Guessing Random Additive Noise Decoding (GRAND) is a family of hard- and soft-detection error correction decoding algorithms that provide accurate decoding of any moderate redundancy code of any length. Here we establish a method through which any soft-input GRAND algorithm can provide soft output in the form of an accurate a posteriori estimate of the likelihood that a decoding is correct or, in the case of list decoding, the likelihood that the correct decoding is an element of the list. Implementing the method adds negligible additional computation and memory to the existing decoding process. The output permits tuning the balance between undetected errors and block errors for arbitrary moderate redundancy codes including CRCs

翻译：猜测随机加性噪声解码（GRAND）是一类硬检测和软检测纠错解码算法，能够对任意长度的任何中等冗余码进行精确解码。本文提出了一种方法，使得任何软输入GRAND算法都能以准确的后验估计形式提供软输出，用于评估解码正确的可能性，或在列表解码的情况下，评估正确解码结果属于列表的可能性。实现该方法仅需在现有解码过程中增加极少的计算量和内存开销。该输出可针对任意中等冗余码（包括循环冗余校验码CRC）调节未检测错误与块错误之间的平衡。