  Bi-modal (respectively, multi-modal) constrained coding refers to an encoding
model whereby a user input block can be mapped to two (respectively, multiple)
codewords. In current storage applications, such as optical disks, multi-modal
coding allows to achieve DC control, in addition to satisfying the runlength
limited (RLL) constraint specified by the recording channel. In this work, a
study is initiated on bi-modal fixed-length constrained encoders. Necessary and
sufficient conditions are presented for the existence of such encoders for a
given constraint. It is also shown that under somewhat stronger conditions, one
can guarantee a bi-modal encoder with finite decoding delay.
