Question

A source generates symbols with probabilities (0.5, 0.25, 0.25) at a rate of 300 symbols per second. The most efficient source encoder would have average bit rate:

• A. 150 bits/sec
• B. 300 bits/sec
• C. 450 bits/sec
• D. 600 bits/sec

Hint:

Minimum bits = Entropy × Symbol rate.

Answer 1

The Correct Option is B

Concept: Minimum average bit rate is given by: \[ R = H \times \text{symbol rate} \]

Step 1: Compute entropy \[ H = -[0.5\log_2 0.5 + 0.25\log_2 0.25 + 0.25\log_2 0.25] \] \[ = -[0.5(-1) + 0.25(-2) + 0.25(-2)] \] \[ = 0.5 + 0.5 + 0.5 = 1.5 \text{ bits/symbol} \]

Step 2: Compute bit rate \[ R = 1.5 \times 300 = 450 \text{ bits/sec} \] \[ \therefore \text{Correct answer is (C)} \]