Abstract — We consider coding schemes for channels with nonuniform 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). I