Performance Analysis And Optimization Design Of Digital Fountain Codes

With the rapid increase in the number of users and the improvement of application requirements in the age of Internet,it has drawn extensive research attention to how to ensure the reliable transmission of data in network environments through effective coding and decoding techniques.Considering the variability and complexity of networks,there still occurs a problem known as‘‘feedback storm'' when applying fixed-rate channel coding in network environments based on retransmission protocols.The concept of digital fountain provides a new idea for data distribution and effective transmission in large-scale networks.Different from traditional fixed-rate codes,digital fountain codes can generate encoded symbols of arbitrary length by using a certain probability distribution,which are rateless and can well adapt to the change of channel state.Similar to traditional channel coding,how to design codewords with superior performance plays an important role in the research of digital fountain codes,this dissertation therefore focuses on the fundamental theories and design methods of digital fountain codes in different channels and two-way relay networks,including encoding and decoding theories,asymptotic performance analysis and optimization design.The main work and contributions of this dissertation are shown in the following four aspects:LT codes in the binary erasure channel(BEC)are studied.An improved asymptotic optimization model of degree distribution is proposed,as well as a finite-length LT codes design method based on ripple size models.Firstly,using And-Or tree analysis,the asymptotic bit error rate(BER)of LT codes at the high overhead regime is derived,and a linear optimization model of degree distribution is established for LT codes in the BEC,which is constrained by the derived asymptotic BER.The proposed optimization model can solve the problem of high computational complexity occurred in the traditional linear optimization model.Secondly,the multi-symbol release model in a single decoding step is proposed.Furthermore,based on the proposed release model,the improved ripple size model is established.In addition,the least squares results of degree distribution design for finite-length LT codes are provided with the proposed ripple size model.Finally,robust soliton distribution and the ripple size model are jointly considered to propose a suboptimal degree distribution,which is suitable for finite-length LT codes in the BEC.The suboptimal degree distribution effectively avoids the high computational complexity caused by finding a least squares non-negative solution in the process of degree distribution design by using ripple size models.Compared with those in the literature for BEC,the degree distributions generated by the proposed ripple size model and the suboptimal one can decrease the overhead as well as the consuming time for decoding.Asymptotic analysis and optimization design of systematic LT(SLT)codes in binary input additive white Gaussian noise(BIAWGN)channels are presented.Firstly,the asymptotic performance under belief propagation(BP)decoding and the overhead threshold for successful decoding of SLT codes in the BIAWGN channel is analyzed using the Gaussian approximation method.Secondly,under the assumption that the overhead or signal-to-noise ratio(SNR)tends to infinity,the theoretical lower bound on BER of SLT codes under BP decoding in the BIAWGN channel is derived,including some approximate closed-form expressions.Finally,considering the lower bound on BER as the main constraint to control the decoding performance,an efficient optimization model of degree distribution design is proposed,which aims at minimizing the average degree.Compared with the traditional linear optimization model in the BIAWGN channel,degree distributions generated by the proposed model effectively reduce BER performance of SLT codes.In addition,using the proposed degree distributions,BER of long-length SLT codes can approach the theoretical lower bound at the large overhead regime.SLT codes with Quadrature Amplitude Modulation(QAM)in AWGN channels,namely the joint QAM-SLT coded modulation system,are studied,including the generalized Gaussian approximation method to analyze asymptotic performance and a novel high-order SLT coded modulation scheme.Firstly,the concept of variance-to-mean ratio(VMR)is introduced.Furthermore,assuming that the initial LLRs of QAM symbols in the AWGN channel follow Gaussian distributions with different VMRs,a generalized Gaussian approximation method for asymptotic analysis is proposed and the lower bound on BER of the joint QAM-SLT coded modulation system is therefore derived.Secondly,for the sake of the overall BP decoding performance of a QAM system,a non-linear optimization model of degree distribution for QAM modulated SLT codes is proposed based on the generalized Gaussian approximation method,when introducing the lower bound on BER as a constraint.Finally,taking Gray-mapped 16 QAM as an example,a novel coded modulation scheme is proposed to improve the performance of high-order modulated SLT codes in the AWGN channel.In the proposed scheme,it modifies the traditional QAM constellation,and utilizes the rateless property of SLT codes to extract only Gaussian distributed LLRs for BP decoding.Compared with the degree distributions and the traditional coded modulation schemes for QAM,the proposed non-linear optimization model and coded modulation scheme significantly improve BER performance of the joint QAM-SLT coded modulation system in AWGN channels,in high and low SNR regimes,respectively.The analysis and design of digital fountain codes in three-stage two-way relay networks over flat Rayleigh fading channels are presented.A relay forwarding scheme based on multiplication is proposed.Firstly,in order to solve the error expansion problem of the traditional amplify-and-forward(AF)scheme,a relay cooperative scheme named multiply-and-forward(MF)is proposed.Using the moment generating function,the average symbol error rates of two different forwarding schemes over the flat Rayleigh fading channel are derived and compared.The comparison result shows that the MF scheme outperforms the traditional AF scheme under the same SNR.Secondly,by establishing the equivalent point-to-point fading channel model between source nodes,the asymptotic analysis of digital fountain codes in the two-way MF relay networks over the flat Rayleigh fading channel is carried out.Moreover,constrained by the average BER of the two-way network,the corresponding optimization model of degree distribution is established.With the effective design of degree distribution,numerical results show that digital fountain codes can perform well in the two-way MF networks from the perspectives of BER and throughput.