Problem 9.2
Let the event S=sk denote the emission of symbol sk by the source, Hence,
I(sk) = log2 bits
P
I(sk) bits 1.322 1.737 2.322 3.322
Problem 9.3
Entropy of the source is
H(S)
pologz -1 + pllogz -1 + p210g2 3- + P310g2 1
P0 P1 P2
Z.
_ J
1
Problem 8.18
For the problem at hand, we have M = N = 2. Therefore,
M - N+l = l
and so the weight subspace W is onedimensional. We thus have the following representation for
the action of the antenna array:
C2
(Interferer)
Onedimensional
0
H(S) = 2 Pk 1032[1]
, k=0
K1 1
= _ log2K = log2K
k=0
The coding efciency is therefore
n = H(S) = 10g2K
13 1o
For 11:1, we have
10 = 10g2K
To satisfy this requirement, we choose
K = 210
where 10 is an integer.
Problem 9.10
A prex code is dened as a