License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.06111.19
URN: urn:nbn:de:0030-drops-6025
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2006/602/
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Andreev, Alexander E.

The optimal sequence compression

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06111.AndreevAlexander.Paper.602.pdf (0.1 MB)

Abstract

This paper presents the optimal compression for sequences with
undefined values.

Let we have $(N-m)$ undefined and $m$ defined positions in the
boolean sequence $vv V$ of length $N$. The sequence code length
can't be less then $m$ in general case, otherwise at least two
sequences will have the same code.

We present the coding algorithm which generates codes of almost $m$
length, i.e. almost equal to the lower bound.

The paper presents the decoding circuit too. The circuit has low
complexity which depends from the inverse density of defined values
$D(vv V) = frac{N}{m}$.

The decoding circuit includes RAM and random logic. It performs
sequential decoding. The total RAM size is proportional to the
$$logleft(D(vv V)
ight) ,$$
the number of random logic cells is proportional to
$$log logleft(D(vv V)
ight) * left(log log logleft(D(vv V)
ight)
ight)^2 .$$
So the decoding circuit will be small enough even for the very low
density sequences. The decoder complexity doesn't depend of the
sequence length at all.

BibTeX - Entry

@InProceedings{andreev:DagSemProc.06111.19,
  author =	{Andreev, Alexander E.},
  title =	{{The optimal sequence compression}},
  booktitle =	{Complexity of Boolean Functions},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6111},
  editor =	{Matthias Krause and Pavel Pudl\'{a}k and R\"{u}diger Reischuk and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2006/602},
  URN =		{urn:nbn:de:0030-drops-6025},
  doi =		{10.4230/DagSemProc.06111.19},
  annote =	{Keywords: Compression, partial boolean function}
}

Keywords: Compression, partial boolean function
Collection: 06111 - Complexity of Boolean Functions
Issue Date: 2006
Date of publication: 09.10.2006

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