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# The optimal sequence compression

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DagSemProc.06111.19.pdf
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• 11 pages

## Cite As

Alexander E. Andreev. The optimal sequence compression. In Complexity of Boolean Functions. Dagstuhl Seminar Proceedings, Volume 6111, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)
https://doi.org/10.4230/DagSemProc.06111.19

## 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.
##### Keywords
• Compression
• partial boolean function

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