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Unformatted text preview: ± . (Note that P b ( E ) ≤ P ( E ).) 2. If R > C , then no system whatsoever can have arbitrarily small error probability. In fact as K → ∞ , P ( E ) → 1 for any system. Properties of channel capacity: We have C = W log 2 (1 + P WN ) bits/sec. Then R < C = ⇒ R W < log 2 (1 + P RN R W ) 1 or since P RN = E b N , 2 R W < 1 + E b N R W which gives E b N > 2 R W-1 R W This is the R W vs. E b N graph we have plotted in the handouts. Note that 1. As P → ∞ , C → ∞ . 2. As W → ∞ , C → P N Ln (2) . Thus as W → ∞ , the orthogonal signals are optimal. For orthogonal signal set if R < P N Ln (2) , and K → ∞ , we can get arbitrarily small P ( E ). 2...
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- Fall '11
- Signal Processing, Bit rate, Shannon–Hartley theorem, spectrum, Telecommunication theory