Analysis And Optimization Of Network Digital Fountain Codes Over Erasure Channel

With the development of broadband communication technology,the use of mobile Internet has become an indispensable part of people's daily life.The rapid growth of the number of users and network data puts forward new requirements for the speed and reliability of network transmission.In order to improve the network transmission efficiency and the overall throughput of the system,a large number of scholars devote themselves to the research of network communication technology.Thus a large number of emerging technologies,digital fountain coding technology and network coding technology is one of the more effective two.Both use time and space resources respectively to achieve the purpose of improving network transmission efficiency.The network fountain code will combine the two,more fully use of time space two dimensional resources to maximize network throughput.As a novel and good coding technology,network fountain code provides a new effective means for real-time transmission and storage of network data.Based on the traditional fountain codes,this paper uses network coding technology to produce better network fountain codes.The research focuses on LT code.For the simple direct transmission network,generalized cooperative distributed network and multi-objective butterfly network,the degree distribution description and degree distribution design method of network fountain codes in each model are proposed.Main works are as follows:1.In the simple direct transmission model,we derive the asymptotic performance of LT codes over binary erasure channel,obtain the lower bounds of the performance.Simulations results show that asymptotic performance and low bound match each other perfectly.The low bound and asymptotic performance provide us a theoretical basis to design optimization models LP 1 and LP 2.Both models can minimize complexity of encoding and decoding.The new optimization models also have a good effect on LT Codes in direct transmission model,the degree distributions optimized by the models are more outstanding than traditional robust soliton distribution(RSD).Especially the LP 2 model,it has lower computational complexity,more obvious optimization effect and stronger control to overhead and BER,which means that desired BER would be reached within the overhead we set.Above properties and optimization models of LT codes are extended to SLT codes.The asymptotic performance of SLT is elicited with And-Or Tree analysis method.Optimization models SLP 1 and SLP 2 for SLT improve the performance of degree distributions,which make them outperform RSD and TDD.2.Generalized cooperation distributed fountain codes(GCDFC)are studied.Firstly,Adding direct path in the generalized model for distributed heterogeneous networks,a novel model for codes cooperation networks is proposed.Secondly,the concept of multivariate degree distribution is introduced to describe the GCDFC.With the traditional And-Or tree,decoding performance of the proposed codes is analyzed,a set of density evolution formulas and the low bound are derived.Using these,the model LP 2 is extended to GCDFC,which provides an idea for instantiation of the cooperation networks.Finally,modify original optimization algorithm using an improved differential evolution algorithm.The new optimization algorithm can be applied to the situation that the source number is greater than two.3.Further study for multiple objective network model is done.Focusing on the most simple butterfly network,the asymptotic behavior and low bound of each source to each objective are given.In order to provides a new basis for the evaluation and optimization for network fountain codes' performance,the definition of asymptotic throughput is proposed.With some approximate processes,expression of the throughput is got.The simulation results show that the expression of the throughput is suitable for the degree distributions whose BER curves act as "Z",and the gap between the real value and the theoretical value is very small.Based on above expressions,we design the optimization model for the butterfly network to achieve maximal throughput,provide a realization design of network fountain codes for butterfly network.