Low-Density Parity-Check Codes: Research Status and Development Direction

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.

Block Markov superposition transmission of LDPC codes

In this paper,based on the block Markov superposition transmission(BMST)technique,we present a new class of coupled low-density parity-check(LDPC)codes for the transport block(TB)-based transmission to improve the error-correcting performance.For encoding,the previous LDPC codewords corresponding to a TB(at prior time slot)are interleaved and superimposed onto the current LDPC codewords,resulting in the transmitted codewords.For decoding,the sliding window decoding algorithm with sum-product or min-sum implementations can be employed,inheriting a relatively low-latency decoding.A distinguished advantage of the proposed coded transmission over spatially coupled LDPC(SC-LDPC)codes is that the encoder/decoder of the proposed codes can be designed by reusing the encoder/decoder architecture of component block LDPC codes.To analyze the waterfall performance of BMST-LDPC code ensembles,we present the protograph-based EXIT chart analysis,which can efficiently predict the error-correcting performance in waterfall region.To analyze the error-floor performance of BMST-LDPC codes,we employ the genie-aided(GA)lower bound,which can efficiently predict the error-correcting performance in error-floor region.For ease of implementation,the BMST-LDPC codes are constructed by taking the(2,4)-raptor-like LDPC codes or the 5G LDPC codes as the basic components.The numerical results reveal that the proposed codes can have capacity-approaching performance,exhibiting a gap of 0.007 dB away from the corresponding Shannon limit.They also reveal that,by using the proposed BMST construction,the error-correcting performance of the original 5G block LDPC codes can be significantly improved,achieving coding gains up to one dB over the AWGN channels and two dB over the fast fading channels.

Semi-LDPC Convolutional Codes:Construction and Low-Latency Windowed List Decoding

This paper presents a new coding scheme called semi-low-density parity-check convolutional code(semi-LDPC-CC),whose parity-check matrix consists of both sparse and dense sub-matrices,a feature distinguished from the conventional LDPC-CCs.We propose sliding-window list(SWL)decoding algorithms with a fixed window size of two,resulting in a low decoding latency but a competitive error-correcting performance.The performance can be predicted by upper bounds derived from the first event error probability and by genie-aided(GA)lower bounds estimated from the underlying LDPC block codes(LDPC-BCs),while the complexity can be reduced by truncating the list with a threshold on the difference between the soft metrics in the serial decoding implementation.Numerical results are presented to validate our analysis and demonstrate the performance advantage of the semi-LDPC-CCs over the conventional LDPC-CCs.