not using upper limits in the analysis can be understood as our overall detection rate is lower than 50%. Therefore we emphasize that the faint end deviation from empirical relation with high statistical significance level is only observed in the sample of detected objects, which may potentially be biased in a subtle way. The discrepancy between the empirical relation and the full sample result (i.e. with censored data) is only marginal at the faint end. We are not able to make solid conclusion whether the empirical FRC is already broken or not.

In summary, LVHIS galaxies are consistent with a tight linear FRC, though a marginal offset from the empirical relation [$q=2.34$, @2001ApJ...554..803Y] is observed at faint end. Our detections suggest a slightly super-linear FIR-radio relation, consistent with measured larger $q$ for faint galaxies (mostly dwarf galaxies). Our detected dwarf galaxies clearly deviate from the empirical relation.

FIR/radio flux densities and star formation rate {#subsec:sfr}
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It is known that both FIR and radio luminosities are correlated with star formation rates for massive non-AGN galaxies . And indeed, it is the basis for FRC studies on galactic scale. For LVHIS galaxies, we calculate the star formation rate from the GALEX 