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IEEE Access

Modified CC-PEG Algorithm for Protograph-Based QC-LDPC Codes Over Non-Uniform Channel

H. Lee, Jae-Won Kim

Published Jan 1, 2024• 3 citations
Publisher

Abstract

In this paper, we propose the modified cycle-concentrating progressive-edge-growth (CC-PEG) algorithm for lifting protograph-based quasi-cyclic low-density parity-check (QC-LDPC) codes over the non-uniform additive white Gaussian noise (AWGN) channel. By introducing various selection criteria for shift values based on the non-uniform channel characteristics, we improve the decoding performances of lifted LDPC codes. From numerous simulation results, we demonstrate that each selection criterion is effective for the performance improvement and the modified CC-PEG algorithm outperforms the conventional lifting methods over the non-uniform AWGN channel. Furthermore, we analyze these simulation results based on some metrics such as the girth, number of cycles, and approximate cycle extrinsic message degree (ACE).

DOI
10.1109/access.2024.3502712

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In this paper, we propose the modified cycle-concentrating progressive-edge-growth (CC-PEG) algorithm for lifting protograph-based quasi-cyclic low-density parity-check (QC-LDPC) codes over the non-uniform additive white Gaussian noise (AWGN) channel. By introducing various selection criteria for shift values based on the non-uniform channel characteristics, we improve the decoding performances of lifted LDPC codes. From numerous simulation results, we demonstrate that each selection criterion is effective for the performance improvement and the modified CC-PEG algorithm outperforms the conventional lifting methods over the non-uniform AWGN channel. Furthermore, we analyze these simulation results based on some metrics such as the girth, number of cycles, and approximate cycle extrinsic message degree (ACE).
For a given base graph, the lifted graph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the lifted graph corresponds to a quasi-cyclic (QC) protograph low-density parity-check (LDPC) code. The girth of the QC protograph LDPC code is determined by the girth of the base graph and the permutation shifts. In this paper, we first derive a lower bound on the lifting degree to achieve a large girth lifted graph. Then, motivated by the cycle searching and girth maximizing features of the progressive edge-growth (PEG) algorithm, we introduce the permutation shifts determining (PSD) PEG algorithm, which can construct large girth base graph and determine the optimal permutation shifts, simultaneously. It is shown that the computational complexity of PSD-PEG algorithm is much lower than that of the PEG algorithm and the PEG-QC algorithm for the same codeword length. Furthermore, we show that the PSD-PEG algorithm can also be used to construct nonbinary QC protograph LDPC codes without low weight codes. Simulation results show that the binary and nonbinary QC protograph LDPC codes constructed by the PSD-PEG algorithm have good bit error rate performance and frame error rate performance over the additive white Gaussian noise channel.
In this paper, we propose the cycle-concentrating progressive edge growth (CC-PEG) algorithm for lifting protograph generalized low-density parity-check (GLDPC) codes. In GLDPC codes,undoped variable nodes(VNs) that are not connected to generalized constraint (GC) nodes are more vulnerable to channel errors thandoped VNsprotected by GC nodes. We observe that among GLDPC codes sharing the same protograph structure, codes with fewer local cycles at undoped VNs have better decoding performances. Inspired by this observation, the CC-PEG algorithm is proposed to concentrate local cycles at doped VNs and avoid local cycles at vulnerable undoped VNs during the lifting process. Specifically, the CC-PEG algorithm first collects edges that result in the maximumundoped girth, defined as the length of the shortest cycle containing undoped VNs. Following this, the CC-PEG algorithm selects the edge with the lowestconcentrated cycle metric. Consequently, the lifted codes exhibit asymmetric cycle distributions concentrated around robust doped VNs. Simulation results for various protographs show that the CC-PEG algorithm achieves a performance gain of up to 20 times lower frame error rate compared to conventional lifting algorithms.
The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.
In this paper, we propose a method to construct parity-check matrices of Quasi Cyclic (QC) LDPC codes based on the progressive edge-growth (PEG) algorithm with maximized girth property. The proposed algorithm can eliminate short cycles and improve the decoding performance. Simulation results illustrate that the codes constructed with the proposed algorithm have superior performance to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel. At the BER of 10-7, the coding gain of 0.005 dB.
We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to maximize the components of the approximate cycle extrinsic message degree (ACE) spectrum of the code's Tanner graph in a greedy fashion. As a consequence, the designed code would perform well in the error floor region. Moreover, the proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.
We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.