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International Conference on Wireless Communications, Networking and Mobile Computing

Optimization of Bilayer Lengthened QC-LDPC Code for Relay Channel Based on Differential Evolution

Hua Xu

Published Sep 1, 2011• 1 citation
Publisher

Abstract

A novel optimization algorithm to design a bilayer lengthened QC-LDPC code for relay channel is proposed in this paper, which combine differential evolution algorithm and bilayer graph for LDPC codes. We aim to construct QC-LDPC codes with best girth(maximum girth and minimum numbers of shortest cycles)both at relay node and destination node. Proposed algorithm is composed of two steps, first the exponent matrix of QC-LDPC code for lower graph is searched by differential evolution algorithm, then the exponent matrix of QC-LDPC code for overall graph is also found by differential evolution algorithm based on the obtained exponent matrix for lower graph. Simulation results verify the validity of proposed algorithm. Constructed QC-LDPC codes may perform well both at relay node and destination node.

DOI
10.1109/wicom.2011.6040191

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arXiv:1210.3906•IEEE Transactions on Information Theory•Jun 14, 2013•30 citations
A novel optimization algorithm to design a bilayer lengthened QC-LDPC code for relay channel is proposed in this paper, which combine differential evolution algorithm and bilayer graph for LDPC codes. We aim to construct QC-LDPC codes with best girth(maximum girth and minimum numbers of shortest cycles)both at relay node and destination node. Proposed algorithm is composed of two steps, first the exponent matrix of QC-LDPC code for lower graph is searched by differential evolution algorithm, then the exponent matrix of QC-LDPC code for overall graph is also found by differential evolution algorithm based on the obtained exponent matrix for lower graph. Simulation results verify the validity of proposed algorithm. Constructed QC-LDPC codes may perform well both at relay node and destination node.
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.
This paper presents a new bilayer-expurgated LDPC (BE-LDPC) code design for decode-and-forward relay system. The code design is based on the multi-edge type LDPC (MET-LDPC) code structure. The lower and upper graphs' edges of the BE-LDPC codes are represented via different edge types. We call the codes as multi-edge type bilayer-expurgated LDPC (MET-BE-LDPC) codes. We derive the relationship between the lower and the overall graphs of the MET-BE-LDPC codes using the multi-edge type multinomials. This relationship acts as a constraint in optimizing the MET-BE-LDPC codes under the density evolution. We apply the differential evolution algorithm to search for the best MET-BE-LDPC codes. Applying the proposed methodology, two MET-BE-LDPC codes are designed. The codes perform asymptotically within 0.08474-0.5087 dB from the theoretical limits. Finally, we demonstrate that the proposed methodology can be used to design the BE-LDPC codes at a larger source-to-relay and source-to-destination SNR differences.
In this paper, we consider the construction of irregular QC-LDPC codes by jointly optimizing the girth, the number and approximate cycle extrinsic message degree (ACE) of short cycles to further improve the error-floor performance of irregular QC-LDPC codes with given degree distributions. By selecting the best edges, each of which must make the cycles consisting of the current variable node have the best lower bound of ACE or the minimum number of cycles with ACE lower bound, for each variable node via the progressive Edge growth (PEG) approaches, irregular QC-LDPC codes with better tradeoff between girth, the shortest cycle number and ACE could be constructed. Simulation results show that the proposed codes achieve better error-floor performance compared with the codes using the same degree distributions constructed by the recent proposed methods.
For a given base graph, the protograph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the protograph corresponds to a quasi-cyclic (QC) protograph LDPC code. The girth of the QC protograph LDPC code is determined by the girth of the base graph and the permutation shifts. Progressive edge-growth (PEG) construction builds up a Tanner graph, or equivalently a parity-check matrix, for an LDPC code by maximizing the local girth at symbol nodes in a greedy algorithm. In this paper, we introduce a modified version of the PEG algorithm which can construct large girth base graph and determine the optimal permutation shifts, simultaneously, for QC protograph LDPC codes. Simulation results show that the QC protograph LDPC codes constructed by the proposed modified PEG algorithm have good frame error rate (FER) performance over the AWGN channel.
To obtain efficient and pragmatic channel codes high signal-to-noise ratios (SNRs), an optimized construction of short and high rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is presented. Based on an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base quasi-cyclic (QC) matrix is generated with required code rate and length. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive edge growth (PEG) algorithm is employed to find the optimized positions of the QC submatrices, which brings larger girth for better code performance. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC improved approximated cycle extrinsic message degree (QCI-ACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph and thus it improves the error floor. Simulation results show that the codes produced by the proposed method demonstrate quite good bit error rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency by the high code rate, as well as the low complexity by the short code length. Therefore, the proposed code construction can be efficiently applied in the design of short and high rate protograph QC-LDPC codes with high rate and rational complexity.
There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them focus on protographs with single edges and little research has been done for the construction of QC LDPC codes lifted from protographs with multiple (i.e., parallel) edges. Compared to single-edge protographs, multiple-edge protographs have benefits such that QC LDPC codes lifted from them can potentially have larger minimum Hamming distance. In this paper, all subgraph patterns of multiple-edge protographs, which prevent QC LDPC codes from having large girth by inducing inevitable cycles, are fully investigated based on a graph-theoretic approach. By using combinatorial designs, a systematic construction method of multiple-edge protographs is proposed for regular QC LDPC codes with girth at least 12 and another method is proposed for regular QC LDPC codes with girth at least 14. Moreover, a construction algorithm of QC LDPC codes based on certain liftings of multiple-edge protographs is proposed and it is shown that the resulting QC LDPC codes have larger upper bounds on the minimum Hamming distance than those lifted from single-edge protographs. Simulation results are provided to compare the performance of the proposed QC LDPC codes with progressive edge-growth (PEG) LDPC codes and with PEG QC LDPC codes.