From LINC

This paper appeared in the proceedings for Allerton Conference on Communication, Control, and Computing.

Abstract

The traditional notion of network coding is that of the output being linear combinations of incoming vectors at each node in the network. This simple but powerful strategy has been proved to possess multiple properties, from both a throughput and a robustness/security perspective. This paper seeks to take this strategy from the realm of vector spaces to (unital free) modules over rings for two reasons: a. modules are more general algebraic entities than vector spaces, allowing for a larger set of options in picking code constructions and thus allowing for a wider range of possibilities and tradeoffs among parameters that govern network coding. b. Properties such as non-commutativity and non-invertibility (no-inverse element) of elements in the underlying ring may permit the network designer to control the amount of information available at nodes in the network, both on the data and the structure (topology) of the network itself. This paper’s main focus is to show that using modules based on rings (with identity) does not cause a loss in throughput, i.e., that with or without inverse elements and commutativity, the network-coding strategy achieves the cut-set bound in unicast and multicast networks. The task of exploiting the more general structure of such a coding scheme (for security or robustness purposes) is left to a later document.

Citation

Shweta Agrawal and Sriram Vishwanath . "Network Coding using Unital Modules over Rings."

BibTeX

@inproceedings{ {{{bitex cite}}},
  author = "Shweta Agrawal and Sriram Vishwanath",
  title = { Network Coding using Unital Modules over Rings },
  booktitle = { {{{proceedings}}} }
}