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Structure and properties of strong prefix codes of pictures

Published online by Cambridge University Press:  28 May 2015

MARCELLA ANSELMO ,
DORA GIAMMARRESI  and
MARIA MADONIA
MARCELLA ANSELMO
Affiliation:
Dipartimento di Informatica, Università di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy Email: [email protected]
DORA GIAMMARRESI
Affiliation:
Dipartimento di Matematica, Università di Roma ‘Tor Vergata,’ Via della Ricerca Scientifica, 00133 Roma, Italy Email: [email protected]
MARIA MADONIA
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125 Catania, Italy Email: [email protected]
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Abstract

A set X ⊆ Σ** of pictures is a code if every picture over Σ is tilable in at most one way with pictures in X. The definition of strong prefix code is introduced. The family of finite strong prefix codes is decidable and it has a polynomial time decoding algorithm. Maximality for finite strong prefix codes is also studied and related to the notion of completeness. We prove that any finite strong prefix code can be embedded in a unique maximal strong prefix code that has minimal size and cardinality. A complete characterization of the structure of maximal finite strong prefix codes completes the paper.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 2: Special Issue: XIV ICTCS , February 2017 , pp. 123 - 142
Copyright
Copyright © Cambridge University Press 2015 

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