Research On Coupled LDPC Codes

Based on the check matrix/generation matrix structure,low-density parity-check(LD-PC)codes can be divided into coupled LDPC codes and block LDPC codes.Due to their good iterative decoding performance,coupled LDPC codes have attracted a great deal of attention.This dissertation investigates the construction,analysis,and decoding etc.of s-patially coupled LDPC(SC-LDPC)codes and globally coupled LDPC(GC-LDPC)codes with widespread academic concern.Specifically,it includes the improvement of binary and nonbinary non-uniform SC-LDPC codes,analysis and construction of tail-biting GC-LDPC codes,construction of protograph-based GC-LDPC codes over the Gaussian channel with burst erasures,the list-aided sliding window decoding scheme,and the modified two-stage iterative decoding algorithm of GC-LDPC codes.The specific research content and achieve-ments of this dissertation are as follows:(1)Since the requirements of a hardware resource for a time-varying SC-LDPC code over the continuous flow date are quite large,and it is difficult to guarantee the reliability of a time-invariant or periodic SC-LDPC code.Combining with unwrapping,lifting and mask-ing operations,a method of constructing the periodic time-varying SC-LDPC code based on two-stage lifting is proposed.This method effectively reduce the hardware resource of the time-varying SC-LDPC code by the two-stage lifting operation.The parity-check ma-trix of a SC-LDPC code in one period is designed by the algebra construction of the LDPC block code,which can effectively reduces the error floor and improves the reliability.To construct a nonbinary SC-LDPC code which performance well over different domain or-ders,a decoding threshold analysis method for the non-uniformly coupled LDPC ensem-bles formed by randomly coupled and protograph-based coupled ensembles was proposed.The results show that the proposed nonbinary SC-LDPC codes not only can achieve excel-lent close-to-capacity threshold,and have good waterfall error performances for both FSD(Flooding-Schedule Decoding,FSD)and SWD schemes.The codes perform smoothly down to a BLER of 10-4 without showing error floor.(2)Due to the fact that the high connectivity of global CNs may lead to the generation of many high-degree CNs which are easily involved in short cycles in the Tanner graph of a GC-LDPC code for satellite and ground communications,a new type of globally-coupled low-density parity-check(GC-LDPC)codes is presented.The resulting codes are referred to as tail-biting GC-LDPC(TB-GC-LDPC)codes.This paper proposes two methods to construct TB GC quasi-cyclic LDPC(TB-GC-QC-LDPC)codes.For the first method,we extract a replicated version of a constructed base matrix and mask it with a designed masking matrix.This construction method not only ensures the RC-constraint in the global part for the parity-check matrix of TB-GC-QC-LDPC codes,but also provides more reliability and flexibility in code length for TB-GC-QC-LDPC codes.Inspired by the balanced incomplete block designs(BIBDs)for constructing LDPC block codes and time-invariant SC-LDPC codes,this paper derives a type of packings,called special-packings,to obtain another type of TB-GC-QC-LDPC codes.It is based on designing the incidence matrix of a special type of packings.Simulation results show that the constructed TB-GC-QC-LDPC codes perfor-m well over the additive white Gaussian noise channel(AWGNC)and the binary erasure channel(BEC).(3)Due to the fact that the reliability of GC-LDPC codes are hard to guarantee in the applica-tion of satellite communication and storage with burst noise,this paper presents a construc-tion method for the protograph-based GC-LDPC code.A channel model,which incorporates both Gaussian noise and burst erasures,is presented and is denoted by the Gaussian channel with burst erasures(BuEC-G).The channel capacity of this model is discussed.The Gaus-sian approximation(GA)and the protograph-based extrinsic information transfer(P-EXIT)analysis are then generalized over the BuEC-G.This paper presents two types of protograph-based GC-LDPC codes formed by a new edge spreading operation.This operation is called the global edge spreading.Furthermore,the stability condition for BuECs-G is proved and an edge spreading optimization method is proposed to design the structured GC-LDPC codes by predicting the iterative decoding thresholds of corresponding protographs.Sim-ulation results show that the optimized GC-LDPC codes can achieve better thresholds and error performances than existing well-designed GC-LDPC codes,and provide near-capacity performances over BuECs-G.(4)The improved decoding algorithms for the SWD scheme of SC-LDPC codes and the two phase decoding scheme of GC-LDPC codes are proposed to reduce the decoding com-plexity and latency for the high reliable and low latency scenario in satellite and ground communications.This paper proposes a list-aided sliding windowed decoding(list-aided SWD)scheme for nonbinary SC-LDPC codes with low decoding latency.Numerical results show that the list-aided WD which outperforms conventional SWD can perform better at low SNRs than the flooding-schedule decoding with much lower decoding latency on the additive white Gaussian noise channel.To reduce the decoding complexity of the two-phase local/global iterative decoding scheme for GC-LDPC codes at low SNRs,a modified two-phase local/global iterative decoding scheme is proposed.Numerical results show that the proposed decoding scheme can reduce the unnecessary cost of local decoder at low and moderate SNRs,without increase in the number of decoding iterations in global decoder at high SNRs.Then,the comparison between TB-GC-LDPC/GC-LDPC codes and TB-LDPCC/LDPCC codes in terms of their decoding performance,decoding complexity are shown.