Computer Science – Information Theory
Scientific paper
2012-01-31
Computer Science
Information Theory
Minor edits from version 1
Scientific paper
Matroidal networks were introduced by Dougherty et al. and have been well studied in the recent past. It was shown that a network has a scalar linear network coding solution if and only if it is matroidal associated with a representable matroid. A particularly interesting feature of this development is the ability to construct (scalar and vector) linearly solvable networks using certain classes of matroids. The current work attempts to establish a connection between matroid theory and network-error correcting codes. In a similar vein to the theory connecting matroids and network coding, we abstract the essential aspects of network-error correcting codes to arrive at the definition of a matroidal error correcting network. An acyclic network (with arbitrary sink demands) is then shown to possess a scalar linear error correcting network code if and only if there it is a matroidal error correcting network associated with a representable matroid. Therefore, constructing such network-error correcting codes implies the construction of certain representable matroids that satisfy some special conditions, and vice versa. We then present algorithms which enable the construction of scalar linearly solvable multicast and multiple-unicast networks with a specified capability of network-error correction. Using these construction algorithms, a large class of hitherto unknown scalar linearly solvable networks with multicast and multiple-unicast network-error correcting codes is made available for theoretical use and practical implementation, with parameters such as number of information symbols, number of sinks, number of network coding nodes, error correcting capability, etc. being arbitrary but for computing power (for the execution of the algorithms).
Prasad Kamakshi
Rajan Sundar B.
No associations
LandOfFree
A Matroidal Framework for Network-Error Correcting Codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Matroidal Framework for Network-Error Correcting Codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Matroidal Framework for Network-Error Correcting Codes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-56545