While decades of theoretical research have led to the invention of several classes of error-correction codes, the design of such codes is an extremely challenging task, mostly driven by human ingenuity. Recent studies demonstrate that such designs can be effectively automated and accelerated via tools from machine learning (ML), thus enabling ML-driven classes of error-correction codes with promising performance gains compared to classical designs. A fundamental challenge, however, is that it is prohibitively complex, if not impossible, to design and train fully ML-driven encoder and decoder pairs for large code dimensions. In this paper, we propose Product Autoencoder (ProductAE) -- a computationally-efficient family of deep learning driven (encoder, decoder) pairs -- aimed at enabling the training of relatively large codes (both encoder and decoder) with a manageable training complexity. We build upon ideas from classical product codes and propose constructing large neural codes using smaller code components. ProductAE boils down the complex problem of training the encoder and decoder for a large code dimension $k$ and blocklength $n$ to less-complex sub-problems of training encoders and decoders for smaller dimensions and blocklengths. Our training results show successful training of ProductAEs of dimensions as large as $k = 300$ bits with meaningful performance gains compared to state-of-the-art classical and neural designs. Moreover, we demonstrate excellent robustness and adaptivity of ProductAEs to channel models different than the ones used for training.

翻译：尽管数十年的理论研究已催生出多类纠错码，但此类码的设计仍是极具挑战性的任务，主要依赖人类智慧。近年研究表明，通过机器学习（ML）工具可有效实现这类设计的自动化与加速，从而催生ML驱动的纠错码类别，相较于经典设计展现出显著性能优势。然而，一个根本性挑战在于：对于大维度码字，设计并训练完全由ML驱动的编码器-解码器对是极其复杂的，甚至难以实现。本文提出乘积自编码器（ProductAE）——一种计算高效的深度学习驱动（编码器，解码器）对家族——旨在以可控的训练复杂度实现较大规模码字（包括编码器和解码器）的训练。我们借鉴经典乘积码的思想，提出通过小型码组件构建大型神经码。ProductAE将大维度$k$与码长$n$的编码器-解码器训练这一复杂问题，简化为较小维度与码长的编码器-解码器训练子问题。训练结果表明，我们成功训练了维度高达$k=300$比特的ProductAE，相较于最先进的经典与神经设计方案取得了有意义的性能增益。此外，我们证明了ProductAE对不同于训练时的信道模型具有优异的鲁棒性与自适应性。