We propose a massive parallel decoding GRAND framework. The framework introduces two novelties: 1. A likelihood function for $M$-QAM demodulated signals that effectively reduces the symbol error pattern space from $\mathcal{O}(5^{N/\log_2 M})$ down to $\mathcal{O}(4^{N/\log_2 M})$; and 2. A massively parallel matrix-vector multiplication for matrices of size $K\times N$ ($K \leq N$) that performs the multiplication in just $\mathcal{O}(\log_2 N)$ steps. We then apply the proposed GRAND approach to codes and operational modulation techniques used in the current 5G NR standard. Our framework is applicable not just to short codewords but to the full range of codewords from 32 bits up to 1024 bits used in the control channels of 5G NR. We also present simulation results with parity-check matrices of Polar codes with rate $R=1/2$ obtained from the 5G NR universal reliability sequence.

翻译：我们提出了一种大规模并行解码的GRAND框架。该框架包含两项创新：1. 针对$M$-QAM解调信号的似然函数，将符号错误模式空间从$\mathcal{O}(5^{N/\log_2 M})$有效缩减至$\mathcal{O}(4^{N/\log_2 M})$；2. 针对规模为$K\times N$（$K \leq N$）的矩阵，实现仅需$\mathcal{O}(\log_2 N)$步的大规模并行矩阵向量乘法。随后，我们将所提出的GRAND方法应用于当前5G NR标准中采用的编码及操作调制技术。该框架不仅适用于短码字，更覆盖5G NR控制信道中使用的32比特至1024比特全范围码字。我们还展示了基于5G NR通用可靠性序列得到的Polar码（码率$R=1/2$）校验矩阵仿真结果。