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The following table gives the frequencies of the letters of the English language (includin...

The following table gives the frequencies of the letters of the English language (including the blank for separating words) in a particular corpus.

blank

18.3%

r

4.8%

y

1.6%

e

10.2%

d

3.5%

p

1.6%

t

7.7%

l

3.4%

b

1.3%

a

6.8%

c

2.6%

v

0.9%

o

5.9%

u

2.4%

k

0.6%

i

5.8%

m

2.1%

j

0.2%

n

5.5%

w

1.9%

x

0.2%

s

5.1%

f

1.8%

q

0.1%

h

4.9%

g

1.7%

z

0.1%

(a) What is the optimum Huffman encoding of this alphabet?

(b) What is the expected number of bits per letter?

(c) Suppose now that we calculate the entropy of these frequencies

(see the box in page 143). Would you expect it to be larger or smaller than your answer above? Explain.

(d) Do you think that this is the limit of how much English text can be compressed? What features of the English language, besides letters and their frequencies, should a better compression scheme take into account?

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