# Construction of QC-LDPC Codes with Low Error Floor by Efficient Systematic Search and Elimination of Trapping Sets

## TL;DR

This paper introduces a systematic method for designing QC-LDPC codes that significantly reduces error floors by eliminating specific trapping sets through an efficient search algorithm, outperforming existing codes in size and trapping set elimination.

## Contribution

The paper presents a novel systematic design approach for QC-LDPC codes that effectively eliminates targeted trapping sets using an efficient layered search algorithm, improving code performance.

## Key findings

- Designed codes are free of certain trapping sets with smaller block lengths.
- Codes outperform existing ones by eliminating larger trapping set collections.
- The search algorithm enables designing codes with larger degrees and trapping set ranges.

## Abstract

We propose a systematic design of protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with low error floor. We first characterize the trapping sets of such codes and demonstrate that the QC structure of the code eliminates some of the trapping set structures that can exist in a code with the same degree distribution and girth but lacking the QC structure. Using this characterization, our design aims at eliminating a targeted collection of trapping sets. Considering the parent/child relationship between the trapping sets in the collection, we search for and eliminate those trapping sets that are in the collection but are not a child of any other trapping set in the collection. An efficient layered algorithm is designed for the search of these targeted trapping sets. Compared to the existing codes in the literature, the designed codes are superior in the sense that they are free of the same collection of trapping sets with a smaller block length, or a larger collection of trapping sets with the same block length. In addition, the efficiency of the search algorithm makes it possible to design codes with larger degrees which are free of trapping sets within larger ranges compared to the state-of-the-art.