lecture18

# lecture18 - EE455/591 C hanne C l oding Re ading Re S ction...

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

EE455/591 EE455/591 Channel Coding Channel Coding Reading: Read Section 9.5 pages 601-606 Reading: Read Section 9.5 pages 601-606 Review: MSK. Shannon Channel Capacity Review: MSK. Shannon Channel Capacity Topics: Topics: 1. 1. Random Coding Random Coding 2. 2. Hamming Coding Hamming Coding 3. 3. Algebraic Coding Algebraic Coding

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

View Full Document
Note: for Q channel, delay by ½T turns the cosine pulse shape into a sine pulse shape. OQPSK with Half Cosine (HC) pulse shape (± depends on data) Review: MSK = OQPSK with Half Cosine Pulse (2Es/T) X cos(2 π f c t) X sin(2 π f c t) I channel data a i Q channel data b i Delay ½ T h(t) (2Es/T) h(t) ) ] 4 1 [ 2 cos( 2 ) 2 2 cos( 2 ) 2 sin( ) 2 sin( 2 ) 2 cos( ) 2 cos( 2 ) ( t T f T E T t t f T E t f T t T E t f T t T E t y c b c b c b c b ± = ± = ± ± = π h(t)= (2E b /T)cos( π t/2T) -½ T t ½ T ≤ ≤ Frequency shifts ± ½ Δ f = ± ¼(1/T) of MSK (Twice in [0,T])
Per Claude Shannon, we can reach zero error utopia! No need to repeat message in a dumb manner! We remove error altogether provided that the data transmission rate R (bits/s) is less than channel capacity C! For example, consider sending sequence of 0 or 1 over a Binary Symmetric Channel (BSC): The channel turns a 0 into a 1, or a 1 into a 0 with probability p The input-output of the BSC can be represented as: Shannon shows that for this BSC: C=1-H(p) The binary entropy function is H(p)= -p log 2 p – (1-p)log 2 (1-p) For p=0.1, C=0.469 bit/symbol; for p=0, C=1 bit/symbol; for p=½, C=0 How can we achieve capacity by channel coding? Input X

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.

## This note was uploaded on 11/01/2009 for the course EEE 455 taught by Professor Hui during the Spring '09 term at ASU.

### Page1 / 12

lecture18 - EE455/591 C hanne C l oding Re ading Re S ction...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online