We establish that a large and 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 concatenated codes that outperform low-density parity-check (LDPC) codes found in the 5G New Radio standard. The concatenated structure enables many desirable features, including: low-complexity hardware-friendly encoding and decoding; high levels of flexibility in length and rate through modularity; and high levels of parallelism in encoding and decoding that enable low latency. Central to this 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 key distinguishing feature of SOGRAND in comparison to other methods 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. Crucially, implementing SOGRAND adds negligible computation and memory to the existing decoding process, and using it results in a practical alternative to LDPC codes.

翻译：我们证明，通过猜测随机加性噪声解码（GRAND）可高效且准确地解码一类规模庞大且灵活的长长度、高冗余纠错码。性能评估表明，能够构建出超越5G新无线电标准中低密度奇偶校验（LDPC）码的简单级联码。该级联结构具备多项理想特性，包括：编码与解码的低复杂度硬件友好性；通过模块化实现长度与码率的高度灵活性；以及支持低延迟的高并行度编码与解码。其核心在于开发了一种方法，使任意软输入（SI）GRAND算法能够以精确的后验估计形式提供软输出（SO），用于评估解码正确的可能性，或在列表解码情况下评估列表中每个元素正确的可能性。与其他方法相比，SOGRAND的关键区别在于，即使在仅提供单一解码时，也能给出未找到正确解码的估计值。这种逐块SO可通过包含SI项在内的加权求和转换为精确的逐比特SO。至关重要的是，实现SOGRAND仅需对现有解码过程增加可忽略的计算量与存储开销，且其应用为LDPC码提供了切实可行的替代方案。