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We establish that a large, flexible class of long, high redundancy errorcorrecting codes can be efficiently and accurately decoded with guessing randomadditive noise decoding (GRAND). Performance evaluation demonstrates that it ispossible to construct simple product codes with lengths of approximately 200 to4000 bits and rates between 0.2 and 0.8 that outperform low-densityparity-check (LDPC) codes from the 5G New Radio standard in both AWGN andfading channels. The concatenated structure enables many desirable features,including: low-complexity hardware-friendly encoding and decoding; significantflexibility in length and rate through modularity; and high levels ofparallelism 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 accuratea-posteriori estimate of the likelihood that a decoding is correct or, in thecase of list decoding, the likelihood that each element of the list is correct.The distinguishing feature of soft-output GRAND (SOGRAND) is the provision ofan estimate that the correct decoding has not been found, even when providing asingle decoding. That per-block SO can be converted into accurate per-bit SO bya weighted sum that includes a term for the SI. Implementing SOGRAND addsnegligible computation and memory to the existing decoding process, and usingit results in a practical, low-latency alternative to LDPC codes.

Soft-output (SO) GRAND and Iterative Decoding to Outperform LDPCs