网络喷泉码的基础理论与设计方法研究

The combination of digital fountain codes and network coding can give full play to their own superiorities, and improve the overall throughput of the network. However, the degree distributions of digital fountain codes are changed by network coding, thus the transmission efficiency is decreased. This project considers digital fountain codes and network coding as a whole, and studies the basic theory and design method of network fountain codes. The concrete research content of this project is mainly focused on: ① the heterogeneous network models and their network coding strategies; ② the general concept of network fountain codes and their description methods; ③ the method of asymptotic performance analysis for network fountain codes; ④ the design models of network fountain codes; ⑤ the solutions of the multiple objective constrained nonlinear programming models and the design cases of network fountain codes. The main contributions of this project are as follows: ① to propose the concept of multivariate degree distributions and the unified description method of network fountain codes with heterogeneous source and heterogeneous channels, and consider the UEP/URT fountain codes as the special cases; ② to solve the asymptotic performance analysis problem of network fountain codes using the joint multivariate desity evolution equations; ③ to propose the design models of network fountain codes and the multiple objective nonlinear programming solutions; ④ to propose the concept of wireless network fountain codes and the product-based physical layer network coding model. This project is aimed to make a breakthrough of the key theoretical and design problems for the network fountain codes, and establish the corresponding theoretical analysis framework. The research achievements are of great importance in both theories and applications.

数字喷泉码和网络编码的有机结合可以发挥各自的优势，提高整个网络的吞吐量。然而，网络编码破坏了数字喷泉码的度分布，从而降低了传输效率。本项目将数字喷泉码和网络编码作为整体，研究网络喷泉码的基础理论和设计方法。主要研究内容：①异构网络模型及其网络编码策略；②网络喷泉码的一般概念及描述方法；③网络喷泉码的性能分析方法；④网络喷泉码的设计模型；⑤多目标非线性约束模型的求解方法及网络喷泉码实例设计。创新点：①提出了多元度分布函数的概念和异构信源/异构信道网络喷泉码的统一描述方法，以UEP/URT数字喷泉码为特例；②采用联合多元密度演化方程解决网络喷泉码的渐近性能分析问题；③提出了网络喷泉码的设计模型及多目标非线性规划求解方法。④提出了无线网络喷泉码的概念和"乘积"型物理层网络编码模型。旨在突破网络喷泉码的关键理论和设计问题，建立起网络喷泉码的理论分析框架，研究成果具有重要的理论意义和应用价值。

本项目将数字喷泉码和网络编码作为整体，研究网络喷泉码的基础理论和设计方法，主要开展的研究工作包括：①异构网络模型及其网络编码策略；②网络喷泉码的一般概念及描述方法；③网络喷泉码的性能分析方法；④网络喷泉码的设计模型；⑤多目标非线性约束模型的求解方法及网络喷泉码实例设计；⑥数字喷泉码在删除信道和无线信道中的性能分析与设计方法。本项目已完成的主要创新点如下：①提出了多元度分布函数的概念和异构信源/异构信道网络喷泉码的统一描述方法，以UEP/URT数字喷泉码作为分布式异构网络喷泉码的特例进行研究；②采用联合多元密度演化方程解决网络喷泉码的渐近性能分析问题；③提出了网络喷泉码的设计模型及多目标非线性规划求解方法。④提出了无线网络喷泉码的概念和“乘积”型物理层网络编码模型。⑤建立无线信道中数字喷泉码渐进性能分析的统一方法。在该项目支持下，课题组申请发明专利15项，发表学术论文25篇，其中SCI检索论文10篇，培养硕士和博士研究生23名。本项目突破了网络喷泉码的关键理论和设计问题，建立起网络喷泉码的理论分析框架，研究成果具有重要的理论意义和应用价值。