Topic: Communication Systems
We wish to transmit a digital voice at 32 Kbps through a communication channel having bandwidth of 3000 Hz. The received signal to noise power ratio is 30 dB. State which of the following statement is true?
- A. To transmit data error-free through this channel, channel equalizer circuit should be used at the receiver.
- B. To transmit data error-free through this channel, the voice signal should be compressed by 2.
- C. To transmit data error-free through this channel, a channel code with coding gain of 3 dB should be used.
- D. It is not possible to transmit data error-free through this channel.
Answer: D. It is not possible to transmit data error-free through this channel.
Explanation: $R = 32\text{ kbps}$, $B = 3000\text{ Hz}$, $SNR = 30\text{ dB} = 1000$.
Using Shannon's channel capacity: $C = B\log_2(1+SNR) = 3000\log_2(1001) \approx 3000 \times 9.967 \approx 29.9\text{ kbps}$.
As $C < R$, it is not possible to transmit data error-free through the channel.