多信源多播网络编码问题的信息率区域刻画  

Characterization of the rate region for multi-source multicast network coding

作　　者：杨济杭 张儒泽 李丹 光炫[1] YANG Jihang;ZHANG Ruze;LI Dan;GUANG Xuan(School of Mathematical Sciences,Nankai University,300071;Department of Mathematics,Tianjin University of Technology,300384,Tianjin,PRC)

机构地区：[1]南开大学数学科学学院,300071 [2]天津理工大学理学院,天津市300384

出　　处：《曲阜师范大学学报（自然科学版）》2024年第3期9-18,F0002,共11页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(62171238,61771259);天津市普通高等学校本科教学改革与质量建设研究计划(B231005533).

摘　　要：该文研究多信源多播网络编码问题,其中每个信宿节点都希望正确解码由多个信源节点所生成的信源消息.对于该问题,率区域定义为平均使用一次网络时,信源节点可以将信源消息多播至所有信宿节点的码率元组所形成的集合.该文完全刻画了多信源多播网络编码问题的率区域,并且研究了码的构造.首先证明了对于信源节点集的任意子集,其码率和的上界为该子集到所有信宿节点的最小割容量的最小值.使用变换方法进一步发展了向量线性网络编码的系统构造.这种码的构造方式适用于任何可行的码率元组.基于已得到的率区域的外界以及码的构造,完整刻画出任意多信源多播网络编码问题的率区域.The model of multi-source multicast network coding is investigated in this paper,where each sink node desires to decode correctly the source messages generated by multiple source nodes.For this model,the rate region is defined as the set of rate tuples of source nodes at which the source nodes can multicast source messages to all sink nodes for one use of the network on average.In this paper,we fully characterize the rate region and investigate the code construction for the model of multi-source multicast network coding.We first prove that for any subset of source nodes,the sum rate is upper bounded by the smallest minimum cut capacity separating a sink node from the subset of source nodes.We further develop a systematic construction of vector-linear network codes by using a transformation approach.This code construction is applicable to an arbitrary rate tuple that is achievable.Based on the upper bounds obtained and the developed code construction,we fully characterize the rate region for any model of multi-source multicast network coding problem.

关 键 词：网络编码 多信源多播 率区域 向量线性网络编码 码的构造 

分 类 号：O236[理学—运筹学与控制论]