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：随机加性噪声猜解（GRAND）近期受到广泛关注，其变体有序可靠性比特GRAND（ORBGRAND）因有效利用软信息且易于硬件实现而尤为突出。最新研究表明，在反极性输入下的加性高斯白噪声信道中，ORBGRAND几乎能实现信道容量。本文首先将ORBGRAND的可达速率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。该分析结果也有助于理解ORBGRAND可达速率与信道互信息之间的差距。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，ORBGRAND可达速率与信道互信息之间的差距通常很小，从而证明了ORBGRAND在高阶编码调制信道中的可行性。