This paper deals with the Low-Density Parity-Check codes with the constituent Hamming codes (H-LDPC codes) and two different iterative hard-decision low-complexity decoding algorithms. Both algorithms are based on the same main idea: the decreasing of the syndrome weight on each step of the decoding algorithm. The first decoding algorithm uses the properties of the constituent Hamming code. The best known lower-bound on the guaranteed corrected errors fraction for the H-LDPC codes under the first decoding algorithm was obtained in 2011. The second decoding algorithm considers H-LDPC as the irregular LDPC code and uses the well-known majority decoding algorithm. The lower-bound on the guaranteed corrected errors fraction for H-LDPC code under the second decoding algorithm is introduced for the first time in this paper. Numerical results for the lower-bound, obtained in this paper for H-LDPC code under the second decoding algorithm, significantly exceed the numerical results for the best known lower-bounds, obtained previously for H-LDPC code under the first decoding algorithm.
This paper use serial BP decoding algorithm to decode nonbinary LDPC codes in order to reduce decoding latency in optical fiber communication system.Then we introduce the serial BP decoding algorithm for nonbinary LDPC codes and the simulation model of optical communication system in detail.After that we show the performance effect of the maximum iterations of serial BP decoding algorithm in LDPC decoder and compare the performance of the decoder with traditional BP decoding algorithm and serial BP decoding algorithm.The result indicates that serial BP decoding algorithm can really increase the convergence speed of LDPC decoder.