NIELIT 2021 Dec Scientist B - Section B: 67

Question

The channel capacity of a noise free channel having $\text{M}$ symbols is given by :

• A. $\text{M}$
• B. $2^{\text{M}}$
• C. $\log \text{M}$
• D. None of these

Answer 1

C. log M …

 

Noise free channel is both lossless and deterministic,

i.e. Noise free channel = Loseless + deterministic ….

For loseless channel,

H(x|y) = 0 ..

I(x ; y) = H(x)

So, Cs = max H(x) = log2 m ..

 

Where, m = numbers of symbols in X ...

For deterministic channel

H(y|x) = 0..

I(x ; y) = H(y)

So, Cs = max H(y) = log2 n ..

 

Where, n = number of symbols in Y

Hence, for Noiseless channel,

we can write: I(x ; y) = H(x) = H(y),

i.e. Cs = log2 m = log2 n …