论文标题
简单的Modulo可以大大优于基于深度学习的深编码
Simple Modulo can Significantly Outperform Deep Learning-based Deepcode
论文作者
论文摘要
DeepCode（H.Kim等人的2018年）是最近建议的基于深度学习的方案，该方案在AWGN通道上具有嘈杂的反馈，声称比文献中所有以前的方案都优于文献。 DeepCode对非线性编码（通过深度学习）的使用受到了线性反馈方案的已知缺点（Y.-H。Kim等2007）的启发。在2014年，我们使用少量的基本操作没有任何类型的神经网络，基于经典SK方案和Modulo-Arithmetic的组合提出了一种非线性反馈编码方案。由于使用共同的随机性（抖动），该模型-SK方案已从深代码纸中的性能比较中省略了，并且在以后的版本中，因为它被错误地解释为可变长度的编码方案。但是，Modulo-SK中的抖动仅用于可进行疗法性能分析的标准目的，而在实践中不需要。在此简短说明中，我们表明，完全确定的模量SK（无抖动）可以超过深编码。例如，要以1/3 modulo-sk的速率达到10^（-4）的误差概率比deepcode所需的反馈SNR要少3DB。为了获得带有无噪声反馈的10^（-6）的错误概率，DeepCode需要150轮通信，而Modulo-SK也只需要15发，即使反馈很吵（具有27dB SNR）。 我们进一步解决了深代码纸中报告的原始SK方案的数值稳定性问题，并解释了如何避免它们。我们通过在线可用，功能齐全的MATLAB模拟为经典和Modulo-SK方案增强了此报告。最后，请注意，Modulo-SK绝不是声称是最好的解决方案。特别是，将深度学习与模量算术结合使用可能会带来更好的设计，并且仍然是未来研究的引人入胜的方向。
Deepcode (H.Kim et al.2018) is a recently suggested Deep Learning-based scheme for communication over the AWGN channel with noisy feedback, claimed to be superior to all previous schemes in the literature. Deepcode's use of nonlinear coding (via Deep Learning) has been inspired by known shortcomings (Y.-H. Kim et al 2007) of linear feedback schemes. In 2014, we presented a nonlinear feedback coding scheme based on a combination of the classical SK scheme and modulo-arithmetic, using a small number of elementary operations without any type of neural network. This Modulo-SK scheme has been omitted from the performance comparisons made in the Deepcode paper, due to its use of common randomness (dither), and in a later version since it was incorrectly interpreted as a variable-length coding scheme. However, the dither in Modulo-SK was used only for the standard purpose of tractable performance analysis, and is not required in practice. In this short note, we show that a fully-deterministic Modulo-SK (without dithering) can outperform Deepcode. For example, to attain an error probability of 10^(-4) at rate 1/3 Modulo-SK requires 3dB less feedback SNR than Deepcode. To attain an error probability of 10^(-6) with noiseless feedback, Deepcode requires 150 rounds of communication, whereas Modulo-SK requires only 15 rounds, even if the feedback is noisy (with 27dB SNR). We further address the numerical stability issues of the original SK scheme reported in the Deepcode paper, and explain how they can be avoided. We augment this report with an online-available, fully-functional Matlab simulation for both the classical and Modulo-SK schemes. Finally, note that Modulo-SK is by no means claimed to be the best possible solution; in particular, using deep learning in conjunction with modulo-arithmetic might lead to better designs, and remains a fascinating direction for future research.
