a4 - CSE 489/589 Homework Assignment 4 Due at the end of...

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CSE 489/589 Homework Assignment 4 Due at the end of class on Wed, Dec 08. * November 23, 2010 Problem 1. Recall that the CRC code allows us to compute the redundancy string R to be appended to the data string D given the generator string G . (a) Suppose D = 111010101100 and G = 10011 . What is R as a binary string? Show your work using the polynomial division method I’ve shown in class. (b) Show that the CRC code can detect any odd number of bit errors if the generator polynomial G ( x ) contains a factor ( x + 1) . (In practice, the CRC-1 code uses G ( x ) = x + 1 itself. The CRC-12 code used in some telecom systems uses G ( x ) = x 12 + x 11 + x 3 + x 2 + x + 1 = ( x + 1)( x 11 + x 2 + 1) which has a ( x + 1) -factor.) Problem 2. Consider the Clos fabric design C (3 , 3 , 2) shown in figure 2. We have shown in class that Figure 1: The Clos network C (3 , 3 , 2) the network is rearrangeably non-blocking (RNB) because m = n = 3 in this case. RNB means every valid 1-1 mapping from inputs to outputs can be realized. RNB also means that a new request from a free input to a free output can always be routed through the fabric if we are allowed to rearrange existing routes. Instructor HN thinks that, perhaps, if the algorithm for finding routes is smarter then we might
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