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IEEE Computers, Communications and IT Applications Conference (ComComAp)

The performance analysis of QC-LDPC codes constructed by Dayan sequence for coded cooperative relay

Yan Zhang, Fengfan Yang

Published Oct 1, 2014• 1 citation
Publisher

Abstract

This paper presents Dayan sequence to construct QC-LDPC codes through the combination of mathematical theory. The paper introduces the procedure of the coding principle and coding. Dayan sequence constructed QC-LDPC codes is compared with rate compatible QC-LDPC, Simulation results show that the bit error rate (BER)performance of Dayan sequence constructed QC-LDPC is improved by 0.5dB. Then QC-LDPC codes constructed by the Dayan sequence are used in coded cooperative communication. Compared it with PEG algorithm, array code and Mackey code,the results show that the performance of Dayan sequence is superior. That is to say that Dayan sequence code constructed QC-LDPC is effective in coded cooperative communication.

DOI
10.1109/comcomap.2014.7017175

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This paper presents Dayan sequence to construct QC-LDPC codes through the combination of mathematical theory. The paper introduces the procedure of the coding principle and coding. Dayan sequence constructed QC-LDPC codes is compared with rate compatible QC-LDPC, Simulation results show that the bit error rate (BER)performance of Dayan sequence constructed QC-LDPC is improved by 0.5dB. Then QC-LDPC codes constructed by the Dayan sequence are used in coded cooperative communication. Compared it with PEG algorithm, array code and Mackey code,the results show that the performance of Dayan sequence is superior. That is to say that Dayan sequence code constructed QC-LDPC is effective in coded cooperative communication.
The relay channel is the common approach to cooperative communication. Quasi-cyclic low-density parity-check (QC-LDPC) code design for the relay channel is important to cooperative communication. This paper proposes a bilayer QC-LDPC code design scheme for the relay channel. Combined with the bilayer graphical code structure, an improved Chinese remainder theorem (CRT) method, the Biff-CRT method is presented. For the proposed method we introduce a finite field approach. The good performance of the finite field based QC-LDPC code can improve the performance of its corresponding objective QC-LDPC code in the proposed scheme. We construct the FF code and the FA code by the Biff-CRT method. The FF code and the FA code are both named as their two component codes. For the FF code, the two component code are both finite field based QC-LDPC codes. For the FA code, one of the component codes is the finite field based QC-LDPC code and the other is the array code. For the existing CRT method, the shortened array code and the array code are usually used as the component codes to construct the SA code. The exponent matrices of FF code, FA code and SA code are given both for the overall graph and the lower graph. Bit error rate (BER) simulation results indicate that the proposed FF code and FA code are superior to the SA code both at the relay node and the destination node. In addition, the theoretical limit and the BER of the bilayer irregular LDPC code are also given to compare with the BER of the proposed QC-LDPC codes. Moreover, the proposed Biff-CRT method is flexible, easy to implement and effective for constructing the QC-LDPC codes for the relay channel, and it is attractive for being used in the future cooperative communication systems.
Due to quasi-cyclic structure of parity-check matrices, Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes reduce hardware requirements, and thus they have a higher practical value than random LDPC codes. This paper proposes an improved construction method of QC-LDPC based on PEG Algorithm, and the girth of the QC-LDPC codes has an increase of 2. Firstly, a base matrix is generated by the PEG algorithm, and then the base matrix is expanded using the unit circle permutation matrix, at the same time, the short loop of the base matrix is eliminated. This approach has the advantages of the PEG algorithm and the QC-LDPC codes, and simulation results show that bit error rate (BER) performance of the QC-LDPC codes presented in this paper is the same as or exceeds the one of randomly constructed LDPC codes.
Forward error correcting codes are successfully implemented in high speed communication for error-free transmission with high data rate. One such code is Low Density Parity Check (LDPC) code. In this paper, Quasi Cyclic (QC) construction of LDPC code is used and we investigate the performance of various decoding algorithms of QC-LDPC code. Their performances in terms of error correction and complexity are compared. The speed of convergence of various decoding algorithms of LDPC code is analyzed by using the Density Evolution theory. With this thresholding in iterations, the BER performances of different algorithms are simulated. Our results show that the same BER performance can be achieved with reduced number of iterations or the speed of the system can be improved without much sacrifice in BER performance.
According to the fact that the random construction method of LDPC(Low Density Parity Check) codes are lack of structure and are difficult to be implemented in hardware, two construction methods of QC-LDPC(Quasi-Cyclic LDPC) codes-sequential and random search method based on distance graph are proposed. The two algorithms can produce flexible QCLDPC codes by setting the parameters such as code length, rates and girth according to requirement. The simulation shows that: the random search method performs better than the sequential search method and the QC-LDPC codes constructed by random search method have equivalent BER performance with PEG construction method. Compared with the existing random construction method, the two methods proposed are faster, and can obtain quasi-cyclic codes which are easy to be implemented in hardware.
Based on the Balanced Incomplete Block Design(BIBD),a novel construction method of Quasi-Cyclic Low-Density Parity-Check(QC-LDPC) codes is further analyzed and researched.And the three QC-LDPC codes with the same code-rate and different code-length are constructed by applying the proposed method.The simulation analysis shows that under the condition of the same code-rate,the QC-LDPC code with the longer code-length has better error-correction performance.Simultaneously,at the condition of the bit error rate(BER) of 10-6 and the same code rate of 93.7%,the net coding gain(NCG) of the constructed BIBD-QC-LDPC(5392,5056) code is respectively 2.13 dB and 1.41 dB higher than that of the classic RS(255,239) code widely used in optical communication systems and that of the LDPC(32640,30592) code in ITU-T G.975.1.Therefore,the BIBD-QC-LDPC(5392,5056) code has much superior error-correction performance and is better suitable for high-speed long-haul optical communication systems.
A novel construction method of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code is proposed in this paper, which is based on protograph and Balanced Block Design (BIBD) in combinational mathematics.The method is to fill the base matrix of protograph with the base set elements of BIBD in accordance with certain mathematical rules.And the base matrix of protograph proposed in the paper has special double diagonal structure, which overcomes the low weight code words in general structure and achieves rapid encoding at the same time.The QC-LDPC code in this paper possesses lower encoding complexity and less memory occupation; therefore it is easy for hardware implementation.In addition, it effectively avoids girth 4. Simulation results show that when the Bit Error Rate (BER) is 10 -7 , QC-LDPC codes based on Protograph and BIBD (PBIBD-LDPC) proposed in this paper has 0.5dB Net Coding Gain (NCG) compared with the protograph QC-LDPC codes that based on Vander monde matrix and PEG algorithm structure, and has 0.15dB NCG compared with the excellent code QC-LDPC that based on the lifting structure.