HW6 - 1 EE 7615 Problem Set 6 Due 11,22,10 1 Please attempt...

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1 EE 7615 Problem Set # 6 Due: 11,22,10 1) Please attempt each problem on a new page. 2) Show all your work clearly. 1) The following code is used to transmit a binary source with rate R b across an AWGN channel with noise power spectral density of N 0 2 . s 1 = q E c (+1 , +1 , +1 , +1) , s 2 = q E c ( - 1 , - 1 , - 1 , - 1) s 3 = q E c (+1 , +1 , - 1 , - 1) , s 4 = q E c ( - 1 , - 1 , +1 , +1) s 5 = q E c (+1 , - 1 , +1 , - 1) , s 6 = q E c ( - 1 , +1 , - 1 , +1) s 7 = q E c (+1 , - 1 , - 1 , +1) , s 8 = q E c ( - 1 , +1 , +1 , - 1) a) Find the input blocklength K , output blocklength L and the code rate. b) Diagram a complete communication system that uses this code to transmit over the AWGN channel. Your system should include an optimum receiver. Be sure to specify the operation of each block. c) Use the union bound to obtain an upper bound to block error probability. d) Find an expression for the block error probability (what kind of signal set is this?) e) Find the E b N 0 needed to get block error probability of 10 - 5 (you can use the results from the book). f) Repeat part (1e) using the upper bound in part (1c).
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