cooperation
facilitator is not continuous with respect to the output edge capacities of the
facilitator. This shows that there exist networks where sharing even a
negligible number of bits per channel use with the encoders yields a
non-negligible benefit.Comment: 27 pages, 3 figures. Submitted to the IEEE Transactions on
Information Theor
Negligible Cooperation: Contrasting the Maximal- and Average-Error Cases
In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as the total rate delivered across the network. This work studies encoder cooperation in the setting of a discrete multiple access channel (MAC) with two encoders and a single decoder. A network node, here called the cooperation facilitator (CF), that is connected to both encoders via rate-limited links, enables the cooperation strategy. Previous work by the authors presents two classes of MACs: (i) one class where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero, and (ii) a second class of MACs where the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work contrasts the power of the CF in the maximal- and average-error cases, showing that a constant number of bits communicated over the CF output link can yield a positive gain in the maximal-error sum-capacity, while a far greater number of bits, even numbers that grow sublinearly in the blocklength, can never yield a non-negligible gain in the average-error sum-capacity
Towards an Operational Definition of Group Network Codes
Group network codes are a generalization of linear codes that have seen several studies over the last decade. When studying network codes, operations performed at internal network nodes called local encoding functions, are of significant interest. While local encoding functions of linear codes are well understood (and of operational significance), no similar operational definition exists for group network codes. To bridge this gap, we study the connections between group network codes and a family of codes called Coordinate-Wise-Linear (CWL) codes. CWL codes generalize linear codes and, in addition, can be defined locally (i.e., operationally). In this work, we study the connection between CWL codes and group codes from both a local and global encoding perspective. We show that Abelian group codes can be expressed as CWL codes and, as a result, they inherit an operational definition