# Binary Message Passing Decoding of Product-like Codes

## TL;DR

This paper introduces a binary message passing decoding algorithm called iBDD-SR for product-like codes, which leverages channel reliabilities to improve decoding performance while maintaining low data flow, achieving significant gains over traditional methods.

## Contribution

The paper presents a novel soft-in, hard-out decoding algorithm that combines channel reliabilities with bounded distance decoding, reducing data flow and improving performance for product-like codes.

## Key findings

- Achieves up to 0.31 dB performance gain over conventional iBDD.
- Density evolution analysis determines optimal scaling factors.
- Approaches the performance of ideal iBDD that prevents miscorrections.

## Abstract

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to $0.29$ dB and $0.31$ dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.