What is the maximum capacity of a perfectly noiseless channel whose bandwidth is 120H2, in which the values of the data transmitted may be indicated by any one of the 10 different amplitudes.

Ans: A given communication system has a maximum rate of information C known as the channel capacity.

If the information rate R is less than C, then one can approach arbitrarily small error probabilities by using intelligent coding techniques.

To get lower error probabilities, the encoder has to work on longer block of signal data, this entails longer delays and higher computation requirements.

Thus, if R $\leq$ C then transmission may be accomplished without error in the presence of noise.

The band width and the noise power place a restriction upon the rate of information that can be transmitted by a channel, it may be shown that in a channel which is disturbed by a white Gaussian noise, one can transmit information at a rate of C bits per second, where C is the channel capacity and is expressed as

$c = Blog_2 \ (1+\frac{S}{N})$

Where

B $\rightarrow$ channel bandwidth in $H_2$

S $\rightarrow$ Signal power

N $\rightarrow$ Noise power.

According to Hartley law.

$C = 2B \ log_2 \ N$

$= 2 \times 120 \times 1og_2 \ (10)$

C = 797.26 bits/seconds.