Data-Driven Neural Polar Codes for Unknown Channels With and Without Memory

TL;DR

This paper introduces a neural network-based polar code decoder that adapts to unknown channels with or without memory, providing a flexible, theoretically supported approach with complexity advantages over traditional methods.

Contribution

It proposes a novel neural successive cancellation decoder for polar codes that works with black-box channels, including channels with memory, with theoretical guarantees and lower complexity.

Findings

Neural SC decoder performs well on memoryless channels.

The method is applicable to channels with memory where traditional decoders fail.

Complexity does not increase with channel memory size.

Abstract

In this work, a novel data-driven methodology for designing polar codes for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a "black-box" and the designer has access to the channel for generating observations of its inputs and outputs, but does not have access to the explicit channel model. The proposed method leverages the structure of the successive cancellation (SC) decoder to devise a neural SC (NSC) decoder. The NSC decoder uses neural networks (NNs) to replace the core elements of the original SC decoder, the check-node, the bit-node and the soft decision. Along with the NSC, we devise additional NN that embeds the channel outputs into the input space of the SC decoder. The proposed method is supported by theoretical guarantees that include the consistency of the NSC. Also, the NSC has computational complexity that does not grow with the channel memory size. This sets its main advantage over successive cancellation trellis (SCT) decoder for finite state channels (FSCs) that has complexity of $O(|\mathcal{S}|^3 N\log N)$, where $|\mathcal{S}|$ denotes the number of channel states. We demonstrate the performance of the proposed algorithms on memoryless channels and on channels with memory. The empirical results are compared with the optimal polar decoder, given by the SC and SCT decoders. We further show that our algorithms are applicable for the case where there SC and SCT decoders are not applicable.