Protograph-Based LDPC Codes with Local Irregularity

TL;DR

This paper addresses improving LDPC code performance by introducing protograph-based codes with local irregularity (PLI), which extend conventional protographs with edge-wise local degree distributions. By developing the PLI-EXIT algorithm, the authors estimate iterative decoding thresholds on BI-AWGN channels and optimize local VN degrees to lower these thresholds, starting from the rate-$1/2$ AR4JA protograph. The optimized codes (e.g., $ ext{C}_1$ and $ ext{C}_2$) achieve substantial threshold gains (up to ~0.4 dB closer to capacity) but may incur higher error floors due to increased degree-2 VNs. The proposed framework offers a tractable optimization path compared to MET-LDPC codes and has potential for practical high-throughput applications, while highlighting the trade-off between threshold improvement and error-floor behavior.$E_b/N_0$-aware design and explicit local-degree modeling are central to the approach.

Abstract

Forward error correcting (FEC) codes are used in many communication standards with a wide range of re quirements. FEC codes should work close to capacity, achieve low error floors, and have low decoding complexity. In this paper, we propose a novel category of low-density parity-check (LDPC) codes, based on protograph codes with local irregularity. This new code family generalizes conventional protograph-based LDPC codes and is capable of reducing the iterative decoding threshold of the conventional counterpart. We introduce an adapted version of the protograph extrinsic information transfer (PEXIT) algorithm to estimate decoding thresholds on the binary input additive white Gaussian noise channel, perform optimiza tions on the local irregularity, and simulate the performance of some constructed codes.

Figures (2)

• Figure 1: Example of a protograph.
• Figure 2: Simulated error rates as a function of $E_{\text{b}}/N_0$ for sum-product decoding. For each legend entry, the decoding threshold/ capacity is stated.