Constellation labeling and compression for M-ary symbols with unequal a priori probability

It is well known that the binary reflected Gray code (BRGC) is the optimal labeling for binary symbols with equal a priori probability. However, the BRGC is not a good candidate for those transmitted symbols without equal a priori probability. In this paper, we propose a novel constellation labeling principle and a concept of constellation compression for M-ary symbols with unequal a priori probability. The simulation results verify that the proposed methods can provide some labeling gain and compression gain without any additional computational cost.