# Group 2 - andChainRule Overview another...

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Entropy of Symbol Blocks  and Chain Rule What is it in particular?

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Overview The entropy of symbol blocks considers  the information content of a block of  symbols rather than one symbol after  another. In this consideration, the entropy is a joint  entropy where its value depends on the  joint probability of the symbols in the  block. Reference:  . Pearson, 1999.
Overview If the symbols in the sequence (or block)  are statistically independent, the source is  called a "memoryless source," meaning it  doesn't "remember" from one time to the  next what symbols it has previously  emitted.

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Overview The Chain Rule for Entropy says that the  entropy for a symbol block is equal to the  entropy of the first symbol in the alphabet  plus the entropy of the second symbol in  the alphabet given the first symbol, and so  on, through the entropy of the last symbol  given all symbols in the alphabet before  that. [H(A 0 , A 1 , . .., A (n-1) ) = H(A 0 ) + H(A 1 |A 0 + H(A 2 |A 0 , A 1 ) + . .. + H(A (n-1) |A 0 , . .., A (n-2) )].
Overview Since the entropy of source B given  source A is less than or equal to the  entropy of source B, the entropy of an  entire symbol block is less than or equal  to the entropy of an entire alphabet (from  which all the symbols in the symbol block  are drawn); but they are equal only if the  source is memoryless.

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## This note was uploaded on 07/24/2011 for the course EEL 3531 taught by Professor Llewelyn during the Spring '09 term at University of Florida.

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Group 2 - andChainRule Overview another...

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