Recursive projection aggregation (RPA) decoding as introduced in [1] is a novel decoding algorithm which performs close to the maximum likelihood decoder for short-length Reed-Muller codes. Recently, an extension to RPA decoding, called sparse multi-decoder RPA (SRPA), has been proposed [2]. The SRPA approach makes use of multiple pruned RPA decoders to lower the amount 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 subspace subsets 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 semi-deterministic subspace selection improves the decoding performance up to $0.2\,\text{dB}$ compared to SRPA. At the same time, the complexity of SRPA decoding for RM codes of order $r\geq 3$ is reduced by up to 81% compared to SRPA.
翻译:在 [1] 中引入的 Recurive 投影汇总(RPA) 解码(RPA) 是一个新的解码算法,它几乎接近于短长 Reed-Muller 代码的最大可能性解码器。最近,有人提议扩大RPA的解码,称为稀少的多解码器 RPA (SRPA) (SRPA) 。SRPA 方法利用多条小号的RPA 解码器来降低计算数量,同时保持与 RPA 解码相比的分解码。然而,使用多种稀释解码器再次增加了计算负担。因此,重点是优化稀释的单解码器(RPA) 解码以保持小的复杂程度。在本文中,提出了一种新方法,选择SRPA 解码的预测和汇总步骤中使用的子空间子区块子块子块,以减少AU 的误差概率。 拟议的方法用一种半确定性选择方法取代了子空间子块的选定方法,其基础选择方法根据一个对 RRM MA 3 的精度比 RSR 的 RPA 的精度, 我们的模拟结果显示显示到分序, 改进了SR 。