Low Complexity Decoding Algorithms for Rate Compatible Modulation

Rate compatible modulation (RCM) has high spectrum efficiency and achieves seamless and blind rate adaptation in wide range of channel conditions. However, due to many convolution operations at symbol nodes, the belief propagation decoding algorithm of RCM has a high level of computational complexity. In this paper, we investigate the low complexity algorithms for fast decoding of RCM. Instead of computing the outgoing messages at symbol nodes via multi-level convolutions, we first design a novel two-level computing structure (2L-RCM) for symbol nodes in the probability-domain, each level is composed of one set of multiplications followed by one set of additions. Based on 2L-RCM, we derive Log-2L-RCM decoding algorithm in the log-domain, which converts the multiplications and additions of 2L-RCM into additions and Jacobian logarithms, respectively. Furthermore, we propose some approximate algorithms to reduce the complexity of Jacobian logarithms. In particular, the improved Max-Log-RCM (IMax-Log-RCM) algorithm obtains good performance-complexity trade-off. The simulation results and the numerical analyses show that IMax-Log-RCM achieves only 0.3-dB worse decoding performance than the original decoding algorithm with much fewer additions.