This paper presents a practical solution that provides uncoordinated access to a family of BinaryInput Binary-Output Multiple-Access Channels (BIBO-MACs), including the OR channel. We propose a solution using Interleaver-Division Multiple Access (IDMA) with single-user decoding. This solution features Nonlinear Trellis Codes (NLTC), that permit low-complexity decoding in support of high-speed applications. We present a design technique for nonlinear trellis codes with controlled ones densities for binary asymmetric channels (BACs), and in particular the Z-Channel, that arise in the BIBO-MAC when single-user decoding is used. Union bound techniques that predict the performance of these codes are also presented. Information theoretical calculations of the achievable sum-rate of these channels are presented as well. Simulation results and from a working FPGA implementation verify the performance and feasibility of the proposed algorithm.