Structured Constructions Of LDPC Codes For AWGN And Rayleigh-Fading Channel

Low-density parity-check(LDPC)codes have been included in the list of capacity approaching codes.Owing to high error-correcting capability,LDPC codes have been adopted by many wireless communication standards for efficient and reliable communication.As compared to other forward error-correcting codes such as Turbo codes and Reed-Solomon codes,LDPC codes provide low-cost encoding and decoding which requires less resources for hardware implementation of an encoder and decoder.Besides good error-correction performance and low-cost encoding and decoding,LDPC codes also provide a large scale in terms of various code parameters such as girth,code-length,and rate selection.However,the decoding of LDPC codes must be executed to meet cost,delay,and power requirements for target applications.Also,the constructed LDPC codes should also satisfy the error-correction requirements for those applications.There is no unique method to construct LDPC codes and they can be constructed over large space with parameters such as girth,minimum distance,code-length,and rate.Existing construction methods of LDPC codes have some limitations in providing high error-correcting performance for a given code rate and length.There is still a need to construct LDPC codes over a flexible scale in term of code-length and rate with excellent error-correction performance for various application.This dissertation is about the construction of Quasi-cyclic(QC)LDPC codes by utilizing some finite fields and combinatorial designs methods.Existing methods for constructing QC-LDPC codes put some restrictions on code-length and rate selection.Proposed finite fields and combinatorial design methods give binary length-4 cycles free QC-LDPC codes of various lengths with flexibility in code length and rate selection.Furthermore,proposed construction methods are utilized to jointly-design length-4 cycles free QC-LDPC codes coded-relay cooperative communication systems over Rayleigh-fading channel in the presence of additive-white Gauss ian-noise.Our main contributions are summarized as follows:1.Firstly,a class of binary length-cycles free QC-LDPC codes is constructed based on finite field approach,known as conjugates of primitive elements over finite fields,by utilizing binary matrix dispersion of elements of finite field.Proposed finite field based construction gives lower rates and short block length QC-LDPC codes over a relative small finite field.Also,proposed QC-LDPC of this class provide an excellent error-correction performance with iterative decoding.Based on simulation results,proposed QC-LDPC codes outperform their competitors in term of bit-error rate(BER)and block-error rate(BLER)over an additive-white Gaussian-noise(AWGN)channel.Secondly,two classes of binary length-4 cycles free QC-LDPC are constructed based on a combinatorial design approach,known as block disjoint difference families(BDDFs),by utilizing some known ingredients like binary matrix dispersion of elements of finite fields and incidence matrices obtained from the base blocks of BDDFs.The BDDFs-based construction of QC-LDPC codes gives parity-check matrices with column weight three and a minimum distance lower-bounded by 4.Proposed BDDFs-based construction method is suitable for constructing QC-LDPC codes for high-rate applications.Base on numerical analysis and simulation results,QC-LDPC codes obtained from BDDFs provide and excellent error-correction performance and outperform their counterparts in higher signal-to-noise(SNR)region over an AWGN channel.Thirdly,an efficient construction of QC-LDPC codes based on a combinatorial design approach,known as cyclic balanced sampling plans excluding contiguous units(CBSEC),is presented.The Proposed CBSEC-based construction gives three classes of length-4 cycles free QC-LDPC codes by utilizing some known ingredients like binary matrix dispersion of elements of finite field,incidence matrices,and circulant decomposition.Resultant parity-check matrices of proposed QC-LDPC codes have column-weights 3 and 4 and a girth lower bounded by 6.Proposed CBSEC-based construction gives QC-LDPC codes of various lengths with flexibility in code length and rate selection.Based on simulation results,proposed CBSEC-based QC-LDPC codes provide an excellent error-correction performance with iterative decoding over an AWGN channel.2.A design theoretic construction of QC-LDPC codes based on a combinatoric design approach,known as Optical Orthogonal Codes(OOC),is presented.Proposed OOC-based construction gives three classes of binary QC-LDPC codes with no length-4 cycles by utilizing some known ingredients including binary matrix dispersion of elements of finite field,incidence matrices,and circulant decomposition.Furthermore,the proposed OOC-based construction gives an effective method to jointly-design length-4 cycles free QC-LDPC codes for coded-relay cooperation,where sum-product algorithm(SPA)-based joint-iterative decoding is used to decode the corrupted sequences coming from the source or relay nodes in different time frames over constituent Rayleigh fading.Based on numerical analysis and simulation results,proposed QC-LDPC coded-relay cooperation outperform their counterparts over a Rayleigh-fading channel channels in the presence of additive-white Gaussian noise.3.The OOC-based construction of QC-LDPC is utilized for jointly-designed QC-LDPC-coded multi-relay cooperation with multiple receive antennas in the destination over a Rayleigh-fading channel,where transmit diversity,receive diversity,and coding gain are combined into one unit by using maximal-ratio combining(MRC)and SPA-based joint iterative decoding to decode the corrupted sequences coming from source and relay nodes in their respective time frames over constituent Rayleigh fading channels in the presence of additive-white Gaussian noise.Theoretical analysis and simulation results show that the proposed jointly-designed QC-LDPC coded-relay cooperations outperform their counterparts under same conditions over a Rayleigh-fading channel in the presence of additive-white Gaussian noise.