Question

a source has two symbols ??? s1 and s2. the probability of s2 is half that of s1. the duration of the s1 is 0.2 and the s2 is 0.4 seconds. what is the information rate of the source (in bits/sec) ?

Answer 1

1.) The probabilities :

Let the probability of S₁ be x.

The probability of S₂ will be 0.5x

The sum of their probabilities is equal to 1 hence :

x + 0.5x = 1

1.5x = 1

x = 1/1.5 = 2/3

Therefore probability of :

S₁ = 2/3

S₂ = 1/3

2.) Average information per symbol

Let the average information per signal be H(x).

H(x) = P(S₁) × log₂ (1/P(S₁)) + P(S₂) × log₂ (1/P(S₂))

= 2/3 × log₂(3/2) + 1/3 × log₂(3)

= 2/3 × 0.58505 + 1/3 × 1.5851 = 0.9184

= 0.9184 bits /symbol

3.) Average Symbol time

= 2/3 × 0.2 + 1/3 × 0.4 = 0.26667

Rate = 1/0.26667 = 3.74995

= 3.74995 symbols per second

Now we want the rate in bits per second. We get it as follows.

3.74995 × 0.9184 = 3.444 bits

Rate = 3.444 bits per second.