A random coding bound for fixed convolutional codes of rate 1/n

Author

Seguin, Gerald

Author_Institution

Dept. of Electr. & Comput. Eng., R. Mil. Coll. of Canada, Kingston, Ont., Canada

Volume

40

Issue

5

fYear

1994

fDate

9/1/1994 12:00:00 AM

Firstpage

1668

Lastpage

1670

Abstract

We show that the ensemble average of the block error probability for the ensemble of terminated rate 1/n fixed convolutional codes, used on the binary symmetric channel with a maximum likelihood decoder, is bounded by exp₂-NE_r(1-K/N), where N=(L+m)n is the block length, L being the message length, K the constraint length, and E _r() is the random coding exponent for block codes. Hence, E _r(1-K/N)>0 for H(p)<K/N⩽1, where H() is the binary entropy function and p is the cross-over probability of the binary symmetric channel

Keywords

block codes; coding errors; convolutional codes; decoding; entropy; error statistics; maximum likelihood estimation; probability; telecommunication channels; binary entropy function; binary symmetric channel; block codes; block error probability; block length; constraint length; cross-over probability; fixed convolutional codes; maximum likelihood decoder; message length; random coding bound; random coding exponent; Block codes; Channel coding; Convolutional codes; Councils; Entropy; Error probability; Maximum likelihood decoding; Military computing; Polynomials; Viterbi algorithm;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.333890

Filename

333890