Which of the following statements are correct?

(A) A given source will have maximum entropy if the produced are statistically independent

(B) As the bandwidth approaches infinity, the channel capacity becomes zero.

(C) For binary transmission the baud rate is always equal to bit rate

(D) The mutual information of a channel with independent input and output is constant

(E) Nat is a unit of information

Choose the correct answer from the options given below:

(1) (A) and (E) only

(2) (A) and (B) only

(3) (C) and (E) only

(4) (A), (D) and (E) only

Concept:- Let us analyze every statement.

Statement (A):- A given source will have maximum entropy if messages produced are equally probable. So statement A given is wrong.

Statement (B):- From Shannon's channel capacity theorem:-

\(C = B{\log _2}\left[ {1 + \frac{S}{N}} \right]\)

Where N = N₀ B

If B → ∞

\(C = \mathop {\lim }\limits_{{\rm{B}} \to \infty } {\rm{B}}{\log _2}\left[ {1 + \frac{{\rm{S}}}{{\rm{N}}}} \right] = 1.44\frac{{\rm{S}}}{{{{\rm{N}}_0}}}\)

Statement B is wrong.

Statement (c):-

Band rate \(=\frac{{{\rm{Bit\;rate}}}}{{{{\log }_2}{\rm{M}}}}\)

For binary transmission M = 2

Band rate \(=\frac{{{\rm{Bit\;rate}}}}{{{{\log }_2}2}}\)

Band rate = Bitrate

Statement (C) is correct.

Statement (D):- it is False

Mutual information I (X, Y) = H (X) – H (X/Y)

= H (Y) – H (Y/X)

For binary symmetric channel

I (X, Y) is dependent on source

Probabilities it is not constant.

Statement (E):- It is correct.

Nat, bit, or Hartley is unit of Information,