Non-binary low-density parity-check (NB-LDPC) codes are known to offer several advantages over their binary counterparts, but the higher complexity, and the resource-hungry nature of decoding algorithms have so far restricted their practical usage. In this paper, we propose a new decoding algorithm for NB-LDPC codes over finite fields of characteristic 2, based on a novel binary expansion of the ${Q}$ -ary Tanner graph. While it offers substantial complexity gains, simulation results demonstrate that the performance loss of the new algorithm, in comparison to the best known decoder, is quite small. Furthermore, due to being based on a binary graph, it is particularly attractive for hardware implementations. We also suggest a simplified version of the algorithm, which offers even higher gains in complexity.

中文翻译：

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NB-LDPC码的新图扩展和解码算法

众所周知，非二进制低密度奇偶校验 (NB-LDPC) 码比其二进制对应码具有多个优势，但解码算法的较高复杂性和资源匮乏的性质迄今为止限制了它们的实际使用。在本文中，我们基于 ${Q}$ -ary Tanner 图的新颖二进制展开，提出了一种新的解码算法，用于特征为 2 的有限域上的 NB-LDPC 码。虽然它提供了显着的复杂度增益，但仿真结果表明，与最著名的解码器相比，新算法的性能损失非常小。此外，由于基于二进制图，它对硬件实现特别有吸引力。我们还建议使用该算法的简化版本，它可以提供更高的复杂度增益。