Aiming at Gaussian channel with power constraint P. A gap exists between the channel capacity and the highest achievable rate of equiprobable uniformly spaced signal. Based on the Box-Muller transform

a method of constructing APSK constellation with equiprobable signaling（ BM-APSK） that achieve the Gaussian capacity as the number of constellation points goes to infinity is proposed. The Gaussian channel is used to simulate the satellite communication environment

and the rate-free code coding and decoding technology is combined with the BM-APSK modulation. The experimental results show that the actual decoding start length is the same as the theoretical length condition when the decoding is calculated by the channel capacity

which indicates that the channel capacity have a good estimation of the initial starting code rate when the actual communication system is decoded.