  The next generation of space-based mm-wave telescopes, such as JAXA's
LiteBIRD mission, require focal planes with thousands of detectors in order to
achieve their science goals. Digital frequency-domain multiplexing (dfmux)
techniques allow detector counts to scale without a linear growth in wire
harnessing, sub-Kelvin refrigerator loads, and other scaling problems. In this
paper, we describe the Digital Signal Processing (DSP) firmware executed in the
design's FPGA. This firmware is responsible for synthesizing bias tones,
performing dynamic feedback control of the bolometer voltage bias and/or
Superconducting Quantum Interference Device (SQUID) nuller currents,
demodulating and decimating bolometer channels into science data, and streaming
the results for storage and eventual downlink. We describe how this firmware
has been tailored for LiteBIRD, including the control path, improvements to
power- and resource-efficiency, the addition of radiation-mitigation functions,
and the integration of new bolometer biasing schemes that may help mitigate
mission-specific design challenges. This paper is a companion piece to the
description of the electronics platform in which the firmware operates.
