We discuss error floor asympotics and present a method for improving the performance of low-density parity-check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do no...
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We discuss error floor asympotics and present a method for improving the performance of low-density parity-check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets from the original code. The advantages of the method are that it is universal, as it can be applied to any LDPC code/channel/decodingalgorithm and it improves performance at the expense of increasing the code length, without losing the code regularity, without changing the decodingalgorithm, and, under certain conditions, without lowering the code rate. The proposed method can be modified to construct convolutional LDPC codes also. The method is illustrated by modifying Tanner, MacKay and Margulis codes to improve performance on the binary symmetric channel (BSC) under the Gallager B decodingalgorithm. decoding results on AWGN channel are also presented to illustrate that optimizing codes for one channel/decodingalgorithm can lead to performance improvement on other channels.
Non-binary low-density parity-check (NB-LDPC) codes show larger coding gain and lower error floor than their binary counterparts in many cases. However, the existing soft decodingalgorithms of NB-LDPC codes generally...
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Non-binary low-density parity-check (NB-LDPC) codes show larger coding gain and lower error floor than their binary counterparts in many cases. However, the existing soft decodingalgorithms of NB-LDPC codes generally suffer from high computational complexity. Recently, the trellis-based extended min-sum (T-EMS) decodingalgorithm has attracted much attention since it can achieve good decoding performance with high parallelism and low computational complexity. In this paper, we propose two new methods to further reduce the computational complexity and enhance the decoding performance. Firstly, we introduce, with theoretical justification, a universal scheme called threshold-based shrinking (TS) scheme, which facilitates significant reduction of computational complexity for decoding of NB-LDPC codes. Secondly, we present a modified two-extra-column (TEC) scheme and apply it to the T-EMS. Furthermore, a high-performance low-complexity decodingalgorithm, named TEC-TEMS algorithm, is obtained. Combining the TS scheme with the TEC-TEMS, the new algorithm, named TS-TEC-TEMS algorithm, achieves much lower computational complexity and has negligible performance loss compared to the TEC-TEMS. For a 256-ary (256, 203) example code, compared to the T-EMS, the computational complexities of the TEC-TEMS and TS-TEC-TEMS algorithms are reduced by more than 50% and nearly 90%, respectively. Moreover, the TEC-TEMS and TS-TEC-TEMS both outperform the T-EMS by about 0.3dB when the frame error rate (FER) is around 10(-5).
This study investigates the decodingalgorithms of binary Reed-Muller (RM) codes. The main goal of the study is to modify majority-logic decoding using sum-product or min-sum decoding algorithms at the highest-order i...
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This study investigates the decodingalgorithms of binary Reed-Muller (RM) codes. The main goal of the study is to modify majority-logic decoding using sum-product or min-sum decoding algorithms at the highest-order information bits in RM codes. Numerical results show that compared with the traditional majority-logic decodingalgorithm, the modified majority-logic decoding method proposed in this study can reduce the bit error rate by a large margin. This is achieved without incurring a significant increase in decoding complexity because soft-decision decoding is only used in the highest information bits in RM codes whereas majority-logic decoding is still applied at the other orders of information bits in RM codes.
In this paper, the dual-threshold-based shrinking (DTBS) scheme for efficient non-binary low-density parity-check (NB-LDPC) decoding, which has been initially presented in our previous work [1], is further studied. Pa...
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ISBN:
(纸本)9781538682401
In this paper, the dual-threshold-based shrinking (DTBS) scheme for efficient non-binary low-density parity-check (NB-LDPC) decoding, which has been initially presented in our previous work [1], is further studied. Particularly, the TIT-MSA is an example to employ this scheme presented in [1]. Its computational complexity is theoretically analyzed in this paper. Numerical results show that more than 70% computational complexity is reduced compared with the SMSA, while the error performance loss is negligible. Besides, when considering memory consumption, we extend this scheme by setting a maximum number of kept values with an efficient searching method, and apply it to the TIT-MSA. Simulation results indicate that the new decodingalgorithm achieves both comparable error performance and significant memory reduction. For example, the memory consumption is reduced by about 61% for a (256, 203) code over GF(2(8)) and about 31% for an (837, 726) code over GF(2(5)).
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