Serially Concatenated Low-density Parity Check Codes as Compatible Pairs

Amjad Ali Jassim,Wael A Hadi,Muhanned Ismael Ibrahim Al-Firas

doi:10.14419/ijet.v7i4.15.23013

Abstract

Low-density parity checks (LDPC) codes are considered good performance error correction codes. However, decoder complexity increases with increasing code length. In this study, we introduce short-length serially concatenated LDPC codes. The proposed technique uses pairs of compatible LDPC codes that act as outer and inner serially concatenated codes. In this code pair, the inner code takes input that is the same length as the outer LDPC encoder output. This study examined two cases of LDPC codes as compatible pairs with low numbers of iterations and compared bit error rate (BER) performance to a standalone LDPC code with an additive white Gaussian noise channel. We also considered the quadrature phase shift keying QPSK, 16-quadrature amplitude modulation (QAM), and 64-QAM system modulation schemes. Simulation results demonstrate that the proposed system has good BER performance compared to a standalone LDPC code, the results summarized in table and performance curves.

Highlights

Low-density parity check (LDPC) codes are a class of codes first introduced by Gallager in 1962 [1]
We have proposed the use of a pair of different serially concatenated LDPC codes rather than two identical LDPC codes
A feedback process is avoided on the receiver side, which reduces the number of iterations and system complexity

Summary

Introduction

Low-density parity check (LDPC) codes are a class of codes first introduced by Gallager in 1962 [1] These codes were later rediscovered by MacKay and Neal in 1996[1]. This class of codes has near-ideal performance BER that close to Shannon’s limit. These codes are linear block codes that construct a sparse binary matrix H distinguished by relatively few “1s” spread among many “0s.”. The LDPC decoder includes an iterative decoding algorithm; this algorithm was beyond the capabilities of electronic processors available in 1962 [1] These codes were not considered until 1996. Note that there are several methods for constructing irregular LDPC codes [3]

Serially concatenated LDPC codes

Proposed system

Simulation results

Conclusion