Test: Information Theory & Coding - Electronics and Communication Engineering (ECE) MCQ

The entropy of the system is

or

Now, rate of outcome r= 16 outcomes/sec (Given)

∴ The rate of information R is

Minimum distance in hamming code = 3.
The minimum distance of a Hamming code is always 3. This property allows Hamming codes to detect up to two-bit errors and correct single-bit errors within a block of data. The minimum distance is not directly related to the block length or rate but is a characteristic of the Hamming code's design.

According to Shannon-Hartley faw, the channel capacity is expressed as

Thus, if signal power is more, bandwidth will be less and vice-versa. Thus, assertion is a true statement. Reason is also a true statement because the rate of information that can be transmitted depends on bandwidth and signal to noise power. Thus, both assertion and reason are true but reason is not the correct explanation of assertion.

We know that the differential entropy of x is given by

Using the given probability density function, we have:

for

a = 1, H(x) = log₂ 1 = 0

(1 - p)ⁿ + np{ 1 - p)^n-1 = Required probability
(Here, n = no. of bits and p = probability) ∴  Required probability

We know that channel capacity is

Since channel capacity remains constant, therefore

The entropy of the system is

Channel capacity is