On the capacity and codes for the Z-channel

Let p be the 1 to 0 bit error probability and h(p)=-p log₂ p-(1-p) log₂ (1-p). The capacity of the Z-channel is given by C_Z=log₂ (1+(1-p)p^p(1-p)/). For small p, it is shown that C_Z≈1-(1/2)h(p) (vs., C_BS(p)=1-h(p) for the binary symmetric channel). Coding schemes are also given that almost achieve the Z-channel capacity.