Ultra-Sparse Non-Binary LDPC Codes for Probabilistic Amplitude Shaping

TL;DR

This paper demonstrates that ultra-sparse non-binary LDPC codes combined with probabilistic amplitude shaping significantly improve power efficiency in communication systems, outperforming binary LDPC codes at similar spectral efficiencies.

Contribution

It introduces the use of ultra-sparse non-binary LDPC codes over GF(64) and GF(256) with PAS, achieving notable power efficiency gains over existing binary LDPC codes.

Findings

Gain of 0.6 dB in power efficiency over binary LDPC codes

Effective combination of non-binary LDPC with PAS for power-efficient communication

Simulation results align with finite length bounds and density evolution analysis.

Abstract

This work shows how non-binary low-density parity-check codes over GF($2^p$) can be combined with probabilistic amplitude shaping (PAS) (B\"ocherer, et al., 2015), which combines forward-error correction with non-uniform signaling for power-efficient communication. Ultra-sparse low-density parity-check codes over GF(64) and GF(256) gain 0.6 dB in power efficiency over state-of-the-art binary LDPC codes at a spectral efficiency of 1.5 bits per channel use and a blocklength of 576 bits. The simulation results are compared to finite length coding bounds and complemented by density evolution analysis.