| The fifth generation(5G)mobile communication network not only includes the traditional human-type communication network,also includes novel massive Internet of Thing(Io T)network with machine-type communication.To meet the transmission requirements of “ultra-reliable,low-latency,and massive connections”,we need to design a efficient coding strategy in short packets for the transmission of Io T business.On the one hand,the transmitted data used for Io T business are transmission in shortpackets,especially in some key business(somatosensory games,autopilot,telemedicine etc.)need to satisfy the requirements of “ultra-reliable and low-latency”.however,existing physical layer coding technology mainly designed based on humantype communication and the properties of approximation principle of coding in the case that the code length tends to infinity,thus,tradition Shannon coding theory can only provide guidance for optimizing the encoding/decoding algorithm under infinite length codes,and the theoretical performance analysis of short packets code is still deficiency.On the other hand,the Raptor code,a kind of rateless codes with linearly encoding/decoding complexity and which approaching to Shannon theory bound is proposed in recent years,have received great attentions from academia and industry.Further,the systematic Raptor code and the systematic Raptor Q codes have become the physical layer coding solutions for 3GPP MBMS in 3G and 4G mobile communication networks.However,there is still lack of complete theoretical framework for the design and optimization of finite-length Raptor codes.Based on this,this thesis focus on the requirements of IoT business “ultrareliable and low-latency”,we deduce the bounds of decoding performance of the finite-length rateless codes,and provide a theoretical guidance and analysis method for the future design of finite-length linear block codes.Specific research contents are as follows:This paper firstly studies the systematic Raptor code,systematic Raptor Q code and the analog fountain codes,and the corresponding theoretical analysis method which named “and-or tree” and “sum-or tree”.We deduce and simulate the decoding performance and complexity of these three kinds of codes.The simulation results demonstrate that the average degree is the most critical factor affecting the decoding performance in finite-length codes,and the maximum likelihood(ML)decoding algorithm can approximate the decoding performance bounds on the rateless codes.In order to accurately evaluate the decoding performance of the finite-length rateless codes,we analysis the maximum likelihood(ML)decoding failure probability(DFP)of Raptor codes with a systematic low-density generator-matrix(LDGM)code as the pre-code.By investigating the rank of the product of two random coefficient matrices,we derive upper and lower bounds of DFP on the Raptor codes under ML decoding algorithm.Then,we verify the accuracy of derived theoretical bounds through the Monte Carlo simulations with different construction of Raptor codes.Finally,based on the coding scheme of the systematic Raptor Q code and the analog fountain code,we propose an novel finite-length Raptor Q code with a highorder systematic LDGM pre-code,and derive the upper and lower bounds of DFP under ML decoding algorithm over Galois fields GF(q).We verify the accuracy of derived theoretical bounds through the Monte Carlo simulations by investigation of the impact of different codes construction.The simulation results show that the DFP of finite-length Raptor Q code under ML decoding is better than binary Raptor code we mentioned above in same code construction.This paper puts forward the upper and lower bounds of DFP on finite-length Raptor/Raptor Q codes under ML decoding algorithm,it can accurately evaluate the optimal decoding performance of the Raptor/Raptor Q codes,which has guiding significance for the finite-length Raptor/Raptor Q codes design and optimization with systematic LDGM pre-code. |
