# Floor Scale Modulo Lifting for QC-LDPC codes

## TL;DR

This paper introduces a novel floor scale modulo lifting method for constructing smaller QC-LDPC codes, generalizing existing techniques and improving cycle properties through probabilistic analysis.

## Contribution

It presents a new lifting method for QC-LDPC codes that allows generating multiple codes from a single matrix with minimal stored parameters.

## Key findings

- Probabilistic improvement in small cycle reduction.
- Construction of a sequence of QC-LDPC codes from one exponent matrix.
- Efficient code generation with minimal memory use.

## Abstract

In the given paper we present a novel approach for constructing a QC-LDPC code of smaller length by lifting a given QC-LDPC code. The proposed method can be considered as a generalization of floor lifting. Also we prove several probabilistic statements concerning a theoretical improvement of the method with respect to the number of small cycles. Making some offline calculation of scale parameter it is possible to construct a sequence of QC-LDPC codes with different circulant sizes generated from a single exponent matrix using only floor and scale operations. The only parameter we store in memory is a constant needed for scaling.