A Construction of High Performance Quasicyclic LDPC Codes: A Combinatoric Design Approach

Nauman Ali Khan,Wuyang Zhou,Muhammad Ajmal,Zain Ul Abiden Akhtar,Muhammad Asif

doi:10.1155/2019/7468792

Abstract

This correspondence presents a construction of quasicyclic (QC) low-density parity-check (LDPC) codes based on a special type of combinatorial designs known as block disjoint difference families (BDDFs). The proposed construction of QC-LDPC codes gives parity-check matrices with column weight three and Tanner graphs having a girth lower-bounded by 6. The proposed QC-LDPC codes provide an excellent performance with iterative decoding over an additive white Gaussian-noise (AWGN) channel. Performance analysis shows that the proposed short and moderate length QC-LDPC codes perform as well as their competitors in the lower signal-to-noise ratio (SNR) region but outperform in the higher SNR region. Also, the codes constructed are quasicyclic in nature, so the encoding can be done with simple shift-register circuits with linear complexity.

Highlights

Low-density parity-check codes [1] are of vital importance for many modern communication systems because of their capacity-approaching performance and low-complexity iterative decoding over noisy information channels
The codes constructed are quasicyclic in nature, so the encoding can be done with simple shift-register circuits with linear complexity
Two classes of binary QC-low-density parity-check (LDPC) codes have been constructed based on a special type of combinatorial designs known as block disjoint difference families (BDDFs)

Summary

Introduction

Low-density parity-check codes [1] are of vital importance for many modern communication systems because of their capacity-approaching performance and low-complexity iterative decoding over noisy information channels. In literature [3, 4], low-complexity decoding algorithms have been presented for LDPC codes. Compared to random-like LDPC codes, the QC-LDPC codes have generator matrices which are quasicyclic in nature, so encoding can be done with shift register circuits having linear complexity. The proposed QC-LDPC codes constructed for short and moderate length applications provide excellent error-correcting performance with iterative decoding over an AWGN channel. The codes constructed are quasicyclic in nature, so the encoding can be done with simple shift-register circuits with linear complexity The remainder of this correspondence is arranged as follows: in Section 2, the basic concepts about design theory and cyclic difference families (CDFs) are given.

Basic Concepts and Definitions

BDDFs-Based Construction of QC-LDPC Codes

Numerical Results

Conclusion

Conflicts of Interest