  In this letter, we present the Parkes-Siegel formulation for the massive
Abelian $N$$=$$1$ super-{\QED} coupled to a self-dual supermultiplet, by
introducing a chiral multiplier superfield. We show that after carrying out a
suitable dimensional reduction from ($2$$+$$2$) to ($1$$+$$2$) dimensions, and
performing some necessary truncations, the simple supersymmetric extension of
the ${\tau}_{3}$QED$_{1+2}$ coupled to a Chern-Simons term naturally comes out.
