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

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 concatenated codes that outperform low...

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Bibliographic Details
Published inarXiv.org
Main Authors Yuan, Peihong, Medard, Muriel, Galligan, Kevin, Duffy, Ken R
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.06.2024
Subjects
Algorithms
Concatenated codes
Decoding
Error correcting codes
Error correction
Low density parity check codes
Modularity
Performance evaluation
Redundancy
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Summary: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 concatenated codes that outperform low-density parity-check (LDPC) codes found in the 5G New Radio standard in both additive white Gaussian noise (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.
ISSN:2331-8422