Ordered Reliability Bits Guessing Random Additive Noise Decoding

Guessing Random Additive Noise Decoding (GRAND) can, unusually, decode any forward error correction block code. The original algorithm assumed that the decoder received only hard decision demodulated to inform its decoding. As the incorporation of soft information is known to improve decoding precision, here we introduce Ordered Reliability Bits GRAND, that, for binary block code of length $n$, avails of no more than $\lceil \log_2(n)\rceil$ bits of code-book-independent quantized soft detection information per received bit to determine an accurate decoding. ORBGRAND is shown to provide better block error rate performance than CA-SCL, a state of the art CA-Polar decoder, with low complexity. Random Linear Codes of the same rate, decoded with ORBGRAND, are shown to have comparable block-error and complexity performance.

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