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Guessing random additive noise decoding (GRAND) has received widespreadattention recently, and among its variants, ordered reliability bits GRAND(ORBGRAND) is particularly attractive due to its efficient utilization of softinformation and its amenability to hardware implementation. It has beenrecently shown that ORBGRAND is almost capacity-achieving in additive whiteGaussian noise channels under antipodal input. In this work, we first extendthe analysis of ORBGRAND achievable rate to memoryless binary-input bitchannels with general output conditional probability distributions. Theanalytical result also sheds insight into understanding the gap between theORBGRAND achievable rate and the channel mutual information. As an applicationof the analysis, we study the ORBGRAND achievable rate of bit-interleaved codedmodulation (BICM). Numerical results indicate that for BICM, the gap betweenthe ORBGRAND achievable rate and the channel mutual information is typicallysmall, and hence suggest the feasibility of ORBGRAND for channels withhigh-order coded modulation schemes.

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