Noise Error Pattern Generation Based on Successive Addition-Subtraction for GRAND-MO

Abstract

Guessing random additive noise decoding (GRAND) is a capacity-approaching universal algorithm. The GRAND Markov order (GRAND-MO) variant is effective to correct burst errors in a Markov chain modeled memory channel, and the core of GRAND-MO is to generate putative noise error patterns in MO effectively. For purpose of a uniform noise error pattern generation scheme of GRAND-MO, this letter proposes a successive addition-subtraction scheme to generate noise/zero error permutations for predefined MO parameters. Detailed procedures of the proposed scheme are presented, and its correctness is also proofed through theoretical derivation. By embedding the “1” and “0” bursts alternately, the proposed scheme can generate all noise error patterns in MO, which is helpful to improve the error correction capability of GRAND-MO decoders for flexible applications.