  It is common practice to collect observations of feature and response pairs
from different environments. A natural question is how to identify features
that have consistent prediction power across environments. The invariant causal
prediction framework proposes to approach this problem through invariance,
assuming a linear model that is invariant under different environments. In this
work, we make an attempt to shed light on this framework by connecting it to
the Gaussian multiple access channel problem. Specifically, we incorporate
optimal code constructions and decoding methods to provide lower bounds on the
error probability. We illustrate our findings by various simulation settings.
