Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Hai Zhu,Liqun Pu,Bo Zhang,Hengzhou Xu

doi:10.1155/2018/5264724

Hai Zhu, Liqun Pu + Show 2 more

Open Access

https://doi.org/10.1155/2018/5264724

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Abstract

Quasi-cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5G enhanced mobile broadband (eMBB) data channel. In this paper, we study the construction of QC LDPC codes based on an arbitrary given expansion factor (or lifting degree). First, we analyze the cycle structure of QC LDPC codes and give the necessary and sufficient condition for the existence of short cycles. Based on the fundamental theorem of arithmetic in number theory, we divide the integer factorization into three cases and present three classes of QC LDPC codes accordingly. Furthermore, a general construction method of QC LDPC codes with girth of at least 6 is proposed. Numerical results show that the constructed QC LDPC codes perform well over the AWGN channel when decoded with the iterative algorithms.

Highlights

Low-density parity-check (LDPC) codes [1] are a class of modern channel coding
We focus on the construction of QC LDPC codes from given expansion factors
In this paper, based on the fundamental theorem of arithmetic, we presented a method for constructing QC LDPC codes with girth of at least 6 from an arbitrary integer

Summary

Introduction

Low-density parity-check (LDPC) codes [1] are a class of modern channel coding. Because of the advantages of approaching the Shannon capacity and the iterative decoding algorithms with lower complexity, LDPC codes have been attracting great interests of the industries and academia. Some low-complexity decoding algorithms of these modern channel codes have been proposed [16, 17] These significant works can facilitate and accelerate the applications of these modern coding techniques in 5G communications. Quasi-cyclic (QC) LDPC codes [29] have advantages of encoding and decoding with low complexity [30, 31], easy hardware implementation [32], and good iterative performance [33], and they have attracted comprehensive attention. The encoding and decoding of QC LDPC codes with expansion factors (or lifting degrees) being the power of two can be implemented by linear shift registers. We focus on the construction of QC LDPC codes from given expansion factors (or lifting degrees).

Fundamentals of Number Theory

Construction of Quasi-Cyclic LDPC Codes with Girth of at Least 6

Conclusion