Quasi-Cyclic LDPC (QC-LDPC) codes are widely accepted as a standard for various wireless communication systems in the present and are recommended for future applications. Girth is an important parameter for designing a good general class of LDPC codes. However, obtaining high girth for a parity-check matrix requires lot of computational and structural complexities. To reduce the complexity, this paper proposes to combine the exponent matrices of QC-LDPC codes using the Chinese Remainder Theorem. Simulation results show that a high girth large block-length QC-LDPC code can be obtained from less girth component of QC-LDPC codes.Quasi-Cyclic LDPC (QC-LDPC) codes are widely accepted as a standard for various wireless communication systems in the present and are recommended for future applications. Girth is an important parameter for designing a good general class of LDPC codes. However, obtaining high girth for a parity-check matrix requires lot of computational and structural complexities. To reduce the complexity, this paper proposes to combine the exponent matrices of QC-LDPC codes using the Chinese Remainder Theorem. Simulation results show that a high girth large block-length QC-LDPC code can be obtained from less girth component of QC-LDPC codes.

International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC)Jun 1, 20150 citations

An Explicit Method to Generate Some QC LDPC Codes with Girth 8

Mohammad Gholami, Zahra Gholami

Iranian Journal of Science and Technology Transactions A ScienceApr 11, 20168 citations

On the Girth of Tanner (3, 13) Quasi-Cyclic LDPC Codes

Hengzhou Xu, Huaan Li, Dan Feng +2 more

Girth is an important structural property of low-density parity-check (LDPC) codes. Motivated by the works on the girth of Tanner (3, 5), (3, 7), (3, 11), and (5, 7) quasi-cyclic (QC) LDPC codes, we, in this paper, study the girth of Tanner (3, 13) QC-LDPC codes of length $13p$ for $p$ being a prime of the form $(39m+1)$ . First, the cycle structure of Tanner (3, 13) QC-LDPC codes is analyzed, and the cycles of length lesser than 12 are divided into five equivalent classes. Based on each equivalent class, the existence of the cycles is equivalent to the solution of polynomial equations in a 39th unit root in the prime filed $\mathbb {F}_{p}$ . By solving these polynomial equations over $\mathbb {F}_{p}$ and summarizing the resulting candidate prime values, the girth of Tanner (3, 13) QC-LDPC codes is obtained. As an advantage, Tanner (3, 13) QC-LDPC codes have much higher code rates than Tanner (3, 5), (3, 7), (3, 11), and (5, 7) QC-LDPC codes, and provide a promising coding scheme for the data storage systems and optical communications.Girth is an important structural property of low-density parity-check (LDPC) codes. Motivated by the works on the girth of Tanner (3, 5), (3, 7), (3, 11), and (5, 7) quasi-cyclic (QC) LDPC codes, we, in this paper, study the girth of Tanner (3, 13) QC-LDPC codes of length$13p$for$p$being a prime of the form$(39m+1)$. First, the cycle structure of Tanner (3, 13) QC-LDPC codes is analyzed, and the cycles of length lesser than 12 are divided into five equivalent classes. Based on each equivalent class, the existence of the cycles is equivalent to the solution of polynomial equations in a 39th unit root in the prime filed$\mathbb {F}_{p}$. By solving these polynomial equations over$\mathbb {F}_{p}$and summarizing the resulting candidate prime values, the girth of Tanner (3, 13) QC-LDPC codes is obtained. As an advantage, Tanner (3, 13) QC-LDPC codes have much higher code rates than Tanner (3, 5), (3, 7), (3, 11), and (5, 7) QC-LDPC codes, and provide a promising coding scheme for the data storage systems and optical communications.

IEEE AccessJan 1, 201840 citations

On the search of smallest QC-LDPC code with girth six and eight

Jasvinder Singh, Manish Gupta, Jaskarn Singh Bhullar

Cryptography and CommunicationsNov 27, 20193 citations

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

Hai Jiang Zhu, Liqun Pu, Hengzhou Xu +1 more

Quasi‐cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5Genhanced 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.Quasi‐cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5Genhanced 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.

Wireless Communications and Mobile ComputingJan 1, 201815 citations

High Rate QC-LDPC Codes with Optimization of Maximum Average Girth

Jianrong Bao, Dan He, Bin Jiang +1 more

Journal of CommunicationsJan 1, 20165 citations

13p

for

p

being a prime of the form

(39m+1)

. First, the cycle structure of Tanner (3, 13) QC-LDPC codes is analyzed, and the cycles of length lesser than 12 are divided into five equivalent classes. Based on each equivalent class, the existence of the cycles is equivalent to the solution of polynomial equations in a 39th unit root in the prime filed

\mathbb {F}_{p}

. By solving these polynomial equations over

\mathbb {F}_{p}

and summarizing the resulting candidate prime values, the girth of Tanner (3, 13) QC-LDPC codes is obtained. As an advantage, Tanner (3, 13) QC-LDPC codes have much higher code rates than Tanner (3, 5), (3, 7), (3, 11), and (5, 7) QC-LDPC codes, and provide a promising coding scheme for the data storage systems and optical communications.