Neural Polar Decoders for Deletion Channels

TL;DR

This paper presents a neural polar decoder (NPD) tailored for deletion channels that significantly reduces computational complexity, enabling practical decoding for longer block lengths and supporting advanced techniques like list decoding.

Contribution

The paper extends the neural polar decoder architecture to deletion channels, reducing complexity from $O(N^4)$ to $O(AN \, \log N)$, facilitating longer block length decoding and improved performance.

Findings

Reduced decoding complexity enables longer block length applications.

NPD achieves accurate decoding verified against trellis decoder.

Incorporating list decoding further enhances performance.

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 $O(AN\log N)$, 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 $\delta\in\{0.01, 0.1\}$ 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.