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IEEE Vehicular Technology Conference

Enhanced EMD-Driven PEG Construction for Structured LDPC Codes

Cornelius T. Healy, Rodrigo C. de Lamare

Published Jun 1, 2013• 1 citation
Publisher

Abstract

A novel algorithm to construct structured LDPC codes based on graph connectivity and cycle quality is proposed. The performance of the constructed QC-LDPC and IRA codes is investigated and a performance improvement in the error floor region is demonstrated. The code constructions provided are flexible in rate and length and demonstrate that the enhanced EMD-driven PEG-based approach proposed may be applied to a number of other structured LDPC code classes, given consideration of correct constraints of the construction.

DOI
10.1109/vtcspring.2013.6692551

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A novel algorithm to construct structured LDPC codes based on graph connectivity and cycle quality is proposed. The performance of the constructed QC-LDPC and IRA codes is investigated and a performance improvement in the error floor region is demonstrated. The code constructions provided are flexible in rate and length and demonstrate that the enhanced EMD-driven PEG-based approach proposed may be applied to a number of other structured LDPC code classes, given consideration of correct constraints of the construction.
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.
Low-density parity-check (LDPC) codes are capable of achieving excellent performance and provide a useful alternative for high performance applications. However, at medium to high signal-to-noise ratios (SNR), an observable error floor arises from the loss of independence of messages passed under iterative graph-based decoding. In this paper, the error floor performance of short block length codes is improved by use of a novel candidate selection metric in code graph construction. The proposed Multipath EMD approach avoids harmful structures in the graph by evaluating certain properties of the cycles which may be introduced in each edge placement. We present Multipath EMD based designs for several structured LDPC codes including quasi-cyclic and irregular repeat accumulate codes. In addition, an extended class of diversity-achieving codes on the challenging block fading channel is proposed and considered with the Multipath EMD design. This combined approach is demonstrated to provide gains in decoder convergence and error rate performance. A simulation study evaluates the performance of the proposed and existing state-of-the-art methods.
Recently, structured LDPC codes have been focused on due to excellent performance and lower complexity. An improved construction of QC-LDPC based on a modified PEG algorithm is proposed in this paper. The modified Progressive Edge-Growth algorithm is a PEG algorithm with Approximated Cycle Extrinsic Message Degree (ACE) metric, which is used to describe the connectivity of cycles. The approach can maximize the girth of the cycles, improve the connectivity of cycles and have the advantages of QC algorithms. The simulation results demonstrate that the PEG algorithm based on ACE has lower Bit Error Rate (BER) and Frame Error Rate (FER) than the original PEG algorithm at the low Signal Noise Ratio (SNR) values, and has a relatively lower computational complexity.
Low-density parity-check (LDPC) codes are capable of achieving excellent performance and provide a useful alternative for the high-performance applications. However, at medium to high signal-to-noise ratios, an observable error floor arises from the loss of independence of messages passed under iterative graph-based decoding. In this paper, the error floor performance of the short block length codes is improved by the use of a novel candidate selection metric in code graph construction. The proposed multipath extrinsic message degree (EMD) approach avoids harmful structures in the graph by evaluating certain properties of the cycles introduced in each edge placement. We present multipath EMD-based designs for several structured LDPC codes, including quasi-cyclic and the irregular repeat accumulate codes. In addition, an extended class of the diversity-achieving codes on the challenging block fading channel is proposed and considered with the multipath EMD design. This combined approach is demonstrated to provide the gains in decoder convergence and error rate performance. A simulation study evaluates the performance of the proposed and existing state-of-the-art methods.
There exist many different algorithms to construct good low-density parity-check (LDPC) codes. To maximize the girth of the bipartite graph, which represents the LDPC code, the progressive edge-growth (PEG) algorithm was introduced. This construction methods leads for irregular LDPC codes to a lower error floor, but also to a performance loss in the waterfall region compared with randomly constructed LDPC codes. In this paper, we describe a modification of the PEG algorithm that improves the performance in the waterfall region. Furthermore, this modified PEG algorithm yields codes with lower error floors and a slightly better performance in the waterfall region than randomly constructed LDPC codes
A modified construction method of LDPC (Low-density Parity-check) codes based on polynomial of cycles of PEG (Progressive-Edge-Growth) is proposed according to reaction on the performance of LDPC codes by polynomial of cycles based on PEG and connectivity of cycles. It can reduce the number of the shortest cycles, increase average local girth and improve connectivity of cycles while deleting short cycles by considering girth of check matrix, number of the shortest cycles and ACE (Approximate Cycle EMD), so that it can improve performance of decoding. At the same time, a construction method of QC-LDPC (quasi-cyclic-LDPC) codes based on ACE and polynomial of cycles of PEG is also proposed to deal with the complexity of implementation on hardware of unstructured codes. Simulation results show that the performance of this code is better than unstructured Mackay code and it is easier for implementation on hardware.