We consider the design of cooperation coding schemes for a two-user multi-access channel (MAC). In particular, we consider two block Markov coding schemes, namely, the multiplexed coding and the superposition coding. Although the fully multiplexed (FMP) coding outperforms the superposition coding in theory, it is difficult to implement with practical error-correction codes. We therefore introduce a partially multiplexed (PMP) coding scheme for code rate R < 0.5, and propose a simplified superposition coding scheme. The outage analysis shows that these cooperation schemes provide significant gains over the non-cooperative MAC in the low-power regime when the bandwidth W . We then propose a PMP code design using irregular repeat accumulate (IRA) codes. The design method can be extended to build the lowrate PMP codes using irregular repeat zigzag Hadamard (IRZH) codes, a new class of capacity achieving low-rate codes. Simulation results demonstrate that the block Markov multiplexed c...