We establish that a large, flexible class of long, high redundancy error correcting codes can be efficiently and accurately decoded with guessing random additive noise decoding (GRAND). Performance evaluation demonstrates that it is possible to construct simple product codes with lengths of approximately 200 to 4000 bits and rates between 0.2 and 0.8 that outperform low-density parity-check (LDPC) codes from the 5G New Radio standard in both AWGN and fading channels. The concatenated structure enables many desirable features, including: low-complexity hardware-friendly encoding and decoding; significant flexibility in length and rate through modularity; and high levels of parallelism in encoding and decoding that enable low latency. Central is the development of a method through which any soft-input (SI) GRAND algorithm can provide soft-output (SO) 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 each element of the list is correct. The distinguishing feature of soft-output GRAND (SOGRAND) is the provision of an estimate that the correct decoding has not been found, even when providing a single decoding. That per-block SO can be converted into accurate per-bit SO by a weighted sum that includes a term for the SI. Implementing SOGRAND adds negligible computation and memory to the existing decoding process, and using it results in a practical, low-latency alternative to LDPC codes.

翻译：我们证明，一类具有高冗余度的长纠错码可通过猜测随机加性噪声解码（GRAND）实现高效且精确的解码。性能评估表明，可以构建长度约200至4000比特、码率介于0.2至0.8之间的简单乘积码，其在AWGN和衰落信道中的性能均优于5G新空口标准中的低密度奇偶校验（LDPC）码。这种级联结构具备诸多优势：支持硬件友好的低复杂度编码与解码；通过模块化实现长度和码率的显著灵活性；以及支持高度并行的编码解码过程以实现低延迟。核心在于我们开发了一种方法，使得任何软输入（SI）GRAND算法均能提供软输出（SO），其形式为对解码正确性的精确后验似然估计（对于列表解码则为列表中每个元素的正确性似然估计）。软输出GRAND（SOGRAND）的显著特征在于：即使在提供单一解码结果时，也能估计出未找到正确解码的可能性。通过包含软输入项的加权求和，可将每块软输出转化为精确的每比特软输出。SOGRAND的实现对现有解码过程增加的计算量和内存可忽略不计，其应用为LDPC码提供了一种实用且低延迟的替代方案。