  Topological subsystem color codes (TSCCs) are an important class of
topological subsystem codes that allow for syndrome measurement with only
2-body measurements. It is expected that such low complexity measurements can
help in fault tolerance. While TSCCs have been studied over depolarizing noise
model, their performance over the erasure channel has not been studied as much.
Recently, we proposed erasure decoders for TSCCs and reported a threshold of
9.7%. In this paper, we continue our study of TSCCS over the erasure channel.
We propose two erasure decoders for topological subsystem color codes. These
decoders use the technique of gauge fixing where some of the gauge operators of
the subsystem code are promoted to stabilizers. We perform gauge fixing using
4-body and 8-body gauge operators. With partial gauge fixing we obtained a
threshold of 17.7% on a TSCC derived from the square octagon lattice. Using an
order maximal gauge fixing decoder we were able to improve the threshold to
44%. The previously known decoder for TSCC over the erasure channel had a
threshold of 9.7%. We also study the correctability of erasures on the
subsystem codes.
