tut2 - entropy for equiprobable source output 2 Binary...

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EE4212 Information and Coding Tutorial 2 1. Binary memoryless source (BMS) is a discrete memoryless source (DMS) with output alphabet u = {0,1} with probability P (0) = p and P (1) = 1 -p. Binary entropy function H ( u ) is defined as the entropy of a BMS. (i) Find the general expression of H ( u ) in terms of p . (ii) Prove that H ( u ) is symmetric about p = ½, i.e., H ( u ) | p = H ( u ) | 1 - p . (iii) A BMS is called a binary symmetric source (BSS) if p = ½. Find the value of H ( u ) when p = ½ and prove that it is a maximum of H ( u ). (i.e., maximum
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Unformatted text preview: entropy for equiprobable source output) 2. Binary symmetric channel (BSC) is a discrete memoryless channel (DMC) with input/output alphabet set u = {0,1} and conditional probabilities of the form P (0|1) = P (1|0) = p P (0|0) = P (1|1) = 1 - p (i) Express channel capacity C of a BSC in terms of p . Show that C = 1 -H ( u ). (ii) Show that C | p = C | 1 - p . (iii) Find the values of C when p = 0, ½ & 1. What can be concluded about the channel when p is at the above values?...
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