Question

If the rows of channel matrix are all equal to each other, then the channel capacity is

• A. \(0\)
• B. \(1\)
• C. \(\infty\)
• D. Equal to bandwidth of channel

Hint:

If every row of a channel matrix is identical, the output is independent of the input and the channel capacity becomes zero.

Answer 1

The Correct Option is A

Concept: Channel capacity measures the maximum information that can be transmitted reliably through a channel.

Step 1: Interpret equal rows of channel matrix.
If all rows are identical, the output distribution becomes independent of the transmitted input symbol. Thus the receiver cannot distinguish which input symbol was sent.

Step 2: Evaluate mutual information.
Since output gives no information about input, \[ I(X;Y)=0 \]

Step 3: Compute channel capacity.
Channel capacity is \[ C=\max I(X;Y) \] Hence, \[ C=0 \]

Step 4: Final Answer.
\[ \boxed{C=0} \] Therefore, \[ \boxed{\text{Correct Option (A)}} \]