Research On Construction Method Of QC-LDPC Codes Based On Finite Field

Low-Density Parity-Check?LDPC?codes are a class of linear block codes with near-capacity performance.As a subclass of structured LDPC codes,Quasi Cyclic?QC?-LDPC codes have received much research and popularization,because of linear encoding complexity achieved by shift register.In this thesis,the main focus is the construction method of QC-LDPC codes,furthermore,two construction methods of QC-LDPC codes based on the finite field are proposed.A construction method of QC-LDPC code based on two different primitive elements of the finite field is proposed.The Tanner graph of parity check matrix of the code constructed by this method has no cycles of length 4,which makes it has the excellent decoding convergence characteristic.Besides,under the different condition of code length and code rate,the structure of the parity check matrix is adjusted by properly combining the two primitive elements in the base matrix,so that the constructed code has an improvement of the error correction performance.Simulation results show that when the bit error rate?BER?is 10^-6,in the same simulation environment,the Net Coding Gain?NCG?of the proposed QC-LDPC?504,252?code with the code rate of 50%in this thesis is respectively improved 0.17dB and 0.34dB than those of the APS-QC-LDPC?504,252?code based on the Arithmetic Progression Sequence?APS?and the APE-QC-LDPC?504,252?code based on the All Primitive Elements?APE?of finite field.In addition,The NCG of the proposed QC-LDPC?1260,1008?code is 0.15dB higher compared with the PEG?504,252?code constructed by Progressive Edge-Growth?PEG?algorithm.A construction method of QC-LDPC code based on a specific element of the multiplicative group over a finite field is proposed.In the design of the code structure,a arbitrary element in the finite field is added into the base matrix without introducing new short cycles,the element is regard as a specific element.By considering the minimum distance property of the code,a good distance property can be acquired by selecting the appropriate specific element,so as to the excellent error correction performance is achieved.Simulation results show that when the BER is 10^-6,in the same simulation environment,the NCG of the proposed QC-LDPC?3780,3540?code with the code rate of 93.3%in this thesis is improved 0.38dB than that of the IE-QC-LDPC?3780,3540?code based on the Inverse Element?IE?of finite field.In addition,the NCG of the proposed QC-LDPC?3780,3540?code is respectively 0.2dB and 1.54dB higher compared with the SG-QC-LDPC?3780,3540?code based on the two different Sub-Groups?SG?over finite field,which is suitable for optical communication and the LDPC?32640,30592?code in ITU-T G.975.1,which has been widely used in optical communication.Furthermore,over different finite fields,many kinds of QC-LDPC codes with high code rate can be constructed,which can meet the need of different optical communication systems.