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Algorithm Design of Quantized Min-Sum Decoder for Low-density Parity-Check (LDPC) Codes Based on Density Evolution

Xinmei Wang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Design of quantized Min-Sum decoder for low-density parity-check (LDPC) codes is very important for the application of LDPC codes.Based on the theory of density evolution,the paper proposes an algorithm to optimize the uniform or ununiform quantized Min-Sum decoder for regular or irregular LDPC codes.Compared with the continuous Sum-Product decoder,the proposed quantized decoder can reduce computational cost with little performance degradation, involving only integer addition calculations.

Related papers

Performance of Quantized Min-Sum Decoding Algorithms for Irregular LDPC Codes

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This paper analyzes the performance of quantized min-sum decoding algorithms for irregular low-density parity-check (LDPC) codes. For regular LDPC codes, it is known that the normalized or offset min-sum decoding algorithm with quantization bits less than 6 bits achieves good performances over wide range of signal-to-noise ratios (SNR). However, finite precision effects in decoding irregular LDPC codes are different from that in decoding regular LDPC codes which is caused by the difference of convergence speeds between low degree nodes and high degree nodes. This paper proposes a novel method to improve the performance of the conventional normalized or offset min-sum decoding algorithm when it is approximated with finite precision for hardware implementations. The proposed method applies down-scaling factors to intrinsic information which has effects on increasing the reliability of extrinsic information at variable nodes and compensating the quantization errors caused by finite precision. Computer simulation results for irregular LDPC codes show that the proposed normalized and offset min-sum decoding algorithms achieve better performances at high SNR compared to the conventional normalized and offset min-sum algorithms under (6:2) quantization scheme.

IEEE International Symposium on Circuits and Systems proceedings•May 1, 2007•15 citations

Discrete density evolution and LDPC codes designwith asymmetric channels

涛 袁, 征 马, 琦珂 庞 +1 more

To design low-density parity-check (LDPC) codes with asymmetric channels and analyze their performance, an achievable asymmetric discrete density evolution method is proposed, which is based on offset min-sum decoding. First, the iterative formula of low-complexity asymmetric channel discrete density evolution is derived by means of combinatorics, difference method and the binomial theorem. The iterative formula is applied to further optimize the design of the LDPC codes using the offset min-sum decoding, and the optimal degree distributions and performance of the LDPC codes under different quantization ranges and step sizes are obtained under the asymmetric channel. Finally, the optimal offset values under high-precision quantization are obtained. The results show that under the asymmetric channel, the complexity of the proposed asymmetric density evolution method based on the offset min-sum decoding is reduced by an order of magnitude than that using the original method. For a fixed code rate, the smaller the variable node degree of the regular codes, the better the performance and the smaller the optimal offset value. For irregular LDPC codes, the optimal degree distributions and offset values are determined according to the differential evolution algorithm. For a fixed code rate, the larger the maximum variable node degree, the better the performance of irregular codes.

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Optimized Min-Sum Decoding Algorithm for Low Density Parity Check Codes

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•Oct 31, 2015•2 citations

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Rajarshini Mishra

Low-density parity-check (LDPC) have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost , time, power and bandwidth requirements of target applications. Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important subclass of LDPC codes that are known as one of the most effective error controlling methods. Quasi cyclic codes are known to possess some degree of regularity. Many important communication standards such as DVB-S2 and 802.16e use these codes. The proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.Proposed decoder is well matched for VLSI implementation and will be implemented on Xilinx FPGA family

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Low Density Parity Check (LDPC) approaches Shannon -limit performance for binary field and long code lengths. However performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding, while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.

International Conference on Advanced Communication Technology•Jan 1, 2012•5 citations
Design of quantized Min-Sum decoder for low-density parity-check (LDPC) codes is very important for the application of LDPC codes.Based on the theory of density evolution,the paper proposes an algorithm to optimize the uniform or ununiform quantized Min-Sum decoder for regular or irregular LDPC codes.Compared with the continuous Sum-Product decoder,the proposed quantized decoder can reduce computational cost with little performance degradation, involving only integer addition calculations.
This paper analyzes the performance of quantized min-sum decoding algorithms for irregular low-density parity-check (LDPC) codes. For regular LDPC codes, it is known that the normalized or offset min-sum decoding algorithm with quantization bits less than 6 bits achieves good performances over wide range of signal-to-noise ratios (SNR). However, finite precision effects in decoding irregular LDPC codes are different from that in decoding regular LDPC codes which is caused by the difference of convergence speeds between low degree nodes and high degree nodes. This paper proposes a novel method to improve the performance of the conventional normalized or offset min-sum decoding algorithm when it is approximated with finite precision for hardware implementations. The proposed method applies down-scaling factors to intrinsic information which has effects on increasing the reliability of extrinsic information at variable nodes and compensating the quantization errors caused by finite precision. Computer simulation results for irregular LDPC codes show that the proposed normalized and offset min-sum decoding algorithms achieve better performances at high SNR compared to the conventional normalized and offset min-sum algorithms under (6:2) quantization scheme.
To design low-density parity-check (LDPC) codes with asymmetric channels and analyze their performance, an achievable asymmetric discrete density evolution method is proposed, which is based on offset min-sum decoding. First, the iterative formula of low-complexity asymmetric channel discrete density evolution is derived by means of combinatorics, difference method and the binomial theorem. The iterative formula is applied to further optimize the design of the LDPC codes using the offset min-sum decoding, and the optimal degree distributions and performance of the LDPC codes under different quantization ranges and step sizes are obtained under the asymmetric channel. Finally, the optimal offset values under high-precision quantization are obtained. The results show that under the asymmetric channel, the complexity of the proposed asymmetric density evolution method based on the offset min-sum decoding is reduced by an order of magnitude than that using the original method. For a fixed code rate, the smaller the variable node degree of the regular codes, the better the performance and the smaller the optimal offset value. For irregular LDPC codes, the optimal degree distributions and offset values are determined according to the differential evolution algorithm. For a fixed code rate, the larger the maximum variable node degree, the better the performance of irregular codes.
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Low-density parity-check (LDPC) have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost , time, power and bandwidth requirements of target applications. Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important subclass of LDPC codes that are known as one of the most effective error controlling methods. Quasi cyclic codes are known to possess some degree of regularity. Many important communication standards such as DVB-S2 and 802.16e use these codes. The proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.Proposed decoder is well matched for VLSI implementation and will be implemented on Xilinx FPGA family
Low Density Parity Check (LDPC) approaches Shannon -limit performance for binary field and long code lengths. However performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding, while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.