The Study And Application Of Layered Low-Density Parity-Check Codes With Polarization Effect

The efficiency and the accuracy of information transmission are the most two critical concerns of the wireless communication system.Channel coding is one of the most important technologies to guarantee the accuracy.Low-density parity-check codes(LDPC codes)are the most widely used channel coding scheme in these days,with a flexible structure of code word,encoding algorithm with linear complexity,parallel decoding structure,and the near-shannon-limit transmission efficiency.In 2016,3GPP officially made the announcement that LDPC codes were chosen to be the data channel coding scheme of enhanced mobile broadband(eMBB)in the fifth generation mobile communication system(5G).Nowadays,there still are challenges in the application of LDPC codes in the wireless communication system,including the obvious error floor phenomenon and the poor performance on the terminal with limited computing resource.Inspired by the structure of polar codes,this paper proposes the layered LDPC code with polarization effect to improve decoding performance with the organized structure of the LDPC code,instead of changing encoding and decoding algorithms.With the analysis of Gallager decoding algorithm and density evolution algorithm using Gaussian approximation,the paper states that nodes with different degree would have different reliability and error correcting ability,that is,variable nodes with higher degree and check nodes with lower degree would have much more reliability and error correcting ability in the decoding iteration.Based on the above fact,the paper creates layers with different code rate in the code word by polarizing nodes in LDPC codes,that is,check nodes with lower degree only linked to variable nodes with higher degree.Different layers of the code word would exchange information by several common nodes in the decoding iteration.The new code is named as " the layered LDPC code with polarization effect".Using the successive cancellation,it could be decoded layer by layer.To reveal the influence of polarization on the error correcting ability of nodes,the paper introduces "polarized" density evolution algorithm.The simulation results point out that check nodes with lower degree would have faster convergence rate in the density evolution algorithm,more error correcting ability and more gain after "polarization".It aligns with the expectation of our discussion.Considering the code length of LDPC codes having much effect on the code construction and performance analysis,the paper introduces two ways to construct the code separately:1.For the case with magnitude order of code length being 104 bits or more,we construct the code words based on the input degree polynomials directly.In the simulation,we construct several 16384 bits code words using different degree polynomials and compare with standard short code in DVB-S2 and the proposed code word of 5G eMBB data channel on the binary symmetric channel.2.For the case with magnitude order of code length being 102 bits or 103 bits,we construct codes layer by layer.In the simulation,we construct code words with length of 264bits,1024bits and 83 84bits.These code words are compared with the proposed code words of 5G eMBB data channel on the binary symmetric channel and the binary-input addictive Gaussian white noise channel.The simulation results indicate that different layers of code word have different error correcting abilities in the layered LDPC code with polarization effect,and the high layer sub-code has a much lower word error rate(WER)in comparison with the standard code.With appropriate degree polynomials and code structure,the phenomenon of error floor could be reduced even vanish.The layered LDPC code with polarization effect could reduce the probability of re-transmitting and improve the utilization of channel in the communication system demanding the mixed transmission of data with different quality of service(QoS).