Secrecy Capacities On Several Extended Models Of Wiretap Channel ?

Wiretap channel II is a communication model introduced by Ozarow and Wyner in 1984,which plays an extremely important role in information theory.To be particular,it provides the following two kinds of application.1.The study on wiretap channel II is helpful to deal with the security problem on wiretap network.Network coding has drawn more and more attention,since being proved to be able to provide better performance than the traditional routing method.Meanwhile,it is clear that the security problem over wiretap networks is a significant part of network coding.Cai and Yeung regarded the wiretap channel II as a spe-cial wiretap network without intermediate nodes,and they studied the information theoretic security problem on general wiretap network.The random linear network coding was devel-oped by them to achieve the secrecy capacity of the wiretap network.However,that coding scheme requires a sufficiently large coding field,which is a great constraint on engineering application.Though many researchers have introduced some methods decreasing the size of the coding field,it is still impossible to design secure code over binary field.2.Study of the security problem on wiretap channel II may provide some ideas to that on arbitrarily varying wiretap channel?AVWC?.Wiretap channel II is a special kind of AVWC,and AVWC is the most general wiretap channel model in discrete memoryless systems?DMSs?.If the secrecy capacity of the AVWC were known,almost all the security problems on DMSs would be solved.However,there were few capacity results on the general AVWC.Most results are inner or outer bounds of capacities over special cases of AVWC.This dissertation establishes the secrecy capacities of the following three communication models.The first model is a special class of wiretap networks without intermediate nodes,which is a special case of network model studied by Cai and Yeung from the viewpoint of topology.The network is supposed to have one single source node and K sink nodes.The legitimate receivers are able to obtain subsequences from arbitrary?₁=K?₁sink nodes.Meanwhile,there exist eavesdroppers who are able to observe subsequences from arbitrary?₂=K?₂sink nodes,where 0??₂<?₁?1.Unlike the linear network coding scheme designed by Cai and Yeung,our coding scheme is based on Csisz?ar's almost independent coloring scheme,which achieves the strong secrecy capacity of that network model with the vanishing decoding error probability.The advantage of our coding scheme is that it works on the binary field and hence the length of codewords is independent of the scale of the network.The second and the third channel models are both wiretap channels with noises,both of which are special cases of AVWC.In the second model,the source message is encoded into a digital sequence X^N,and transmitted to the legitimate receiver through a discrete memoryless main channel.An eavesdropper is able to observe?=N?symbols of the main channel output Y^N,where 0<?<1.The third model is an extension of the second one.In the third channel model,the source message is encoded into a digital sequence of length N,and transmitted to the legitimate receiver through a DMC.There exists an eavesdropper who is able to observe arbitrary?=N?digital symbols from the transmitter through a second DMC.This communication model includes a various of wiretap channels,such as wiretap channels of type I and II,as special cases.To prove the achievability,we design a coding scheme based on Csisz?ar's almost indepen-dent coloring scheme to achieve the strong secrecy capacities of the second and third models.Meanwhile,a coding scheme,originated from that designed by Ozarow and Wyner for wire-tap channel II,is constructed to achieve the weak secrecy capacities of those two models.Furthermore,it is easy to prove that Ozarow and Wyner's coding scheme also achieves the weak secrecy capacity of the first model.Therefore,we have actually designed two kinds of coding schemes achieving the weak and strong secrecy capacities of the three models,respectively.In fact,the weak and strong secrecy capacities are identical for each of the models.Comparison between the coding scheme of Csisz?ar's coloring scheme and that of classic wiretap channel II designed by Ozarow and Wyner is given.Firstly,the coding scheme of classic wiretap channel II does not decrease the complexity of the coding process,even though it achieves a weaker secrecy criterion.Secondly,the coding complexity would de-crease as the decrease of transmission rate when Csisz?ar's coloring scheme is applied.How-ever,it is not true for the coding scheme of wiretap channel II.From the viewpoints above,Csisz?ar's coloring scheme is better.The disadvantages of Ozarow and Wyner's scheme are caused by the fact that the requirement for a secure partition is too severe there.