The multiple coding gain with two criteria in an attenuated quantum channel

Recently, the capacity of an attenuated quantum channel which is a model of a long distance optical fiber channel was derived. This capacity is in principle achieved by a continuous modulation and a random coding. However, a continuous modulation and a random coding are not practical. Therefore, we need discussion about capacity used for more practical modulation and coding. In this paper, we show characteristics of both information and error probability criteria for an attenuated channel using M-ary PSK modulation and pseudo-cyclic codes.