Problem 2 - Information Theory Consider the following channel X, DI . a) Calculate entropy of...
3. The Nyquist formula informs us about the capacity in a noiseless channel and the Shannon's formula informs us of the capacity of a noisy channel. In practice, we mostly encounter noisy channels so why do we still need the Nyquist formula? [2 marks] Nyquist formula: Bit rate 2 x bandwidth x log2 L Shannon formula: C-Bx log: (1+ SNR) a. Answer:
Let us consider a binary symmetric channel, as shown in Figure 1, where the probabilities of the input X are Pr(X-0] = m and Pr(X-1-1-m, and the error probability during the transmission from X and Y is p. 0 1-p Figure 1: A typical binary symmetric channel, where the input is X and the output is Y. a) Given that p-1/3 and m-3/4, find H(X), H (Y), H (YİX), and 1(X:Y). (8 marks) b) Still given p = 1 /3....
Information bits {0,1} are sent over binary symmetric communication channel with conditional probabilities P(YX) as shown below. The priory probabilities of 0 and 1 are P(X=0)=0.3, P(X=1)=0.7. The error probability {=0.2. transmitter X 0 1-€ receiver Y 0 ៩ w 1-€ a) If 1 is transmitted, what are the probabilities of receiving 0 and 1? P(Y=0|X=1) and P(Y=1X=1) b) If 0 is received, what are the probabilities that 0 and 1 information bit is transmitted? P(X=0 Y=0) and P(X=1 Y=0)
1. Suppose log10(x) = 25. Calculate log2 (x) by calculating x and then calculating log2 (x). Be sure to show the instructions you gave to R, as well as the value of x and the final result. 2. Find log2 (x), as in (1) without calculating x, by multiplying by something. 3. Suppose log2 (x) = 25. Calculate log10(x) for y = 25 by calculating x and then calculating log10(x). Be sure to show the instructions you gave to R,...
In information theory Shannon entropy is defined by H(x) = -Sum(P(x)*log(P(x)) where P is probability mass function of random variable x, and log to base 2. Given loaded die with P(6)=0.5 and P(1)=P(2)=P(3)=P(4)=P(5), compute entropy of observed rolls 654266. Note: To answer the question you do not need to know any more information about Shannon entropy.
tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y. tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y.
Please help me these questions of "Principles of Communications" subject. Thanks in advance! Problem 2: PCM system (40 points)coo h Consider a polar binary PCM system with number of bits per sample v 8 and the 4 KHz. Assumed that the channel is AWGN. voice bandwidth a) Assumed that one voice signal is transmitted using above PCM system, find the bit rate at the output of PCM transmitter and the minimum channel bandwidth. b) Assumed that 24 voice signals are...
8. There are three urns. Urnl contains 2 white and 3 black marbles, Urn2 contains 3 white and 2 black marbles, and Urn3 contains 1 white and 4 black marbles. First, the urn is selected equally likely, than a ball is drawn from the urn. a) We know that a white marble is chosen. What is the probability that the marble came from Urn2? b) We know that a black marble is chosen. What is the probability that the marble...
The following periodic signal is input to an ideal low pass filter of bandwidth 25 KHz. 1. x(t) 2 a) Determine the average power of the signal x(t). b) If T 0.1 ms, give the output of the filter as a function of time, y(t) e) Determine the average power of the signal y(t) d) Determine the bandwidth of the signal y(), considered as a baseband signal. e) Now assume that the signal x() (with T-0.1 ms) is instead input...
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...