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Andreev, Alexander E.

The optimal sequence compression

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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

  author =	{Alexander E. Andreev},
  title =	{The optimal sequence compression},
  booktitle =	{Complexity of Boolean Functions},
  year =	{2006},
  editor =	{Matthias Krause and Pavel Pudl{\'a}k and R{\"u}diger Reischuk and Dieter van Melkebeek},
  number =	{06111},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Compression, partial boolean function}

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

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