lecture18

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

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

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

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