I understand how the hard-decision Viterbi algorithm works, it uses the Hamming distance to calculate branch metrics. But what about soft-decision? Assuming an AWGN channel, QPSK modulation and 8-bit binary-offset format for soft symbols, how do you actually calculate the branch metrics? How does the Viterbi use the extra information it gets with the binary-offset format, e.g. 11110000 means it's a "1" but we're not a 100% sure, so how is the "1110000" part used in calculating the branch metric?

EDIT: I have read the question and answer from QPSK soft decoding, but that was about "how to go from a QPSK symbol to a soft-bit pair" which is a step before entering the Viterbi decoder. I'm asking how to use the soft symbol in binary-offset format to calculate the branch metric.

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  • Possible duplicate of QPSK soft decoding – MBaz Nov 8 at 16:24
  • @MBaz The QPSK soft decoding answer (a nice, but very dense, hard to read answer, by the way) is more about the meaning of soft symbols, as opposed to explaining how one can use the extra "uncertainty" bits to guide the Viterbi algorithm. If it answers that questions, I don't see it. Maybe you could elaborate, if you do, under this question or the other one? – Tomislav Nakic-Alfirevic Nov 8 at 16:52

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