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# Problem 4. This problem concerns the code based on the 31hat game. Here the message should be decomposed into blocks of length 3} 5 = 25. Suppose...

This problem concerns the code based on the 31-hat game. Here the message should be decomposed into blocks of length 31 − 5 = 26. Suppose that one of the 26-blocks in the starting message has eight 0s followed by eleven 12s, followed by four 0s, then a 1 and finally two 0's.

That is: M = 00000000111111111110000100.

(a) Find its associated L-node, which is the code word which will be transmitted.

(b) Suppose that in the transmission, there is an error in the 17th character. Give a detailed account of the calculations made by the decoder to recover the original message.

The below images are an example from last year, just with the values changed, still confused though please help!

Problem 4. This problem concerns the code based on the 31—hat game. Here the message
should be decomposed into blocks of length 3} — 5 = 25. Suppose that one of the 26-blocks in the starting message has. seven 0’s followed by eleven 1’s, followed by six 0’s, then a l and
ﬁnallyr a 0. That is: M = 00000001111111111100000010. (3) Find its associated L-nodc, which is the code word which will be transmitted. (1)) Suppose that in the transmission, there is an error in the 17th character. Give a detailed
account of the calculations made by the decoder to recover the original message. Solution. (3.) The codeword will be C = x.320340001'30001111:1:l5111111100000010. There- fore,
0 0 0 0 D l
l U U U l 0
H0: 1 +£1 0 +333 0 +224 1 +Ig D +3313 0
1 0 1 U D U
0 1 0 0 U 0 and so we need an = 3:“; = 0 and \$2 = \$4 = 1'3 = 1. The transmitted code word is C = 0 l 0 1 000 1 0001111 0 111111100000010. 3.1 32 34 310 (b) In this case, the code word received would be . oops C = 0 1 0 1 000 1 0001111 0 0 11111100000010. 21 I: 34 316 Then, the decoder would compute m &quot;'1': ||
Hcccw and so the decoder would know to ﬂip back the 17th character.

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