5assignment - ECEN 455 Assignment 5 Due Monday Reading...

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ECEN 455: Assignment 5 Due Monday 11/14/11 Reading: Required: First Course in Digital Communications Chapter 6 Problems: 1. Calculate the probability of message error P B for a 12-bit data sequence encoded with a (24 , 12) linear block code when the probability of a channel symbol error is 10 - 3 . Assume that the code corrects all 0-bit, 1-bit, and 2-bit error patterns and that it corrects no other error patterns. 2. Calculate the improvement in the message error probability P B relative to uncoded trans- mission for a (24 , 12) double-error correcting linear block code. Assume coherent BPSK modulation is used and that E b /N 0 = 10 dB. 3. Consider a (7 , 4) binary code whose generator matrix is G = 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 . (a) Find all codewords in the code. (b) What is the error-correcting capability of the code? What is the error-detecting capa- bility the code? (c) Find the parity-check matrix H of the code.
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