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# problem1 - UNIVERSITY OF CALIFORNIA SAN DIEGO Electrical...

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UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 259B - Winter Quarter 2011 Probabilistic Coding Problem Set #1 Due Thursday, January 13, 2011 1. Recall Shannon’s capacity formula for the band-limited, power-limited Gaussian channel: C = W log 2 (1 + SNR ) where the signal-to-noise ratio (SNR) is given by SNR = P ave /N 0 W. (a) Draw a detailed plot of C versus W , assuming fixed average signal power P ave and two- sided noise spectral density N 0 2 . What is the limiting value of capacity as the bandwidth approaches infinity? Interpret your result. (b) In class we rewrote the capacity formula in terms of the average SNR per bit E b /N 0 and then solved for E b /N 0 in terms of the spectral efficiency C/W . Give the details of the calculation of E b /N 0 corresponding to the limiting case of zero spectral efficiency, and provide your interpretation of the result. 2. This problem will familiarize you with properties of generator matrices and physical encoder realizations for convolutional codes. Consider the following polynomial generator matrices for

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• Spring '11
• Song
• Coding theory, Convolutional code, convolutional, distance df ree, time-varying trellis diagram, free distance df

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problem1 - UNIVERSITY OF CALIFORNIA SAN DIEGO Electrical...

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