Shannon's :calculating simple uncertainty

  • Thread starter Calmstorm
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In summary, the formula for measuring uncertainty at the transmitter when transmitting a two-tone image line-by-line is H(X)= - W{ Pilog(Pi) } -B{Qj log (Qj)}. This formula is based on Shannon's uncertainty formula and takes into account the number of white and black pixels in the sequence and their respective probabilities. The length of the transmitted sequence for a square NxN image would depend on the number of pixels in the image.
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Calmstorm
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Homework Statement



If I were to use a two-tone image e.g. fax, and were to transmit it line-by-line, where the the individual pixels which make up the line were independent of each other, how would I measure the uncertainty at the transmitter? Also what would the length of the the transmited sequence be if the image was a square NxN image?



The Attempt at a Solution



I think the uncertainty is H(X)= - W{ Pilog(Pi) } -B{Qj log (Qj)}
where:
W=number of white pixels in the sequence
Pi=probability of a white pixel.
B=number of black pixels in seqence
Qj=probability of a black pixel.

Any ideas would be very helpful...thank you in advance!
 
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  • #2
How did you come up with the formula "H(X)= - W{ Pilog(Pi) } -B{Qj log (Qj)}"?
 
  • #3


well the general formula of shannon's uncertainty is:

H(x)= -pi log(base 2) pi summed over all i, since I have 2 outcomes i.e a black or white pixel i have used Pi=probab. of white and Qj=probab. of black

also sorry about the cross-posting, it won't happen again.
 

1. What is Shannon's uncertainty formula?

Shannon's uncertainty formula, also known as Shannon's entropy formula, is a mathematical formula developed by Claude Shannon in the 1940s to measure the amount of uncertainty or information contained in a message or data. It is used in fields such as information theory, communication theory, and statistics.

2. How is Shannon's uncertainty formula calculated?

Shannon's uncertainty formula is calculated by taking the negative sum of the probability of each possible outcome multiplied by the logarithm of that probability. It is written as H = -Σp(x)logp(x), where H represents the uncertainty or entropy and p(x) represents the probability of each possible outcome.

3. What does Shannon's uncertainty formula measure?

Shannon's uncertainty formula measures the amount of uncertainty or information contained in a message or data. It is often used to quantify the amount of randomness or unpredictability in a system or event. The higher the uncertainty, the more unpredictable the system or event is.

4. What is the significance of Shannon's uncertainty formula?

Shannon's uncertainty formula has significant implications in fields such as communication and information theory. It is used to calculate the efficiency of data compression techniques and to measure the capacity of communication channels. It also has applications in cryptography, data mining, and machine learning.

5. What are the limitations of Shannon's uncertainty formula?

Shannon's uncertainty formula assumes that all possible outcomes are equally likely and independent of each other. It also does not take into account the context or meaning of the information, only its probability. Therefore, it may not accurately measure uncertainty in complex systems or events where these assumptions do not hold.

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