{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture6

# Lecture6 - Colorado State University Ft Collins ECE 516...

This preview shows pages 1–4. Sign up to view the full content.

1 Colorado State University, Ft. Collins Fall 2008 ECE 516: Information Theory Lecture 6 September 16, 2008 Recap: Theorem: (data processing inequality) If Z Y X , then ( ) ( ) Z X I Y X I ; ; Corollary: In particular, if ( ) Y g Z = , then ( ) ( ) ( ) Y g X I Y X I ; ; Corollary: If Z Y X ( ) ( ) Z X H Y X H | | Corollary: If Z Y X , then ( ) ( ) Z Y X I Y X I | ; ; 2.10 Fano’s Inequality Theorem: (Fano’s Inequality) ( ) ( ) ( ) Y X H P P H e e | 1 log + X Fano’s inequality lower-bounds e P 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 ( ) X log e e P P H + ( ) Y X H | Minimum e P Theorem: If ( ) 0 | = Y X H , then X is a function of Y . Corollary: (Relaxation of Fano’s Inequality) ( ) X log 1 | Y X H P e

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document