QAM32 constellation obtained after decoding with gr-digitalhf |

Using the path metrics of the convolutional decoder it was verified that the whole chain of decoding steps is correct: without puncturing the path metric \(M\) for \(n\) encoded bits at rate \(1/2\) is \(2n\) if there are no errors, so it makes sense to use \(Q=M/2n\) as a measure of data quality. When there is puncturing,

*e.g.*, to rate \(3/4\) with puncturing pattern [11, 10], the expected path metric is \(3.5/4\): three out of four bits are transmitted and the probability for the puncture to be correct is \(1/2\). Therefore in this case \(Q\) has to be rescaled by the factor \(4/3.5=8/7\).
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