# One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation

## TL;DR

This paper introduces one and two bit message passing algorithms for LDPC code decoding, demonstrating their effectiveness with higher-order modulation and probabilistic shaping to achieve high throughput with reduced complexity.

## Contribution

The paper proposes a novel quaternary message passing algorithm and analyzes its performance, showing significant gains over binary and ternary message passing in high spectral efficiency scenarios.

## Key findings

- QMP reduces the gap to unquantized BP decoding to about 0.75 dB.
- QMP outperforms BMP and TMP by approximately 0.7 dB and 0.1 dB, respectively.
- Performance gains are more pronounced at smaller code rates.

## Abstract

Low complexity decoding algorithms are necessary to meet data rate requirements in excess of 1 Tbps. In this paper, we study one and two bit message passing algorithms for belief propagation decoding of low-density parity-check (LDPC) codes and analyze them by density evolution. The variable nodes (VNs) exploit soft information from the channel output. To decrease the data flow, the messages exchanged between check nodes (CNs) and VNs are represented by one or two bits. The newly proposed quaternary message passing (QMP) algorithm is compared asymptotically and in finite length simulations to binary message passing (BMP) and ternary message passing (TMP) for spectrally efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS). To showcase the potential for high throughput forward error correction, spatially coupled LDPC codes and a target spectral efficiency (SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates, the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in the considered example.