Non-adaptive and two-stage coding over the Z-channel

In this paper, we developed new coding strategies for the Z-channel. In particular, we look at the case with two-stage encoding. In this case, the encoder uses noiseless feedback once and adjusts the further encoding strategy based on the previous partial output of the channel. Nevertheless, the developed codes improve the known results with full feedback for small length and 1 error. A tool for the two-stage strategy is the development of a new optimality condition for non-adaptive codes. Finally, we give a new non-adaptive code of length 10 and size 110, which corrects one asymmetric error.