Extend the LLMD decoder to structured noise models

Extend the level-by-level minimum-distance decoder for qudit many-hypercube codes to structured noise models, including amplitude-damping channels whose asymmetric transition probabilities are not captured by ordinary Hamming distance.

Background

The paper’s analysis of the waterfall regime uses Hamming distance because all nontrivial qudit X errors have equal probability in the adopted noise model. For structured physical noise, such as amplitude damping, error probabilities and allowed transitions can depend on the direction and magnitude of the transition. The paper therefore identifies the adaptation of the LLMD decoder to noise-dependent distance measures and physically structured channels as an unresolved problem.