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Journal of Beijing Jiaotong University

Design of multi-rate protograph LDPC codes with fast encoding

Yang Xiao

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The real application of protograph LDPC codes involves two problems: fast encoding and the encoding complexity.Protograph LDPC codes suit for fast decoding comparing with other LDPC codes,but protograph LDPC codes are not necessarily able to achieve fast encoding.The encoding of existing protograph LDPC codes is done by generate matrix,but the generate matrix of protograph LDPC codes is not sparse.Thus,protograph LDPC codes exists encoding complexity,which makes it difficult for encoder hardware implementation.In order to lower the encoding complexity of protograph LDPC codes,this paper proposes a design of multi-rate protograph LDPC codes with fast encoding;The proposed multi-rate protograph LDPC codes do not exist girth-4s;Furthermore,the fast encoding algorithms of the proposed multi-rate protograph LDPC codes can reduce encoding complexity and simplify encoder hardware.The simulation results in AWGN channels show that the BER and correct error ability performance of the proposed multi-rate protograph LDPC codes is much better than that of GB20600 LDPC codes.

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Design of rate-compatible protograph LDPC codes

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Over time-varying wireless channel,it is necessary for error-correction codes to be rate-compatible.Protograph LDPC codes can achieve rate-compatibility through and extending;and solve the problem that the encoders of tradition LDPC codes are more complex.With the AR4JA code which can be represented by protograph,we construct a rate-compatible family of AR4JA codes with rates ranging from 0.5 to 0.8 using the algorithm of puncturing node by node.To obtain the lower rates from 0.5 to 0.25,matrix expansion is also used.Simulation results over AWGN channel show that using both and extending we can construct rate-compatible family of AR4JA codes which do not suffer from error floor when BER is 10-6.

Journal of Chongqing University of Posts and Telecommunications•Jan 1, 2012•0 citations

Construction of protograph LDPC codes based on Jacket matrices

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In this paper, we propose a method to construct the protograph LDPC codes based on Jacket matrices. In the proposed code construction, the Jacket matrices are regarded as derived protograph matrices, the column weights of permutation matrices in parity check matrix depend on the elements' values of Jacket matrices. While the shift rule of the permutation matrices needs to ensure no girth 4. The proposed LDPC codes are easy to be applied for the codec of mobile digital multimedia. The simulation results in AWGN channels show that the BER performance of the proposed codes is better by about 0.5 dB than that of GB20600 LDPC codes.

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We propose a novel design of rate-compatible protograph-based low-density parity-check code families that can cover a wide range of code rates. In contrast to traditional method of lifting, our lifting method use a combination of different circulant matrix sizes for the base protograph and accumulator to increase the number of achievable rates. We apply this method to an existing code family called AR4JA, which can offer variable rates of R = n+1/n+2 by process of extension. The proposed codes namely mixed-circulant rate-compatible protograph code (MCRC-PC) can reduce the rate step within the AR4JA family. We show that the proposed codes can also retain many of the favorable properties of protograph codes such as a fast encoder and decoder implementation. A set of length k=1024 MCRC-PC codes is designed with decoding thresholds obtained from multi-edge type density evolution, and simulation results show that the rate compatible code family can achieve good performance under message passing decoding algorithm.

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Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH

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One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.

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Optimized Construction of Short and High Rate Protograph QC-LDPC Codes

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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.

International Conference on Wireless Communications and Signal Processing (WCSP)•Oct 20, 2021•1 citation
The real application of protograph LDPC codes involves two problems: fast encoding and the encoding complexity.Protograph LDPC codes suit for fast decoding comparing with other LDPC codes,but protograph LDPC codes are not necessarily able to achieve fast encoding.The encoding of existing protograph LDPC codes is done by generate matrix,but the generate matrix of protograph LDPC codes is not sparse.Thus,protograph LDPC codes exists encoding complexity,which makes it difficult for encoder hardware implementation.In order to lower the encoding complexity of protograph LDPC codes,this paper proposes a design of multi-rate protograph LDPC codes with fast encoding;The proposed multi-rate protograph LDPC codes do not exist girth-4s;Furthermore,the fast encoding algorithms of the proposed multi-rate protograph LDPC codes can reduce encoding complexity and simplify encoder hardware.The simulation results in AWGN channels show that the BER and correct error ability performance of the proposed multi-rate protograph LDPC codes is much better than that of GB20600 LDPC codes.
Over time-varying wireless channel,it is necessary for error-correction codes to be rate-compatible.Protograph LDPC codes can achieve rate-compatibility through and extending;and solve the problem that the encoders of tradition LDPC codes are more complex.With the AR4JA code which can be represented by protograph,we construct a rate-compatible family of AR4JA codes with rates ranging from 0.5 to 0.8 using the algorithm of puncturing node by node.To obtain the lower rates from 0.5 to 0.25,matrix expansion is also used.Simulation results over AWGN channel show that using both and extending we can construct rate-compatible family of AR4JA codes which do not suffer from error floor when BER is 10-6.
In this paper, we propose a method to construct the protograph LDPC codes based on Jacket matrices. In the proposed code construction, the Jacket matrices are regarded as derived protograph matrices, the column weights of permutation matrices in parity check matrix depend on the elements' values of Jacket matrices. While the shift rule of the permutation matrices needs to ensure no girth 4. The proposed LDPC codes are easy to be applied for the codec of mobile digital multimedia. The simulation results in AWGN channels show that the BER performance of the proposed codes is better by about 0.5 dB than that of GB20600 LDPC codes.
In this paper we design protograph-based LDPC codes with short block sizes. Mainly we consider rate 1/2 codes with input block sizes 64, 128, and 256 bits. To simplify the encoder and decoder implementations for high data rate transmission, the structure of the codes is based on protographs and circulants. These codes are designed for short block sizes based on maximizing the minimum distance and stopping set size subject to a constraint on the maximum variable node degree. In particular, we consider codes with variable node degrees between 3 and 5. Increasing the node degree leads to larger minimum distances, at the expense of smaller girth. Therefore, there is a trade-off between undetected error rate performance (improved by increasing minimum distance) and the degree of sub-optimality of the iterative decoders typically used (which are adversely affected by graph loops). Various LDPC codes are compared and simulation results are provided.
We propose a novel design of rate-compatible protograph-based low-density parity-check code families that can cover a wide range of code rates. In contrast to traditional method of lifting, our lifting method use a combination of different circulant matrix sizes for the base protograph and accumulator to increase the number of achievable rates. We apply this method to an existing code family called AR4JA, which can offer variable rates of R = n+1/n+2 by process of extension. The proposed codes namely mixed-circulant rate-compatible protograph code (MCRC-PC) can reduce the rate step within the AR4JA family. We show that the proposed codes can also retain many of the favorable properties of protograph codes such as a fast encoder and decoder implementation. A set of length k=1024 MCRC-PC codes is designed with decoding thresholds obtained from multi-edge type density evolution, and simulation results show that the rate compatible code family can achieve good performance under message passing decoding algorithm.
One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.
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.