Structured LDPC Codes And Application In Coded Modulation Systems

Structured LDPC(Low-Density Parity-Check,LDPC)codes are a class of practical good codes which have Shannon-limit approaching performance.Because of the quasi cyclic property of parity-check matries,QC-LDPC(Quasi-Cyclic LDPC)codes have been widely used in practical applications.The LDPC codes coded bit-interleaved coded modulation system with interleaved decoding(BICM-ID)which studied in this thesis is one popular coded modulation system which can achieve good performance in different channels.The main work and innovation of this thesis are summarized as follows.(1)An improved construction method of QC-LDPC codes based on finite field subsets is proposed.The proposed construction method of QC-LDPC codes keeps a balance between complexity and performance,and by combing two subsets of finite field,it can obtain large girth and better performance than general finite field approach.(2)A simple and effective construction method of masking matrix is improved.In order to reduce the density of partiy-check matrix,masking operation is proposed.Then an effective approach is improved to overcome the deficiencies of the construct matrix with small size by PEG(Progressive Edge Growth,PEG)algorithm.Our approach can enlarge the girth and reduce the number of short cycles and obtain good performance.(3)A class of non-uniform constellations are designed and applied in BICM-ID systems.Then the performance of BICM-ID systems with unequal probability shaping is compared.There is no shaping gain in conventional communication systems.In this thesis,shaping gain is obtained by optimization of geometry shaping and probability shaping.In the matter of geometry shaping,some non-uniform constellations with equally probability are designed.The proposedconstellations can achieve better performance than conventional QAM constellations by making every point approach the discrete Gaussian distribution in space.In the repect of probability shaping,some rules of unequal probability mapping areproposed.The usingprobability of each constellation point obeys the discrete Gaussian distribution,too.In order to reduce the error probability,the Hamming distance inside constellation point set and between every group of points are minimized.Simulation result shows that both two methods have better performance in coded modulation systems.