This study shows the effectiveness of the simulation probability densi
ty function (p.d.f.) based on the Bhattacharyya bound  from the poi
nt of view of the twisted distribution. As a result, the simulation p.
d.f. related to the Bhattacharyya bound is asymptotically optimal for
the trellis coded modulation scheme under some practical conditions. A
nd the optimality is also confirmed by a numerical example.