Deep Learning for Decoding of Linear Codes - A Syndrome-Based Approach

TL;DR

This paper introduces a syndrome-based deep learning framework for soft decoding of linear codes, enabling flexible neural network design, robustness to overfitting, and performance close to traditional decoding algorithms.

Contribution

It proposes a novel syndrome-based preprocessing method for neural decoding of linear codes, allowing unconstrained DNN design and improved generalization.

Findings

Performance approaches ordered statistics decoding (OSD)

Robustness to overfitting due to syndrome-based input

Effective use of RNN architecture with permutation preprocessing

Abstract

We present a novel framework for applying deep neural networks (DNN) to soft decoding of linear codes at arbitrary block lengths. Unlike other approaches, our framework allows unconstrained DNN design, enabling the free application of powerful designs that were developed in other contexts. Our method is robust to overfitting that inhibits many competing methods, which follows from the exponentially large number of codewords required for their training. We achieve this by transforming the channel output before feeding it to the network, extracting only the syndrome of the hard decisions and the channel output reliabilities. We prove analytically that this approach does not involve any intrinsic performance penalty, and guarantees the generalization of performance obtained during training. Our best results are obtained using a recurrent neural network (RNN) architecture combined with simple preprocessing by permutation. We provide simulation results that demonstrate performance that sometimes approaches that of the ordered statistics decoding (OSD) algorithm.