  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.
