Title :
A random coding bound for fixed convolutional codes of rate 1/n
Author_Institution :
Dept. of Electr. & Comput. Eng., R. Mil. Coll. of Canada, Kingston, Ont., Canada
fDate :
9/1/1994 12:00:00 AM
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-NEr(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;
Journal_Title :
Information Theory, IEEE Transactions on
