Tutorial Activity 2 - MH 8300 Tutorial Activity 2 Hamming...

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MH 8300 Tutorial Activity 2 Hamming Code Decoding Set A Group Members Name NTU Email ID Marks : /2
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MH 8300 Tutorial Activity 2 Hamming Code Decoding Set A Question 1. (Hamming Decoding Algorithm) Figure 1: Hamming Code Decoder Definition. The Hamming code of length 7 is the set { ( x 1 , x 2 , x 3 , x 4 , x 1 + x 2 + x 4 , x 1 + x 2 + x 3 , x 1 + x 3 + x 4 ) : x i ∈ { 0 , 1 }} . (a) Determine the following codewords from the first four coordinates. x 1 x 2 x 3 x 4 x 5 x 6 x 7 1 1 0 1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 0 1 0 1 (b) For each of the following subset of coordinates of a Hamming codeword, determine if the number of 1s is always odd / always even / sometimes odd, sometimes even . { x 1 , x 2 , x 3 , x 4 } { x 1 , x 2 , x 4 , x 5 } { x 1 , x 2 , x 3 , x 6 } { x 1 , x 3 , x 4 , x 7 } (c) Using Qn 1(b), propose a simple method to determine if a received word belongs to the Hamming code.
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(d) Use Qn 1(b) & 1(c) to determine the following Hamming codewords and fill in the blanks. x 1 x 2 x 3 x 4 x 5 x 6 x 7 0 0 0 1 1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 1 0 0 0 1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 0 0 0 1 0 (e) Given a received word of y = y 1 y 2 y 3 y 4 y 5 y 6 y 7 , where y = 1011101 , use the Hamming decoding algorithm to decode y . A 1 should be coloured A 2 should be coloured A 3 should be coloured So we should flip Hence, determine the output codeword of the Hamming code decoder.
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