assign1 - Algorithms in the Real World (15-853), Fall 09...

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Unformatted text preview: Algorithms in the Real World (15-853), Fall 09 Assignment #1 Due: September 17 Complete all problems. You are not permitted to look at solutions of previous year assignments. You can work together in groups, but all solutions have to be written up individually. Problem 1: Conditional Probabilities (10pt) Given the following conditional probabilities for a two state Markov Chain what factor would one save by using the conditional entropy instead of the unconditional entropy? p ( w | w ) = . 95 p ( b | w ) = . 05 p ( w | b ) = . 2 p ( b | b ) = . 8 Problem 2: Arithmetic Codes (10pt) Given the following probability model: Letter p ( a i ) f ( a i ) a .1 b .2 .1 c .7 .3 Decode the 4 letter message given by 00011011010 assuming it was coded using arithmetic coding. Why is this message longer than if we simply had used a fixed-length code of 2 bits per letter, even though the entropy of the set { . 1 , . 2 , . 7 } is just a little more than 1 bit per letter. Note: once you figure out how to do the decoding, it should not take more than fiveletter....
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assign1 - Algorithms in the Real World (15-853), Fall 09...

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