Tutorial Activity 1

Tutorial Activity 1 - MH 8300 Tutorial Activity 1...

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MH 8300 Tutorial Activity 1 Principles of Error Correction Set A Group Members Name NTU Email ID Marks : /2

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MH 8300 Tutorial Activity 1 Principles of Error Correction Set A Question 1. Let the code C 1 = { 00000 , 11011 , 11100 , 00111 } . Sender sends the codeword 11011 across a channel and the receiver received 11001 . The receiver decodes 11001 using Minimum Distance Decoding to obtain the word 11011 . (a) How many errors have occurred? (b) What is the distance between the sent and received word? (c) The communication model is shown below. Fill in the blanks. Figure 1: Communication Model (d) Find the ball with radius r = 1 for each of the codewords in C 1 . S 1 (00000) = S 1 (11011) = S 1 (11100) = S 1 (00111) = (e) Do any of the balls S 1 (00000) , S 1 (11011) , S 1 (11100) , S 1 (00111) intersect? If yes, produce two balls that intersect. (f) If r = 2 , will the balls intersect? If yes, produce two balls that intersect. If not, explain why. (g) Using Qn 1(f), provide a pair of sent codeword and received word such that the Minimum Distance Decoding produces a codeword different from the sent codeword. Fill up the boxes with your answers.
Question 2. Let the code C 2 = { 000000 , 001101 , 010011 , 011110 , 100110 , 101011 , 110101 , 111000 } .

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