  We describe the correction procedure for Analog-to-Digital Converter (ADC)
differential non-linearities (DNL) adopted in the Bayesian end-to-end
BeyondPlanck analysis framework. This method is nearly identical to that
developed for the official LFI Data Processing Center (DPC) analysis, and
relies on the binned rms noise profile of each detector data stream. However,
rather than building the correction profile directly from the raw rms profile,
we first fit a Gaussian to each significant ADC-induced rms decrement, and then
derive the corresponding correction model from this smooth model. The main
advange of this approach is that only samples which are significantly affected
by ADC DNLs are corrected. The new corrections are only applied to data for
which there is a clear detection of the non-linearities, and for which they
perform at least comparably with the DPC corrections. Out of a total of 88 LFI
data streams (sky and reference load for each of the 44 detectors) we apply the
new minimal ADC corrections in 25 cases, and maintain the DPC corrections in 8
cases. All these correctsion are applited to 44 or 70 GHz channels, while, as
in previous analyses, none of the 30 GHz ADCs show significant evidence of
non-linearity. By comparing the BeyondPlanck and DPC ADC correction methods, we
estimate that the residual ADC uncertainty is about two orders of magnitude
below the total noise of both the 44 and 70 GHz channels, and their impact on
current cosmological parameter estimation is small. However, we also show that
non-idealities in the ADC corrections can generate sharp stripes in the final
frequency maps, and these could be important for future joint analyses with
HFI, WMAP, or other datasets. We therefore conclude that, although the existing
corrections are adequate for LFI-based cosmological parameter analysis, further
work on LFI ADC corrections is still warranted.
