# Design of Improved Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes for Short Block-Lengths

## TL;DR

This paper introduces a new design method for quasi-cyclic PBRL LDPC codes that enhances performance at short block-lengths by improving minimum distance bounds and reducing design complexity.

## Contribution

A novel approach to designing QC PBRL LDPC codes that maximizes minimum distance bounds, leading to better error floor performance for short block-lengths.

## Key findings

- Codes outperform original PBRL codes at short lengths
- Significant error floor improvement across all rates
- Reduced complexity in the design process

## Abstract

Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a recently proposed family of easily encodable and decodable rate-compatible LDPC (RC-LDPC) codes. These codes have an excellent iterative decoding threshold and performance across all design rates. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the RC code family at various design rates. In this work, we propose a design method to obtain better quasi-cyclic (QC) RC-LDPC codes with PBRL structure for short block-lengths (of a few hundred bits). We achieve this by maximizing an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protograph of a PBRL ensemble. The obtained codes outperform the original PBRL codes at short block-lengths by significantly improving the error floor behavior at all design rates. Furthermore, we identify a reduction in complexity of the design procedure, facilitated by the general structure of a PBRL ensemble.