Question

Consider a noisy AWGN (Additive White Gaussian Noise) communication channel with a bandwidth of 12 KHz. Is it possible to transmit reliably over this channel at a bit rate of 150 Kbps with an SNR (Signal to Noise Ratio) of 35 dB? Justify your answer

Answer 1

In real life, we don't have noiseless channels. There is always some noise in channels. Shannon capacity is used to determine the theoretical highest data rate for a noisy channel.

We have, Shannon capacity = Bandwidth * log₂(1 + SNR)

Here, SNR is the signal to noise ratio.

In this question, we have bandwidth = 12 KHz and SNR = 35 dB. Let's calculate the shannon capacity of this channel. Plugging in the values, we get Shannon capacity = 62.04 Kbps.

SNR (dB) = 10 log₁₀(SNR). From this we get the value of SNR to be 10^3.5 = 3162.27.

So the maximum possible bit rate for this channel is equal to 139.53 kbps. Hence, we cannot transmit over this channel at a bit rate of 150 kbps.

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