Title :
Good error detection codes satisfy the expurgated bound
Author :
Hashimoto, Takeshi
Author_Institution :
Dept. of Electron. Eng., Univ. of Electro-Commun., Tokyo, Japan
Abstract :
A q-nary (n,k) linear code is said to be proper if, as an error-detection code, the probability of undetectable error, Pud , satisfies Pud⩽q-(n-k) for completely symmetric channels. We show that a proper code, as an error-correction code, satisfies the expurgated bound on the decoding error probability for a class of channels with the associated Bhattacharyya distance being completely symmetric. Known results on the undetectable error probability then immediately imply that the expurgated exponent is satisfied by many codes which are regarded as good codes
Keywords :
channel coding; decoding; error correction codes; error detection codes; error statistics; linear codes; probability; telecommunication channels; Bhattacharyya distance; completely symmetric channels; decoding error probability; error detection codes; error-correction code; expurgated bound; proper code; q-nary linear code; undetectable error; undetectable error probability; Decoding; Error correction codes; Error probability; Information theory; Linear code;
Conference_Titel :
Information Theory, 1995. Proceedings., 1995 IEEE International Symposium on
Conference_Location :
Whistler, BC
Print_ISBN :
0-7803-2453-6
DOI :
10.1109/ISIT.1995.550330