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X px py y x x xx y y py x y x log x p

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Unformatted text preview: � � ⎛ ⎞ r (x ), ..., P r (x cx PX 1 X |X | ) ⎝ ⎠ � � log � r r r � ) x� ∈X cx PX (x1 ), ..., PX (x|X | PX (x ) � � ∗ (x) PX PY | (y |x) X x∈X y ∈Y ⎛ ⎞ PY |X (y |x) ⎝� ⎠ log r (x� P �) ) Y |X (y |x x� ∈X PX � � ∗ PX (x) PY | (y |x) X x∈X y ∈Y ⎛ � r ⎝ log PX (x� ) x�∈X � �⎞ PY |X (y � |x� ) � �� � � r �� ⎟ � �� y ∈Y PY |X (y |x ) log x�� ∈X PX (x )PY |X (y |x ) ⎟ e ⎠ Convergence of Arimoto-Blahut By considering the K-L distance, we have that � � ∗ x∈X y ∈Y PX (x)PY |X (y |x) �� � ∗ PX (x� )PY |X (y |x� ) � log �x ∈X P r (x�)P (y |x� ) ≥ 0 Y |X x� X ∈X...
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This document was uploaded on 03/19/2014 for the course EECS 6.441 at MIT.

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