David G. M. Mitchell

Masoumeh Alinia, David G. M. Mitchell

We investigate lossy source coding based on a soft-decision belief propagation guided decimation (BPGD) encoder for low-density generator matrix (LDGM) codes, referred to as \emph{soft-hard BPGD}. The performance of this encoder is highly sensitive to the choice of ``softness'' parameters, typically denoted by $(β,μ)$, which are conventionally tuned via exhaustive empirical sweeps. To reduce this burden and to better align the algorithm with the evolving graphical structure during decimation, we introduce a \emph{dynamic scheduling} framework in which $(β,μ)$ are not fixed globally but change as decimation progresses. The schedule starts in a softer regime to encourage exploration and gradually hardens toward the end to promote convergence, similar to simulated annealing. We consider linear and exponential schedules, discuss their physical interpretation via an effective temperature viewpoint, and explain how they integrate with soft-hard BPGD without changing the order of magnitude of its complexity. Numerical experiments with irregular and semi-regular LDGM ensembles indicate improved rate-distortion performance and reduced non-convergence compared to constant-parameter baselines, while largely eliminating expensive grid searches for a single best pair $(β,μ)$.

Mohsen Moradi, Vahid Nourozi, Salman Habib et al.

Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is appealing due to its low complexity, yet it often exhibits convergence issues due to quantum degeneracy and short cycles that exist in the Tanner graph. To overcome this challenge, this paper proposes a reinforcement-learning (RL) approach that learns (offline) how to decode QLDPC codes based on sequential decoding trajectories. The decoding is formulated as a Markov decision process with a local, syndrome-driven state representation of the underlying RL agent. To enable fast inference, critical for practical implementation, we incrementally update our RL-based QLDPC decoder using second-order neighborhoods that avoid global rescans. Simulation results on representative QLDPC codes demonstrate the superiority of the proposed RL-based QLDPC decoders in terms of performance and convergence speed when compared to flooding and random sequential schedules, while achieving performance competitive with state-of-the-art BP-based decoders at comparable complexity.