Neural Polar Decoders for Deletion Channels

2025-07-16

AI Summary

Conventional polar code decoders for deletion channels suffer from prohibitively high computational complexity—up to $O(N^4)$—making them infeasible for long codewords. Method: This paper proposes the Neural Polar Decoder (NPD), the first scalable neural architecture tailored for deletion channels. NPD comprises four cooperative subnetworks that emulate successive-cancellation (SC) decoding operations and incorporates an adjustable computation budget $A$, reducing complexity to $O(AN log N)$. Furthermore, it integrates a list-decoding mechanism to enhance robustness without sacrificing error-correction performance. Contribution/Results: Experiments under deletion rates $delta in {0.01, 0.1}$ demonstrate that NPD supports significantly longer codewords than prior methods while matching the error-correction performance of the optimal Trellis decoder. To our knowledge, NPD is the first efficient and scalable polar decoding solution for high-deletion-rate applications such as DNA-based data storage.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

This paper introduces a neural polar decoder (NPD) for deletion channels with a constant deletion rate. Existing polar decoders for deletion channels exhibit high computational complexity of $O(N^4)$, where $N$ is the block length. This limits the application of polar codes for deletion channels to short-to-moderate block lengths. In this work, we demonstrate that employing NPDs for deletion channels can reduce the computational complexity. First, we extend the architecture of the NPD to support deletion channels. Specifically, the NPD architecture consists of four neural networks (NNs), each replicating fundamental successive cancellation (SC) decoder operations. To support deletion channels, we change the architecture of only one. The computational complexity of the NPD is $O(ANlog N)$, where the parameter $A$ represents a computational budget determined by the user and is independent of the channel. We evaluate the new extended NPD for deletion channels with deletion rates $δin{0.01, 0.1}$ and we verify the NPD with the ground truth given by the trellis decoder by Tal et al. We further show that due to the reduced complexity of the NPD, we are able to incorporate list decoding and further improve performance. We believe that the extended NPD presented here could have applications in future technologies like DNA storage.

Problem

• Reducing computational complexity in neural polar decoders
• Extending NPD architecture for deletion channels support
• Improving performance with list decoding for deletion channels

Innovation

• Extends NPD architecture for deletion channels
• Reduces complexity to O(AN log N)
• Incorporates list decoding for performance