Capacity bounds for the Z channel

We present a new achievable rate region for the discrete memoryless Z channel (DM-ZC) using Marton coding with rate splitting. The region is shown to include previously known achievable rate regions. Secondly we study a class of degraded Z channels, the bijective degraded Z channel (BDZC). An outer bound for the BDZC is proved, which is shown to meet the inner bound for the deterministic settings. For the Gaussian Z channel with weak crossover link, we show that if Gaussian inputs are optimal then a coding scheme based on Marton coding without rate splitting achieves to within half a bit per real dimension from the boundary of the capacity region.