Guessing Random Additive Noise Decoding With Symbol Reliability Information (SRGRAND)

The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon’s 1948 capacity theorem, which established that use noisy channels most efficiently; Berlekamp, McEliece, Van Tilborg’s 1978 theorem on the NP-completeness decoding linear codes. These results shifted focus away from creating code-independent decoders, but recent low-latency communication applications necessitate relatively short codes, providing motivation to reconsider development universal decoders. We introduce a scheme for employing binarized symbol soft information within Guessing Random Additive Noise Decoding, hard detection decoder. incorporate codebook-independent quantization indicate demodulated symbols be reliable or unreliable. algorithms: one identifies conditional Maximum Likelihood (ML) decoding; other either reports ML an error. For random codebooks, we present exponents asymptotic complexity, show benefits over detection. As empirical illustrations, compare performance with majority logic Reed-Muller Berlekamp-Massey Bose-Chaudhuri-Hocquenghem CA-SCL CA-Polar establish Linear Codes, require decoder offer broader palette code sizes rates than traditional