Shannons :calculating simple uncertainty

[Calmstorm]

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?

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!

 

[EnumaElish]

Do not cross-post.

 

[tacman]

It's great that you're looking into calculating the uncertainty in your transmission of a two-tone image. Shannon's theory of communication is a fundamental concept in information theory and it can definitely be applied in this scenario.

To measure the uncertainty at the transmitter, you can use the formula H(X) = -∑P(x)logP(x), where P(x) is the probability of a particular pixel value (white or black) in the sequence. This formula takes into account the different probabilities of each pixel value and calculates the overall uncertainty of the sequence.

In your case, for a two-tone image, there are only two possible pixel values (white or black) and their probabilities can be calculated based on the number of white and black pixels in the sequence. So, the length of the transmitted sequence would be the total number of pixels in the image, which would be N x N for a square NxN image.

I hope this helps! Keep exploring Shannon's theory and its applications in information theory. Good luck!