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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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200214-105545016

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Abstract

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)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2002.00781arXivDiscussion Paper
ORCID:
AuthorORCID
Langberg, Michael0000-0002-7470-0718
Additional Information:Work supported in part by NSF grants CCF-1817241, CCF-1526771 and CCF-1909451.
Funders:
Funding AgencyGrant Number
NSFCCF-1817241
NSFCCF-1526771
UNSPECIFIEDCCF-1909451
Record Number:CaltechAUTHORS:20200214-105545016
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200214-105545016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101297
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:14 Feb 2020 21:02
Last Modified:14 Feb 2020 21:02

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