CIF: Small: Learning To Correct Errors

纠错码在确保无线通信、计算机网络和数据存储等众多应用中的数据完整性方面发挥着至关重要的作用。纠错码的美丽和解码算法的优雅反映了底层数学对象的丰富结构，也反映了人类的创造力和独创性。受深度神经网络（DNN）最近在各种应用中取得的成功的启发，该项目正在研究机器是否、如何以及如何有效地学习这种结构和优雅性，以及如何自动发现新的和改进的解码算法。该项目正在设计基于并行神经网络的解码器，具有超低延迟和改进的错误性能。由此产生的解码器旨在发现新兴的无线标准的广泛适用性（5G及以后）以及新的应用，包括量子计算机解码、机器对机器通信、长距离光通信和数据中心闪存。本项目将纠错问题作为高维信号空间中的点的分类，并且使用DNN来学习复杂码字判决区域边界以接近最大似然解码性能。该项目解决了两个关键的实际挑战：a）与传统机器学习应用相比，实现极低的误分类率（低许多数量级），以及B）通过稀疏和量化的神经网络保持低复杂度的解码。第一个推力利用编码理论领域知识，并利用迭代解码器和神经网络之间的结构相似性，以改善解码器的学习。这是通过使用采样的错误模式从迭代解码算法的神经网络解码器的随机优化。第二个重点是使用一种新的监督学习解码器的方法，其中现有的高复杂度的解码器被用来合成一个低复杂度的基于神经网络的解码器具有可比的性能。第三个推力建立基于神经网络的解码器的泛化能力（包括收敛速度和错误性能）的理论结果。该研究为现代纠错算法和机器学习提供了多方面的见解，并将为通信和计算机行业带来重要的理论和实践进步。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Error-correcting codes play an essential role in ensuring integrity of data in numerous applications, including wireless communications, computer networks and data storage. The beauty of error-correcting codes and elegance of their decoding algorithms reflect the rich structure of the underlying mathematical objects, but also human creativity and ingenuity. Motivated by recent successes of Deep Neural Networks (DNN) in various applications, this project is investigating if, how, and how efficiently this structure and elegance can be learned by a machine, and how the discovery of new and improved decoding algorithms can be automated. The project is devising parallelizable neural network based decoders with ultra-low latency and improved error performance. The resulting decoders are intended to find broad applicability in emerging wireless standards (5G and beyond) as well as new applications including decoding for quantum computers, machine-to-machine communications, long-haul optical communications and flash memories in data centers.This project approaches the error-correction problem as classification of the points in a high-dimensional signal space, and uses DNNs to learn complex codeword decision region boundaries to approach the maximum-likelihood decoding performance. The project addresses two key practical challenges: a) achieving extremely low misclassification rates (many orders of magnitude lower) compared to traditional machine learning applications, and b) maintaining low-complexity of decoding via sparse and quantized neural networks. The first thrust utilizes coding-theory domain knowledge, and harnesses the structural similarities between iterative decoders and neural networks for improved learning of decoders. This is achieved by using sampled error patterns from iterative decoding algorithms for stochastic optimization of neural-network decoders. The second thrust focuses on using a new supervised approach for learning decoders, in which existing high-complexity decoders are employed to synthesize a low-complexity neural-network-based decoder with comparable performance. The third thrust establishes theoretical results on the generalization capabilities of neural-network-based decoders (including convergence rates and error performance). This research is providing multi-faceted insight into modern error-correction algorithms and machine learning, and should lead to both theoretical and practical advances of importance to the communications and computer industry.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.