Coset Error Pattern in Projection-Aggregation Decoding

Projection-aggregation decoding provides state-of-the-art performance for decoding Reed-Muller codes. This type of decoding relies on projecting onto subspaces, decoding the projections, and voting with the decoded projections. This paper investigates the decoding with a limited number of subspaces. By defining a false vote matrix, it demonstrates that this decoding suffers from coset error patterns, even when all projections are decoded successfully. These error patterns are of very small weights and thus induce a significant performance loss. Two rules are then proposed of which one reveals a trade-off between the subspace number and the error-correcting capability and the other provides a guideline for subspace selection. Simulation results verify that following the two rules alleviates the performance loss caused by the coset error patterns.