# Precoded Polar Product Decoder Based on Soft-Output SCL Decoding and Maximization of Generalized Mutual Information

## TL;DR

This paper introduces a novel precoded polar product decoder that combines soft-output SCL decoding with GMI maximization, significantly improving error correction performance and enabling accurate threshold prediction through density evolution.

## Contribution

It proposes a new decoding method that integrates soft message generation and GMI-based scaling, enhancing iterative decoding of product codes with polar components.

## Key findings

- Significant error correction performance improvement over heuristic methods.
- Accurate decoding thresholds predicted by Monte Carlo density evolution.
- Effective extrinsic SCL decoder implementation for performance analysis.

## Abstract

We combine two approaches to optimize the iterative decoding of product codes with precoded polar component codes. On one side, we generate bitwise soft messages based on the codebook probability, an approximation of an auxiliary quantity that considers all valid decoding paths of a successive cancellation list (SCL) decoder. On the other side, we scale the soft information during message passing with offline-computed coefficients, which maximize the generalized mutual information (GMI) between the channel input and the outgoing message in each half iteration. Simulation results show significant improvement of the error-correcting performance compared to heuristic scaling and soft information generation based solely on the candidate list of the decoder. Moreover, we present an extrinsic version of the SCL decoder, which we use in a Monte Carlo density evolution analysis to derive decoding thresholds. The computed thresholds accurately predict the performance of the decoder.