ORBGRAND: Achievable Rate for General Bit Channels and Application in BICM

Guessing random additive noise decoding (GRAND) has received widespread attention recently, and among its variants, ordered reliability bits GRAND (ORBGRAND) is particularly attractive due to its efficient utilization of soft information and its amenability to hardware implementation. It has been recently shown that ORBGRAND is almost capacity-achieving in additive white Gaussian noise channels under antipodal input. In this work, we first extend the analysis of ORBGRAND achievable rate to memoryless binary-input bit channels with general output conditional probability distributions. The analytical result also sheds insight into understanding the gap between the ORBGRAND achievable rate and the channel mutual information. As an application of the analysis, we study the ORBGRAND achievable rate of bit-interleaved coded modulation (BICM). Numerical results indicate that for BICM, the gap between the ORBGRAND achievable rate and the channel mutual information is typically small, and hence suggest the feasibility of ORBGRAND for channels with high-order coded modulation schemes.