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DOI: 10.4230/DagSemProc.06201.4
URN: urn:nbn:de:0030-drops-7849
URL: https://drops.dagstuhl.de/opus/volltexte/2006/784/
Ahlswede, Rudolf ; Deppe, Christian ; Lebedev, Vladimir
Non--binary error correcting codes with noiseless feedback, localized errors, or both
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Abstract
We investigate non--binary error correcting codes with noiseless feedback, localized errors, or both. It turns out that the Hamming bound is a central concept. For block codes with feedback we present here a coding scheme based on an idea of erasions, which we call the {\bf rubber method}. It gives an optimal rate for big error correcting fraction $\tau$ ($>{1\over q}$) and infinitely many points on the Hamming bound for small $\tau$.We also consider variable length codes with all lengths bounded from above by $n$ and the end of a word carries the symbol $\Box$ and is thus recognizable by the decoder. For both, the $\Box$-model with feedback and the $\Box$-model with localized errors, the Hamming bound is the exact capacity curve for $\tau <1/2.$ Somewhat surprisingly, whereas with feedback the capacity curve coincides with the Hamming bound also for
$1/2\leq \tau \leq 1$, in this range for localized errors the capacity curve equals 0.
Also we give constructions for the models with both, feedback and localized errors.
BibTeX - Entry
@InProceedings{ahlswede_et_al:DagSemProc.06201.4,
author = {Ahlswede, Rudolf and Deppe, Christian and Lebedev, Vladimir},
title = {{Non--binary error correcting codes with noiseless feedback, localized errors, or both}},
booktitle = {Combinatorial and Algorithmic Foundations of Pattern and Association Discovery},
pages = {1--4},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2006},
volume = {6201},
editor = {Rudolf Ahlswede and Alberto Apostolico and Vladimir I. Levenshtein},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2006/784},
URN = {urn:nbn:de:0030-drops-7849},
doi = {10.4230/DagSemProc.06201.4},
annote = {Keywords: Error-correcting codes, localized errors, feedback, variable length codes}
}
| Keywords: | Error-correcting codes, localized errors, feedback, variable length codes | |
| Seminar: | 06201 - Combinatorial and Algorithmic Foundations of Pattern and Association Discovery | |
| Issue date: | 2006 | |
| Date of publication: | 07.11.2006 |
