Feedback Codes Achieving the Capacity of the Z-Channel

Abstract

Given the 1 to 0 bit error probability, pisin[0, 1], the capacity of the Z-channel is given by C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> =log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (1+p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p/(1-p)</sup> -p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/(1-p)</sup> ). Some new error free feedback coding schemes that achieve the Z-channel capacity are presented.