A new proof of the channel coding theorem via hypothesis testing in quantum information theory

A new proof of the direct part of the quantum channel coding theorem is shown based on a standpoint of quantum hypothesis testing. A packing procedure of mutually noncommutative operators is carried out to derive an upper bound on the error probability, which is similar to Feinstein´s lemma in classical channel coding. The upper bound is used to show the proof of the direct part along with a variant of Hiai-Petz´s theorem in hypothesis testing.