A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _______
Maximum Entropy Calculation for 16 Symbols
Entropy measures the average uncertainty or information content of a source. The maximum entropy occurs when all possible symbols are equally likely.
Entropy Formula
The entropy $H$ (in bits) for a source with $n$ equally likely symbols is given by the formula:
$ H = \log_2(n) $
Where:
- $n$ is the number of possible symbols (alphabet size).
Applying the Formula
In this problem:
- The alphabet size, $n$, is 16.
Substitute the value of $n$ into the formula:
$ H = \log_2(16) $
Calculating the Result
To find the value of $\log_2(16)$, we need to determine what power of 2 equals 16.
- $2^1 = 2$
- $2^2 = 4$
- $2^3 = 8$
- $2^4 = 16$
Therefore, $\log_2(16) = 4$.
The maximum achievable entropy is 4 bits.
Important Questions from Information Theory
The main processing functions of information system are given below. Arrange them in sequencing order:
(A) Process transaction
(B) Maintain master file
(C) Process enquiry
(D) Process report
(E) Process interactive supper applications
Choose the correct answer from the options given below:
- Consider a discrete memoryless source with an alphabet of four source symbols.
$s(t)$ is a multi-level (-1, 0, +1, +2) signal representing a long sequence of random symbols from the above source which is generating $10^4$ symbols per second.
Which of the following options is the correct value of equivalent Nyquist bandwidth of $s(t)$? - Match items in List – I with items in List – II and select the correct answer from the code given below :
List – I List – II a. The Screening Hypothesis 1. George A. Akerlof b. Job Market Signalling 2. K.J. Arrow c. The problem of moral hazard in the case of medical insurance 3. M. Spencer d. The market for lemons 4. Paul W. Miller and Paul A. Volcker
Codes : The random variable $X$ takes values in $\{-1, 0, 1\}$ with probabilities $P(X = -1) = P(X = 1)$ and $\alpha$ and $P(X = 0) = 1 - 2\alpha$, where $0 < \alpha < \frac{1}{2}$. Let $g(\alpha)$ denote the entropy of $X$ (in bits), parameterized by $\alpha$. Which of the following statements is/are TRUE?
An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $p_1 = p_4 = 0.125$ and $p_2 = p_3$. The information rate (bits/sec) of the message source is ____________
