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by: Deondre Ullrich


Deondre Ullrich
Rice University
GPA 3.54


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Class Notes
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This 1 page Class Notes was uploaded by Deondre Ullrich on Monday October 19, 2015. The Class Notes belongs to ELEC 535 at Rice University taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/224979/elec-535-rice-university in Electrical Engineering & Computer Science at Rice University.

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Date Created: 10/19/15
Two Versions of Capacity In digital transmission systems bits are represented by the analog signals 507 and 517 both having duration 739 When this signaling strategy is used over an additive white Gaussian noise channel the probability of error in decoding the transmission of equally likely bits is given by where rszh If E E the signal s energy and QM is the tail integral of the stan dardized Gaussian probability density function l 3f T6 22 In Imposing an energy constraint on the two signals E50 E5 g EU the smallest achievable probability of error results when 91 f s07 and each signal has the largest possible energy From a discrete channel viewpoint this encoding analog transmission decoding implementa tion can be accurately modeled as a binary symmetric channel BSC with a cross over proba bility equal to I 1 a Find an expression for and plot the capacity of this channel as a function of the signal to noise ratio We also have an expression for the capacity of an additive white Gaussian noise channel having bandwidth W I C It log I b1tss Here I is the signal s power The issue becomes reconciling the two ways of computing capacity b Before performing any calculations which way of computing capacity yields the larger answer or are they the same 0 Calculate expressions for the two capacities so that they can be compared Plot them to determine how they vary with signal to noise ratio


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