  We numerically study the performance of the displacement based quantum
receiver for the discrimination of weak 3- and 4-phase-shift keyed (PSK)
coherent state signals. We show that due to the nontrivial asymmetry of the
receiver structure, optimization of the prior probability increases the mutual
information and achieves sub-shot-noise limit discrimination. Moreover, we
estimate the cutoff rate for a 4-PSK signal and confirm that the prior
probability optimization shortens the code length for a given decoding error
criterion. Such consideration for the asymmetric channel matrix is essential in
a study of the compassable quantum receiver.
