Generating error-correcting codes based on tower of Hanoi configuration graphs

Nadav Voloch, Elazar Birnbaum, Amir Sapir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

There are several researches that base codes on graphs. Some of them in particular present a code based on graphs, choosing a subset of the vertices as representing the code, and considering it, to a certain extent, as a minimal dominating set. If an error occurs, the string received corresponds to a vertex that is adjacent to precisely one code-word. The decision taken by the above-mentioned scheme does not adhere to the Hamming distance. In this research we have devised an 'inflating' algorithm for the graph for specific string lengths, which remedies this problem. Furthermore, we have established a lower bound on the length of the inflation. Correcting an erroneous word now amounts to a local search among its neighbors, assuming we have a suitable data structure to represent the graph, and the ability to reach the vertex corresponding to that word quickly.

Original languageEnglish
Title of host publication2014 IEEE 28th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781479959877
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes
Event2014 28th IEEE Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014 - Eilat, Israel
Duration: 3 Dec 20145 Dec 2014

Publication series

Name2014 IEEE 28th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014

Conference

Conference2014 28th IEEE Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014
Country/TerritoryIsrael
CityEilat
Period3/12/145/12/14

Keywords

  • Codes on graphs
  • Dominating set
  • Error correcting codes
  • Non-linear codes
  • Tower of Hanoi

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