A Balanced Tree Transformation to Reduce GRAND Queries

Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only noise patterns that meet specific constraints imposed by the linear code. In this paper, we introduce a new method to efficiently derive multiple constraints from the parity check matrix. By applying a random invertible linear transformation and reorganizing the matrix into a tree structure, we extract up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\log _{2} n$</tex> constraints, reducing the number of decoding queries while maintaining the structure of the original code for a code length of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex>. We validate the method through theoretical analysis and experimental simulations.