On the size of transducers for bidirectional decoding of prefix codes

Laura Giambruno; Sabrina Mantaci

RAIRO - Theoretical Informatics and Applications (2012)

  • Volume: 46, Issue: 2, page 315-328
  • ISSN: 0988-3754

Abstract

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In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X. We find some bounds of such a number of states in relation with different notions of “size” of X. In particular, we give an exact formula for the number of states of transducers associated to maximal prefix codes. We moreover consider two special cases of codes: maximal uniform codes and a class of codes, that we name string-codes. We show that they represent, for maximal codes, the extreme cases with regard to the number of states in terms of different sizes. Moreover we prove that prefix codes corresponding to isomorphic trees have transducers that are isomorphic as unlabeled graphs.

How to cite

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Giambruno, Laura, and Mantaci, Sabrina. "On the size of transducers for bidirectional decoding of prefix codes." RAIRO - Theoretical Informatics and Applications 46.2 (2012): 315-328. <http://eudml.org/doc/277835>.

@article{Giambruno2012,
abstract = {In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X. We find some bounds of such a number of states in relation with different notions of “size” of X. In particular, we give an exact formula for the number of states of transducers associated to maximal prefix codes. We moreover consider two special cases of codes: maximal uniform codes and a class of codes, that we name string-codes. We show that they represent, for maximal codes, the extreme cases with regard to the number of states in terms of different sizes. Moreover we prove that prefix codes corresponding to isomorphic trees have transducers that are isomorphic as unlabeled graphs.},
author = {Giambruno, Laura, Mantaci, Sabrina},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Variable length codes; prefix codes; bilateral decoding; transducers; variable-length codes},
language = {eng},
month = {4},
number = {2},
pages = {315-328},
publisher = {EDP Sciences},
title = {On the size of transducers for bidirectional decoding of prefix codes},
url = {http://eudml.org/doc/277835},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Giambruno, Laura
AU - Mantaci, Sabrina
TI - On the size of transducers for bidirectional decoding of prefix codes
JO - RAIRO - Theoretical Informatics and Applications
DA - 2012/4//
PB - EDP Sciences
VL - 46
IS - 2
SP - 315
EP - 328
AB - In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X. We find some bounds of such a number of states in relation with different notions of “size” of X. In particular, we give an exact formula for the number of states of transducers associated to maximal prefix codes. We moreover consider two special cases of codes: maximal uniform codes and a class of codes, that we name string-codes. We show that they represent, for maximal codes, the extreme cases with regard to the number of states in terms of different sizes. Moreover we prove that prefix codes corresponding to isomorphic trees have transducers that are isomorphic as unlabeled graphs.
LA - eng
KW - Variable length codes; prefix codes; bilateral decoding; transducers; variable-length codes
UR - http://eudml.org/doc/277835
ER -

References

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  1. M.-P. Béal, J. Berstel, B.H. Marcus, D. Perrin, C. Reutenauer and P.H. Siegel, Variable-length codes and finite automata, in Selected Topics in Information and Coding Theory, edited by I. Woungang. World Scientific. To appear.  
  2. J. Berstel and D. Perrin, Theory of Codes. Academic Press (1985).  
  3. J. Berstel, D. Perrin and C. Reutenauer, Codes and Automata. Cambridge University Press (2010).  
  4. A.S. Fraenkel and S.T. Klein, Bidirectional Huffman coding.Comput. J.33 (1990) 296–307.  
  5. L. Giambruno and S. Mantaci, Transducers for the bidirectional decoding of prefix codes, Theoret. Comput. Sci.411 (2010) 1785–1792.  
  6. B. Girod, Bidirectionally decodable streams of prefix code words. IEEE Commun. Lett.3 (1999) 245–247.  
  7. M. Lothaire, Applied combinatorics on words, Encyclopedia of Mathematics and its Applications104(2005).  
  8. D. Salomon, Variable-Length Codes for Data Compression. Springer-Verlag (2007). 

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