ass3 - SYSC 5504 ELG 6154 Carleton University Department of...

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Carleton University SYSC 5504 Department of Systems and Computer Engineering ELG 6154 Principles of Digital Communications Fall 2010/11 Assignment #3 Due on Tuesday, November 16, 2010 1. Suppose the following signalling scheme is used for transmission over an AWGN channel with single-sided noise power spectral density of N 0 . - ± 6 ? φ 0 ( t ) φ 1 ( t ) 3 A AA 3 A 3 A A A 3 A s 000 s 001 s 111 s 110 s 100 s 101 s 011 s 010 (a) Carefully draw the boundaries of the optimal decision regions in the signal space diagram. Be precise. (b) Use the union bound to Fnd a tight upper bound the probability of a symbol error. Express your answer in terms of N 0 and the average transmitted energy per symbol ( E s ). 2. ±ind the capacity of the following binary channel, expressing your answer in terms of a rational number. 0 1 0 1 XY 1/2 1/2 1/4 3/4 3. Suppose the linear ( n, k ) block code deFned by the generator matrix G = 100101 010110 001011 is used for error detection. Transmission is carried out over an AWGN channel with BPSK with E b / N 0 equal to 7 dB.
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ass3 - SYSC 5504 ELG 6154 Carleton University Department of...

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