Semi-Deterministic Subspace Selection for Sparse Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Inhalt:
Recursive projection aggregation (RPA) decoding is a novel decoding algorithm that performs close to the maximum likelihood decoder for short-length Reed-Muller codes. Recently, an extension to RPA decoding, called sparse multidecoder RPA (SRPA), has been proposed. The SRPA approach uses multiple pruned RPA decoders to lower the number of computations while keeping the performance loss small compared to RPA decoding. However, the use of multiple sparse decoders again increases the computational burden. Therefore, the focus is on the optimization of sparse single-decoder RPA decoding to keep the complexity small. In this paper, a novel method is proposed, to select subsets of subspaces used in the projection and aggregation step of SRPA decoding in order to decrease the decoding error probability on AWGN channels. The proposed method replaces the random selection of subspaces with a semi-deterministic selection method based on a figure of merit that evaluates the performance of each subspace. Our simulation results show that the semideterministic subspace selection improves the decoding performance up to 0.2 dB compared to SRPA. At the same time, the complexity of SRPA decoding for RM codes of order r ≥ 3 is reduced by up to 81% compared to SRPA.