Fong et al.analyzed variable-rate linear network coding for linear broadcast.However,the authors didn't investigate it for the other three types of linear network codes.In this paper,by simple and clear proofs,it ...Fong et al.analyzed variable-rate linear network coding for linear broadcast.However,the authors didn't investigate it for the other three types of linear network codes.In this paper,by simple and clear proofs,it is found that there are similar results for variable-rate linear generic and linear dispersion if the field size is large enough.It means that linear generics and linear dispersions of different dimensions can be implemented on the same network,while each non-source node is required to store only one copy of the local encoding kernel within a session.Moreover,an example is given to show that there isn't a similar result for linear multicast.展开更多
Let G be 4 graph with () edges. We say G has an Ascending Subgraph Decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G1,G2,...,Gn such that |E(Gi)|=i (for i=1,2,...,n) and Gi is...Let G be 4 graph with () edges. We say G has an Ascending Subgraph Decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G1,G2,...,Gn such that |E(Gi)|=i (for i=1,2,...,n) and Gi is isomorphic to a subgraph of Gi+1 for i=1,2,...,n-1.In this paper, we prove that if G is a graph with X'(G)=d and () edges, n2d-3, then G has an ASD. Moreover, we show that if G with () edges, X'(G)=d, satisfying: nd, n4,and there is a matching M of G such that Then G has a matching ASD if dk+2 or And this result is an improvment on all the relevant results about G having a matching ASD obtained before.展开更多
基金Sponsored by the National Natural Science Foundation of China and the Research Grants Council of Hong Kong Joint Research Scheme(Grant No.60731160626)the National Natural Science Foundation of China(Grant No.60821001and61003287)+1 种基金the 111 Project(Grant No.B08004)the Fundamental Research Funds for the Central Universities(Grant No.BUPT2009RC0220)
文摘Fong et al.analyzed variable-rate linear network coding for linear broadcast.However,the authors didn't investigate it for the other three types of linear network codes.In this paper,by simple and clear proofs,it is found that there are similar results for variable-rate linear generic and linear dispersion if the field size is large enough.It means that linear generics and linear dispersions of different dimensions can be implemented on the same network,while each non-source node is required to store only one copy of the local encoding kernel within a session.Moreover,an example is given to show that there isn't a similar result for linear multicast.
文摘Let G be 4 graph with () edges. We say G has an Ascending Subgraph Decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G1,G2,...,Gn such that |E(Gi)|=i (for i=1,2,...,n) and Gi is isomorphic to a subgraph of Gi+1 for i=1,2,...,n-1.In this paper, we prove that if G is a graph with X'(G)=d and () edges, n2d-3, then G has an ASD. Moreover, we show that if G with () edges, X'(G)=d, satisfying: nd, n4,and there is a matching M of G such that Then G has a matching ASD if dk+2 or And this result is an improvment on all the relevant results about G having a matching ASD obtained before.
