Question

An Ideal power limited communication channel with additive white Gaussian noise is having 4 kHz band width and Signal to Noise ratio of 255. The channel capacity is:
1. 8 kilo bits / sec
2. 9.63 kilo bits / sec
3. 16 kilo bits / sec
4. 32 kilo bits / sec

Answer 1

Correct Answer - Option 4 : 32 kilo bits / sec

Concept:

Shannon’s channel capacity is the maximum bits that can be transferred error-free. Mathematically, this is defined as:

\( C = B~{\log _2}\left( {1 + \frac{{\rm{S}}}{{\rm{N}}}} \right){\rm{bits}}\)

B = Bandwidth of the channel

\(\frac{S}{N}=\) Signal to noise ratio

Note: In the expression of channel capacity, S/N is not in dB.

Calculation:

Given B = 4 kHz and SNR = 255

Channel capacity will be:

\({\rm{C}} = 4~{\log _2}\left( {1 + 255} \right){\rm{kbits}}/{\rm{sec}}\)

C = 32 kbits/sec