On unique, multiset, and set decipherability of three-word codes

Author

Blanchet-Sadri, F.

Author_Institution

Dept. of Math. Sci., North Carolina Univ., Greensboro, NC, USA

Volume

47

Issue

5

fYear

2001

fDate

7/1/2001 12:00:00 AM

Firstpage

1745

Lastpage

1757

Abstract

The concepts of unique decipherability (UD), multiset decipherability (MSD), and set decipherability (SD) of codes were developed to handle some special problems in the transmission of information. In unique decipherability, different sequences of codewords carry different information. In multiset decipherability, the information of interest is the multiset of codewords used in the encoding process so that order in which transmitted words are received is immaterial. In set decipherability, it is the set of codewords that is relevant information so the order and the multiplicity of words are immaterial. Lempel (1986) showed that the UD and MSD properties coincide for two-word codes and conjectured that every three-word MSD code is a UD code. Guzman (1995) showed that the UD, MSD, and SD properties coincide for two-word codes and conjectured that these properties coincide for three-word codes. In this paper, we answer both conjectures positively for all three-word codes {C₁, C₂, C₃} satisfying |C₁|=|C₂|⩽|C₃|. Our procedures are based on techniques related to dominoes

Keywords

codes; decoding; set theory; MSD code; MSD property; SD property; UD code; UD property; codeword sequences; dominoes; encoding; information transmission; multiset decipherability; set decipherability; three-word codes; unique decipherability; Automata; Combinatorial mathematics; Decoding; Encoding; Formal languages; Helium; Source coding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.930915

Filename

930915