Optimized puncturing distributions for irregular non-binary LDPC codes

TL;DR

This paper introduces optimized non-uniform puncturing strategies for irregular non-binary LDPC codes, improving decoding thresholds and approaching channel capacity for various puncturing rates.

Contribution

It presents a Monte-Carlo based Density Evolution method for designing puncturing distributions, demonstrating near-capacity performance for small-degree codes.

Findings

Monte-Carlo Density Evolution accurately estimates thresholds.

Optimized puncturing distributions achieve 0.2-0.5 dB gap to capacity.

Distributions vary from clustered to spread puncturing strategies.

Abstract

In this paper we design non-uniform bit-wise puncturing distributions for irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are optimized by minimizing the decoding threshold of the punctured LDPC code, the threshold being computed with a Monte-Carlo implementation of Density Evolution. First, we show that Density Evolution computed with Monte-Carlo simulations provides accurate (very close) and precise (small variance) estimates of NB-LDPC code ensemble thresholds. Based on the proposed method, we analyze several puncturing distributions for regular and semi-regular codes, obtained either by clustering punctured bits, or spreading them over the symbol-nodes of the Tanner graph. Finally, optimized puncturing distributions for non-binary LDPC codes with small maximum degree are presented, which exhibit a gap between 0.2 and 0.5 dB to the channel capacity, for punctured rates varying from 0.5 to 0.9.