{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw4soln

# hw4soln - EE 670 Homework#4 Solution Prof Uf Tureli Stevens...

This preview shows pages 1–2. Sign up to view the full content.

EE 670 : Homework #4 Solution Prof. Uf Tureli, Stevens Institute of Technology email/tel/fax: [email protected], 201.216.5603/8246 Note: Cover and Thomas, Q. 8.6,8.12,9.1,9.3 1. Question: Using two channels at once. Consider two discrete memoryless channels ( X 1 , p ( y 1 | x 1 ) , Y 1 ) and ( X 2 , p ( y 2 | x 2 ) , Y 2 ) with capacities C 1 , and C 2 respectively. A new channel ( X 1 × X 2 , p ( Y 1 | x 1 ) × p ( y 2 | x 2 ) , Y 1 times Y 2 ) is formed in which x 1 ∈ X 1 and x 2 ∈ X 2 are simultaneously sent, resulting in y 1 , y 2 . Find the capacity of this channel. Solution: Suppose we are given two channels, ( X 1 , p ( y 1 | x 1 ) , Y 1 ) and ( X 2 , p ( y 2 | x 2 ) , Y 2 ) which we can use simultaneously. We can define the product channel as the channel, ( X 1 × X 2 , p ( y 1 , y 2 | x 1 , x 2 ) = p ( y 1 | x 1 ) p ( y 2 | x 2 ) , Y 1 × Y 2 ) To find the capacity of the product channel, we must find the distribution of p ( x 1 , x 2 ) on the input alphabet X 1 × X 2 that maximizes I ( X 1 , X 2 ; Y 1 , Y 2 ). Since the joint distribution: p ( x 1 , x 2 , y 1 , y 2 ) = p ( x 1 , x 2 ) p ( Y 1 | x 1 ) p ( y 2 | x 1 ) , Y 1 X 1 X 2 Y 2

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}