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IEEE Vehicular Technology Conference

Construction of Regular Quasi-Cyclic Protograph LDPC codes based on Vandermonde Matrices

Nicholas Bonello, Sheng Chen, Lajos Hanzo

Published Sep 1, 2008• 1 citation
Publisher

Abstract

In this contribution, we investigate the attainable performance of quasi-cyclic (QC) protograph low-density parity-check (LDPC) codes for transmission over both Additive White Gaussian noise (AWGN) and uncorrelated Rayleigh channels. The codes presented are constructed using the Vandermonde matrix and benefit from both low- complexity encoding and decoding, low memory requirements as well as hardware-friendly implementations. Our simulation results demonstrate that the advantages offered by this family of QC protograph LDPC codes accrue without any compromise in the attainable bit error ratio (BER) and block error ratio (BER) performance. In fact, it is also shown that despite their implementational benefits, the proposed codes exhibit slight BER/BLER gains when compared to some of their more complex counterparts of the same length.

DOI
10.1109/vetecf.2008.158

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Construction of Regular Quasi-Cyclic Protograph LDPC Codes Based on Vandermonde Matrices

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In this paper, we investigate the attainable performance of quasi-cyclic (QC) protograph low-density parity-check (LDPC) codes for transmission over both additive white Gaussian noise and uncorrelated Rayleigh channels. The presented codes are constructed using the Vandermonde matrix and thus have a girth of at least six in their corresponding Tanner graph. Furthermore, they also benefit from both low-complexity encoding and decoding, low memory requirements, as well as hardware-friendly implementations. Our simulation results demonstrate that the advantages offered by this family of QC protograph LDPC codes accrue with no compromise in the attainable bit error ratio (BER) and block error ratio (BLER) performances. In fact, it is also shown that despite their implementational benefits, the proposed codes exhibit slight BER/BLER gains when compared to some of their more complex counterparts of the same length.

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In this contribution, we investigate the attainable performance of quasi-cyclic (QC) protograph low-density parity-check (LDPC) codes for transmission over both Additive White Gaussian noise (AWGN) and uncorrelated Rayleigh channels. The codes presented are constructed using the Vandermonde matrix and benefit from both low- complexity encoding and decoding, low memory requirements as well as hardware-friendly implementations. Our simulation results demonstrate that the advantages offered by this family of QC protograph LDPC codes accrue without any compromise in the attainable bit error ratio (BER) and block error ratio (BER) performance. In fact, it is also shown that despite their implementational benefits, the proposed codes exhibit slight BER/BLER gains when compared to some of their more complex counterparts of the same length.
In this paper, we investigate the attainable performance of quasi-cyclic (QC) protograph low-density parity-check (LDPC) codes for transmission over both additive white Gaussian noise and uncorrelated Rayleigh channels. The presented codes are constructed using the Vandermonde matrix and thus have a girth of at least six in their corresponding Tanner graph. Furthermore, they also benefit from both low-complexity encoding and decoding, low memory requirements, as well as hardware-friendly implementations. Our simulation results demonstrate that the advantages offered by this family of QC protograph LDPC codes accrue with no compromise in the attainable bit error ratio (BER) and block error ratio (BLER) performances. In fact, it is also shown that despite their implementational benefits, the proposed codes exhibit slight BER/BLER gains when compared to some of their more complex counterparts of the same length.
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.
In this paper, we proposed a novel method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes based on cyclic subgroup over GF(q) . LDPC codes constructed by this method are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN) with sum product algorithm (SPA). The main advantage is that QC LDPC codes with a variety of block lengths and rates can be easily constructed with no cycles of length four or less. Simulation results show that the proposed QC LDPC codes perform slight better than the random regular LDPC codes for short to moderate block lengths. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.
We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. By carefully designing the parity-check matrix, our approach ensures both structural flexibility and improved error-correction capabilities. We evaluate the performance of these codes under the additive white Gaussian noise (AWGN) channel. Simulation results demonstrate that the proposed QC-LDPC codes outperform the protograph LDPC codes included in the Consultative Committee for Space Data Systems (CCSDS) telecommand standards. Additionally, we benchmark our proposed codes against existing short-length codes with girth 8, observing improvements in the decoding performance while ensuring suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs for the Internet of Things (IoT), machine-to-machine (M2M), and satellite communications.
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.
We introduce the protograph sieving method as a tool for optimization of moderate length Multi-Edge Type Quasi-Cyclic Low-Density Parity-Check (MET QC-LDPC)codes. The proposed method allows to improve code distance property with defined graph balanced cycles and construct MET-LDPC protograph for the code length in gap between Scattering PEXIT-chart and Covariance Evolution methods. We show that this approach improves code distance properties and achieves 0.2 dB gain in terms of block error rate (BLER)over the additive white Gaussian noise (AWGN)channel for information length of 600 bits and rate 1/3, at a target BLER of 10-6when compared to BG2 MET-LDPC code proposed at 5G standard.