  We consider coding schemes for channels with non-uniform inputs (NUI), where
standard linear block codes can not be applied directly. We show that
multilevel coding (MLC) with a set of linear codes and a deterministic mapper
can achieve the information rate of the channel with NUI. The mapper, however,
does not have to be one-to-one. As an application of the proposed MLC scheme,
we present a rateless transmission scheme over the binary symmetric channel
(BSC).
