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arxiv 2305.05777 v1 pith:5LIG5U7Y submitted 2023-05-09 cs.IT math.IT

Upgrade error detection to prediction with GRAND

classification cs.IT math.IT
keywords decodinggrandaccuratecorrecterrorerrorslikelihoodlist
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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

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