A quantum version of Feinstein´s Theorem and its application to channel coding

In this paper, a quantum version of Feinstein´s theorem is developed. This is then used to give a completely self-contained proof of the direct channel coding theorem, for transmission of classical information through a quantum channel with Markovian correlated noise. Our proof does not rely on the Holevo-Schumacher-Westmoreland (HSW) theorem. In addition, for the case of memoryless channels, our method yields an alternative proof of the HSW Theorem