lecture17

# lecture17 - Lecture Outline Channel Coding Reading 1 Review...

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Lecture Outline Channel Coding Reading: 1. Review of Error Probability M PSK: ) 2 2 cos( ) ( ) ( M m t f t g t s c m π + = , m = 0, 1, 2, …, M -1 M FSK: ) ) ( 2 cos( ) ( ) ( t f m f t g t s c m + = , m = 0, 1, 2, …, M -1. Typically, T E t g s 2 ) ( = for T t 0 . Energy per symbol is s E . Energy per bit is M E E s b 2 log = Noise variance per dimension in signal space has variance 2 0 2 N m = σ Each signal point is at distance s E from origin. M PSK M FSK Message error probabilities M PSK M FSK M QAM M N E Q P s M sin 2 2 0 = 0 N E Q P s b - - = 0 2 ) 1 ( 6 ) 1 ( 2 N M E Q M M P av M Seems that error probability goes to zero only if we use very large SNR. Shannon theory: We can transmit at a data rate up to channel capacity while keeping error probability as small as we like. (Quite a surprise!) For a passband channel corrupted by AWGN, Shannon derived channel capacity:

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lecture17 - Lecture Outline Channel Coding Reading 1 Review...

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