Markoff Statistical Model Quiz

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Questions and Answers

What is the formula for joint entropy in terms of conditional entropy and individual entropies?

  • H(X, Y) = H(X) - H(Y)
  • H(X, Y) = H(X) + H(Y)
  • H(X, Y) = H(X|Y) + H(Y) (correct)
  • H(X, Y) = H(Y|X) + H(X)

What is the main objective of the Shannon-Fano algorithm?

  • Channel decoding
  • Modulation
  • Source encoding (correct)
  • Error correction

What does the Shannon-Hartley theorem determine the capacity of?

  • Rayleigh fading channel
  • Binary channel
  • AWGN channel
  • Gaussian channel (correct)

In the Shannon-Fano algorithm, how are symbols sorted based on their frequencies?

<p>From most frequent to least frequent (D)</p> Signup and view all the answers

What do symbols in the first part of the list get assigned in the Shannon-Fano algorithm?

<p>Binary digit 0 (B)</p> Signup and view all the answers

What is a key step in applying the Shannon-Fano algorithm?

<p>Recursively dividing lists based on frequency (D)</p> Signup and view all the answers

What is the formula for the information rate of Markoff sources?

<p>R = rH (C)</p> Signup and view all the answers

Which type of entropy is defined as the average entropy of each state in Markoff sources?

<p>Marginal Entropy (C)</p> Signup and view all the answers

What is the relation between joint entropy and conditional entropy in terms of mutual information?

<p>$H(X,Y) = H(Y) + H(X/Y)$ (D)</p> Signup and view all the answers

What does the mutual information I(X;Y) of a channel represent?

<p>Difference between initial and final uncertainty (B)</p> Signup and view all the answers

Which property of mutual information states that I(X;Y) equals H(X) minus H(X/Y)?

<p>$I(X;Y) = H(X) - H(X/Y)$ (A)</p> Signup and view all the answers

What type of communication channel has both input and output as sequences of symbols?

<p>Discrete communication channel (C)</p> Signup and view all the answers

What is the unit of information as defined in the text?

<p>Bits (B)</p> Signup and view all the answers

When is entropy zero?

<p>When the probability of one symbol is zero (D)</p> Signup and view all the answers

What happens to the amount of information coming from a source in a statistically dependent sequence?

<p>It decreases (D)</p> Signup and view all the answers

What does entropy measure?

<p>The average amount of information conveyed by a message (B)</p> Signup and view all the answers

In a statistically independent sequence, what is true about the occurrence of symbols at different time intervals?

<p>The occurrence of a symbol at one time interval is independent of other time intervals (D)</p> Signup and view all the answers

What is the equation to calculate the total information content of a message consisting of N symbols?

<p>$N \cdot log (1/Pk)$ (C)</p> Signup and view all the answers

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