On the capacity and codes for the Z-channel

Let p be the 1 to 0 bit error probability and h(p)=-p log/sub 2/ p-(1-p) log/sub 2/ (1-p). The capacity of the Z-channel is given by C/sub Z/=log/sub 2/ (1+(1-p)p/sup p/(1-p)/). For small p, it is shown that C/sub Z//spl ap/1-(1/2)h(p) (vs., C/sub BS/(p)=1-h(p) for the binary symmetric channel). Coding schemes are also given that almost achieve the Z-channel capacity.