Question

iid source has six letters a; b; c; d; e; f, with probabilities 0:20; 0:20; 0:10; 0:08; 0:08; 0:34, respectively. calculate the codeword of an arithmetic code for encoding the sequence affd. Show all steps in your design

Answer 1

x	cummulative prob. C(x)
a	0.20
b	0.40
c	0.50
d	0.58
e	0.66
f	1.00

for any x its range will be in CF(x) to C(x)

sequence given = a f f d

for a the range is 0.00 to 0.20 (range a = 0.20-0.00 ){refer cummulative freq table}

a f the range = 0.00 + R(a)*C(e) to 0.00 + R(a)*C(f) = 0.132 to 0.20

(R(af)=0.2-0.132 = 0.068)

a f f the range is = 0.132 + R(af)*C(e) to 0.132 + R(af)*C(f) = 0.17688 to 0.2

R(aff) = 0.2 - 0.17688 = 0.02312

a f f d = 0.17688 + R(aff)*C(c) to 0.17688 + R(af)f*C(d) = 0.18844 to 0.1902896

codeword

the range is 0.18844 to 0.1902896 for sequence 'affd'

P.S. (please upvote if you find the answer satisfactory)