100406-lecture15 - 1 EE522 Communications Theory Spring...

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Unformatted text preview: 1 EE522 Communications Theory Spring 2010 Instructor: Hwang Soo Lee Lecture #15 – Capacity and Channel Coding with Block Codes 2 Announcements ¡ Handout: Lecture #15 Notes 3 Channel Capacity ¡ Let X represent the transmitted symbol at the input to a channel and let Y represent the symbol received at the output to a channel. ¡ If X and Y are related by some probabilistic distribution, then it is possible to define a quantity called channel capacity: where I(X;Y) is the “mutual information” between X and Y. 4 Channel Capacity (continued) ¡ Channel capacity C has units of information rate (either “bits/sec” or “bits/modulation symbol”). ¡ C represents the fastest theoretical rate at which error free transmission is possible over a channel. ¡ This fact is called the “Channel Coding Theorem”. It’s proof is one of the principle results of Information Theory. ¡ We are interested in designing a system to operate as close to this fundamental limit as possible. 5 Channel Capacity of AWGN Channel ¡ For AWGN channel: ¢ = Average signal power ¢ W = Available bandwidth 6 Plot of Capacity for AWGN Channel ¡ Capacity increases with available BW (to a point). ¡ Capacity increases with SNR. 7 Capacity of Binary Symmetric Channel (BSC) ¡ p = probability of error for a binary modulation scheme. 8 Plot of Capacity for BSC ¡ Note that errorless transmission is possible even for nonzero p (just at a slower rate). ¡ Note that curve is symmetrical about p=0.5 9 Can Modulation Alone Achieve Channel Capacity?...
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100406-lecture15 - 1 EE522 Communications Theory Spring...

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