IGRAND: decode any product code

Abstract

We introduce Iterative GRAND (IGRAND), a universal product code decoder that applies iterative bounded distance decoding and decodes component codes using code-agnostic Guessing Random Additive Noise Decoding (GRAND). We empirically determine its accuracy and, based on GRAND hardware measurements, its complexity, showing gains over alternative algorithms. We prove that the class of product codes with random linear component codes, which IGRAND is capable of decoding, are capacity-achieving in hard-decision channels.