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Journal of Chongqing University of Posts and Telecommunications

Design of rate-compatible protograph LDPC codes

Lin Wang

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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In this paper, families of rate-compatible protograph-based LDPC codes that are suitable for incrementalredundancy hybrid ARQ applications are constructed. A systematic technique to construct low-rate base codes from a higher rate code is presented. The base codes are designed to be robust against erasures while having a good performance on error channels. A progressive node puncturing algorithm is devised to construct a family of higher rate codes from the base code. The performance of this puncturing algorithm is compared to other puncturing schemes. Using the techniques in this paper, one can construct a rate-compatible family of codes with rates ranging from 0.1 to 0.9 that are within 1 dB from the channel capacity and have good error floors.

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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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Construction of Efficient High-Rate Protograph QC-LDPC Codes by Joint EXIT Chart, PEG, AWD, and QC-NLACE Techniques

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To obtain efficient channel codes with high power efficiency at moderate signal-to-noise ratios (SNRs), an efficient high-rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is optimally constructed. By 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 QC matrix template is generated with required code rate and length by the extrinsic information transfer (EXIT) chart for better decoding threshold. 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 sub-matrices to obtain larger girth for better error floor performance. Moreover, an asymptotic weight distribution (AWD) is employed to keep a low-code-error floor for the code. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC oriented nested loop approximated cycle extrinsic message degree (QC-NLACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph to cut the error floor. Simulation results show that the codes produced by the proposed method show quite good bit-error-rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency brought by the high code rate, and the low complexity by the short code length. Moreover, a series of different rate-compatible LDPC codes can be generated from the same protograph framework with some variable node extensions, which significantly eases the code design. Therefore, the proposed code construction can be efficiently applied in the optimal construction of high-rate and short-length rate-compatible QC-LDPC codes with a high data rate and rational complexity, which makes the codes extremely suited for use in new-generation power-constrained wireless communications.

Entropy•May 28, 2026•0 citations
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, families of rate-compatible protograph-based LDPC codes that are suitable for incrementalredundancy hybrid ARQ applications are constructed. A systematic technique to construct low-rate base codes from a higher rate code is presented. The base codes are designed to be robust against erasures while having a good performance on error channels. A progressive node puncturing algorithm is devised to construct a family of higher rate codes from the base code. The performance of this puncturing algorithm is compared to other puncturing schemes. Using the techniques in this paper, one can construct a rate-compatible family of codes with rates ranging from 0.1 to 0.9 that are within 1 dB from the channel capacity and have good error floors.
This work investigated the performance of a newly developed protograph-based low-density parity-check code (LDPC) families belonging to accumulate-repeat-4-jagged-accumulate codes. The proposed code has hierarchical irregularity and quasi-cyclic property that retains it to be suitable for fast encoder and decoder implementation. The code used in this work is a rate-compatible linearly punctured code. The modified iterative decoding algorithm as mentioned in the literature is used along with a newly proposed encoder and simulation has been done for proposed LDPC coded orthogonal frequency division multiplexing (OFDM) link over wireless and optical wireless channels with hard- and soft-decision decoding. The code relates to new methods for designing rate-compatible families of protographs of different rates, all having the linear minimum distance property showing small performance degradation compared with the threshold. The parity-check matrix is composed of small identical modules to reduce the routing complexity of the decoder. The main essence of this code lies in the fact that LDPC codes of arbitrarily large size can be built by expanding from individual protographs or rate-compatible protograph families.
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.
We construct a protograph-based rate-compatible family of low-density parity-check (LDPC) codes that cover a very wide range of rates from 1/2 to 16/17, perform within about 0.5 dB of their capacity limits for all rates, and can be decoded conveniently and efficiently with a common hardware implementation. In contrast to alternative methods that create codes of different rates by puncturing, shortening, or expurgation, our method uses a combination of expurgation and lengthening (equivalent to an unusual extension) to produce lower-rate codes. Advantages compared to the alternative methods include roughly uniform utilization of common family decoder hardware for different rates, implementation with uniformly low maximum check node degrees despite high maximum rate, and a large fixed portion of the protograph that can be labeled with a fixed set of edge permutations for all rates. We apply this method to create a rate-compatible code family anchored by a particular code of (nominal) rate 7/8 and length n = 8176 designed by Kou, Lin and Fossorier [1] whose edge permutations are determined by Euclidean geometries (EG). All members of our family retain all of the EG-designed edges and circulant permutations of this anchor code, and this helps to avoid weak spots in the code graph that usually arise when edge permutations are assigned by greedy algorithms. There are also varying numbers of auxiliary and ancillary checks, variables, and edges, allowing realization of different rates, with fixed (nominal) dimension k = 8176 for all rates. Simulations show that all members of this family achieve steeply falling error rate curves without detectable error floors, at least to codeword error rates of about 10-6
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.
To obtain efficient channel codes with high power efficiency at moderate signal-to-noise ratios (SNRs), an efficient high-rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is optimally constructed. By 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 QC matrix template is generated with required code rate and length by the extrinsic information transfer (EXIT) chart for better decoding threshold. 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 sub-matrices to obtain larger girth for better error floor performance. Moreover, an asymptotic weight distribution (AWD) is employed to keep a low-code-error floor for the code. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC oriented nested loop approximated cycle extrinsic message degree (QC-NLACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph to cut the error floor. Simulation results show that the codes produced by the proposed method show quite good bit-error-rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency brought by the high code rate, and the low complexity by the short code length. Moreover, a series of different rate-compatible LDPC codes can be generated from the same protograph framework with some variable node extensions, which significantly eases the code design. Therefore, the proposed code construction can be efficiently applied in the optimal construction of high-rate and short-length rate-compatible QC-LDPC codes with a high data rate and rational complexity, which makes the codes extremely suited for use in new-generation power-constrained wireless communications.