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IEEE International Conference on Communication Technology (ICCT)

Anti-burst PEG Algorithm for P-LDPC Codes with Short-to-Medium Length

Li Juan DENG, Zhiping Shi, Yanxia Li, Rui Hua Tang

Published Oct 1, 2018• 1 citation
Publisher

Abstract

Protograph low-density parity-check (P-LDPC) codes are widely researched in communication systems due to the simple encoder structure and high-speed iterative decoding implementation. The key factors to affect the performance of P-LDPC codes are the base matrix and the lifting method. This paper focuses on the lifting method of P-LDPC codes with short-to-medium length over burst-error channels. An improved anti-burst protograph progressive edge-growth (IPPEG) algorithm based on edge constraints is proposed to improve the bit error rate (BER) performance. Simulation results show that the proposed IPPEG has better burst-resistance performance than the traditional PEG based lifting algorithm (PPEG) with or without random interleaver; additionally, on the premising of correctly decoding, more coding gains of IPPEG can be achieved with condition of larger channel transition probability, shorter code length or smaller coding rate.

DOI
10.1109/icct.2018.8599984

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Protograph low-density parity-check (P-LDPC) codes are widely researched in communication systems due to the simple encoder structure and high-speed iterative decoding implementation. The key factors to affect the performance of P-LDPC codes are the base matrix and the lifting method. This paper focuses on the lifting method of P-LDPC codes with short-to-medium length over burst-error channels. An improved anti-burst protograph progressive edge-growth (IPPEG) algorithm based on edge constraints is proposed to improve the bit error rate (BER) performance. Simulation results show that the proposed IPPEG has better burst-resistance performance than the traditional PEG based lifting algorithm (PPEG) with or without random interleaver; additionally, on the premising of correctly decoding, more coding gains of IPPEG can be achieved with condition of larger channel transition probability, shorter code length or smaller coding rate.
The progressive edge-growth (PEG) algorithm is a general method to construct short low-density parity-check (LDPC) codes and it is a greedy method to place each edge with large girths. In order to improve the performance of LDPC codes, many improved PEG (IPEG) algorithms employ multi metrics to select surviving edges in turn. In this paper, the proposed edges metric (EM) based on message-passing algorithm (MPA) is introduced to PEG algorithm and the proposed EM constrained PEG (EM-PEG) algorithm mainly considers the independence of message passing from different nodes in Tanner graph. The numerical results show that our EM-PEG algorithm brings better bit error rate (BER) performance gains to LDPC codes than the traditional PEG algorithm and the powerful multi-edge multi-metric constrained PEG algorithm (MM-PEGA) proposed recently. In addition, the multi-edge EM constrained PEG (M-EM-PEG) algorithm which adopts multi-edge EM may further improve the BER performance.
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 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 is known to construct low-density parity-check (LDPC) codes at finite code lengths with large girths by establishing edges between symbol and check nodes in an edge-by-edge manner. The linear-encoding PEG (LPEG) algorithm, a simple variation of the PEG algorithm, can be applied to generate linear time encodable LDPC codes whose m parity bits p1, p2, ..., p m are computed recursively in m steps. In this article, we propose modifications of the LPEG algorithm to construct LDPC codes whose number of encoding steps is independent of the code length. The maximum degree of the symbol nodes in the Tanner graph is denoted by ; The m parity bits of the proposed LDPC codes are divided into subgroups and can be computed in only steps. Since , the number of encoding steps can be significantly reduced. It has also been proved that the PEG codes and the codes proposed in this article have similar lower bound on girth. Simulation results showed that the proposed codes perform very well over the AWGN channel with an iterative decoding.
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.
The progressive-edge-growth (PEG) algorithm for constructing Tanner graphs with large girth by progressively establishing edges/connections between symbol nodes and check nodes in an edge-by-edge way is highly known to construct low-density parity-check (LDPC) codes at short block lengths for achieving good performance. This paper proposed an improved PEG construction for irregular codes, which heuristically selects good codes from random graphs for short block lengths. The simulation results are given to demonstrate that the proposed algorithm gians better BER performance for high signal-to-noise (SNR) ratios without performance loss for low-SNR region, i.e. low error floor.