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
For any binary (n, h) linear code with minimum distance (2t + 1) or greater \(n - h \ge {\log _2}\left[ {\mathop \sum \limits_{i = 0}^α \left( {\begin{array}{*{20}{c}} n\\ i \end{array}} \right)} \right]\) where α is:
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:
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 ____________
- 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 $s(t)$?
