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HW8-solution

HW8-solution - Rate1/3 C ovolutional Code 1 2 3 Work with...

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Rate 1/3 Covolutional Code 3 1 2 + + Work with this figureto find output to input as asked
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FiniteStateMachineModel Outputs associated with statetransitions State Output 00->00 000 00->10 111 01->00 011 01->10 100 10->01 001 10->11 110 11->01 010 11->11 101 00 10 11 01 000 111 011 100 101 110 010 001
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Viterbi Decoding for Last Question Input x to be found fromreceived r: 111 111 111 111 111 111 Werun theVA until i=6 with theflushing 00 flushed out Theoutput arefilled in the green boxes. Theaccumulated metric arecomputed, with red backward arrows. Weback back from brown circlefollowing the red arrows. Thedecoded x is: 1 1 1 1 0 0 00 0 10 01 11 000 111 010 001 100 110 101 011 111 00 3 10 0 01 11 00 6 10 3 01 2 11 1 111 00 3 10 4 01 3 11 2 111 00 4 10 3 01 4 11 3 111 00 5 10 4 01 5 11 4 111 i=0 i=1 i=3 i=4 i=5 i=6 i=2 00 6 10 5 01 6 11 5 111 000 111 010 001 100 110 101 011 000 111 010 001 100 110 101 011 000 111 010 001 100 110 101 011 000 111 010 001 100 110 101 011 000 111 010 001 100 110 101 011
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Actually we have 2 equal distance solutions! Notethat the states=01 at i=5 had a tiefrom s=10 and s=11.
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