Reconstruction of LDPC code check matrix based on random extraction at high bit error rate

Abstract

In order to improve the performance of the sparse check matrix reconstruction algorithm of LDPC codes at high BER, an open set recognition algorithm of the check matrix with strong fault tolerance under the condition of sufficient and insufficient number of received code words was proposed.Firstly, a new code word space was constructed by randomly extracting part bits of the code words for many times.Gaussian elimination method was used to solve the dual vector and restore the check vector in a lower dimension.Secondly, using the check vector, the proportion of error-free code groups in the received data was continuously increased by using the methods of “eliminating error code words” or“flipping the lowest unreliable bits” for iterative processing.Simulation results show that the proposed algorithm is superior to comparison algorithm under different bit error rates, different code lengths, different code rates and different number of code words.For (648,324) LDPC codes in IEEE 802.11n protocol, when the number of received code words is sufficient, the reconstruction rate of check matrix can reach more than 95% under the condition of bit error rate of 0.003.When the number of received code words is insufficient (the number of code words is 450), the reconstruction rate of check matrix can reach more than 90% under the condition of bit error rate of 0.0015.

Keywords

• LDPC;sparse check matrix;Gaussian elimination;eliminate error code word;log-likelihood ratio