Rate-compatible modulation (RCM) can achieve adaptive transmission in a variable channel environment. However, there are two problems with conventional RCM. Firstly, there is a large number of four rings in the mapping matrix of the conventional RCM, which blocks the delivery of messages in the decoding. Secondly, in the conventional decoding of RCM, the soft information of the last decoding will be discarded when cyclic redundancy check (CRC) is failed, which decreases the performance significantly. In order to address these two problems, in this paper, we propose a new method to construct a mapping matrix without four rings (MMwoFR) and an improved belief propagation (IBP) algorithm for RCM decoding. On the one hand, by using MMwoFR, the constructed matrix is able to prevent the existence of four rings which have much side influence of reliability performance. On the other hand, the IBP is able to make the most use of the soft information in RCM decoding. Simulation results show that using MMwoFR and IBP can bring at least 12% goodput gain for RCM at the high signal-to-noise ratio (SNR) region while maintaining the same performance in the low and moderate SNR regions. Moreover, complexity analysis shows that the new scheme has comparable complexity compared with a conventional RCM
