提出无需训练的最优纠错解码器，性能超越现有神经网络方法。
On the Optimality of Single-label and Multi-label Neural Network Decoders
- 基于码本直接构造最优解码结构，不依赖训练
- 在汉明(7,4)、极化(16,8)等码上实现理论最优性能
- 适合短码场景，复杂度低于现有近优方案
本文研究了用于前向纠错的单标签神经网络（SLNN）和多标签神经网络（MLNN）解码器的设计。已有研究称其分别达到接近最优的码字级与比特级性能，且对多种短码有效。本文首次从理论上证明：特定的SLNN与MLNN架构可始终实现最优解码，不受码种限制。这些最优架构及其二值权重由码本直接决定，无需训练或优化。所提方法本质并非神经网络，而是最大似然解码规则的新实现方式。数值实验验证了其在汉明(7,4)、极化(16,8)和BCH(31,21)码上的最优性能。结果表明，该架构比文献中提出的近优架构更简单，后者实际仅能达到近优。长码因维度灾难仍难应用，因此尽管现有SLNN/MLNN可实现最大似然解码，但无法用于中长码。
原文摘要 · Abstract (English)
We investigate the design of two neural network (NN) architectures recently proposed as decoders for forward error correction: the so-called single-label NN (SLNN) and multi-label NN (MLNN) decoders. These decoders have been reported to achieve near-optimal codeword- and bit-wise performance, respectively. Results in the literature show near-optimality for a variety of short codes. In this paper, we analytically prove that certain SLNN and MLNN architectures can, in fact, always realize optimal decoding, regardless of the code. These optimal architectures and their binary weights are shown to be defined by the codebook, i.e., no training or network optimization is required. Our proposed architectures are in fact not NNs, but a different way of implementing the maximum likelihood decoding rule. Optimal performance is numerically demonstrated for Hamming $(7,4)$, Polar $(16,8)$, and BCH $(31,21)$ codes. The results show that our optimal architectures are less complex than the SLNN and MLNN architectures proposed in the literature, which in fact only achieve near-optimal performance. Extension to longer codes is still hindered by the curse of dimensionality. Therefore, even though SLNN and MLNN can perform maximum likelihood decoding, such architectures cannot be used for medium and long codes.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。