HW8-solution

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

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Rate 1/3 Covolutional Code 3 1 2 + + Work with this figure to find output to input as asked
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Finite State Machine Model Outputs associated with state transitions 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 01 001
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Viterbi Decoding for Last Question Input x to be found fromreceived r: 111 111 111 111 111 111 We run the VA until i=6 with the flushing 00 flushed out The output are filled in the green boxes. The accumulated metric are computed, with red backward arrows. We back back from brown circle following the arrows. The decoded x is: 1 1 1 1 0 0 00 0 10 01 11 000 111 010 001 100 110 101 011 3 0 6 3 2 1 3 4 3 2 4 3 4 3 5 4 5 4 i=0 i=1 i=3 i=4 i=5 i=6 i=2 6 5 6 5
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Actually we have 2 equal distance solutions! Note that the state s=01 at i=5 had a tie from s=10 and s=11. The shortest path to that state could have come from 10 also! If we back trace to 10 instead, we would have the decoded x instead as 1 0 0 1 0 0 rather than 1 1 1 1 0 0. As we shall see later that d free =6. With accumulated metric equal to 6, we have
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This note was uploaded on 11/01/2009 for the course EEE 455 taught by Professor Hui during the Spring '09 term at ASU.

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

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