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.

翻译：猜测随机加性噪声解码（GRAND）近年来受到广泛关注，其中有序可靠度比特GRAND（ORBGRAND）因其对软信息的有效利用和易于硬件实现的特性而尤为突出。已有研究表明，在对极输入下，ORBGRAND在加性高斯白噪声信道中几乎可达信道容量。本文首先将ORBGRAND可达速率的分析扩展至具有一般输出条件概率分布的无记忆二进制输入比特信道。该分析结果也为理解ORBGRAND可达速率与信道互信息之间的差距提供了理论洞见。作为该分析的应用，我们研究了比特交织编码调制（BICM）下ORBGRAND的可达速率。数值结果表明，对于BICM而言，ORBGRAND可达速率与信道互信息之间的差距通常很小，从而验证了ORBGRAND适用于高阶编码调制信道的可行性。