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Towards an Operational Definition of Group Network Codes

Wei, Fei and Langberg, Michael and Effros, Michelle (2020) Towards an Operational Definition of Group Network Codes. . (Unpublished)

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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.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Langberg, Michael0000-0002-7470-0718
Additional Information:Work supported in part by NSF grants CCF-1817241, CCF-1526771 and CCF-1909451.
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Record Number:CaltechAUTHORS:20200214-105545016
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101297
Deposited By: George Porter
Deposited On:14 Feb 2020 21:02
Last Modified:14 Feb 2020 21:02

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