{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sample_final

# sample_final - EE 376A/Stat 376A Prof T Weissman...

This preview shows pages 1–3. Sign up to view the full content.

EE 376A/Stat 376A Information Theory Prof. T. Weissman Friday, March 17, 2006 Practice Final Problems These problems are sampled from a couple of the actual finals in previous years. 1. ( 20 points) Errors and erasures. Consider a binary symmetric channel (BSC) with crossover probability p . - - · · · · · · · ·3 Q Q Q Q Q Q Q Qs 1 0 1 0 1 - p 1 - p p p A helpful genie who knows the locations of all bit flips offers to convert flipped bits into erasures. In other words, the genie can transform the BSC into a binary erasure channel. Would you use his power? Be specific. 2. (20 points) Code constraint. What is the capacity of a BSC( p ) under the constraint that each of the codewords has a proportion of 1’s less than or equal to α , i.e., 1 n n X i =1 X i ( w ) α, for w ∈ { 1 , 2 , . . . , 2 nR } . (Pay attention when α > 1 / 2.) 1

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

View Full Document
3. ( 20 points) Partition. Let ( X, Y ) denote height and weight. Let [ Y ] be Y rounded off to the nearest pound. (a) Which is greater I ( X ; Y ) or I ( X ; [ Y ]) ? (b) Why? 4. ( 20 points) Amplify and forward. We cascade two Gaussian channels by feeding the (scaled) output of the first channel into the second. · ¶‡ - - ? - ? · ¶‡ q - - · ¶‡ - ? X 1 P X 2 P Y 1 Y 2 Z 1 N (0 , N ) α Z 2 N (0 , N ) Thus noises Z 1 and Z 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

sample_final - EE 376A/Stat 376A Prof T Weissman...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online