The Research On The Capacity Of Symmetrizable AVC When The Jammer Wiretap Channel Input

Coding for arbitrarily varying channel (AVC) may be considered as a zero-sum game between communicators, a pair of encoder (sender) and decoder (receiver), and a jammer. The encoder wants to send as many as possible messages to the decoder reliably and the jammer wants to disturb the communication between encoder and decoder by choosing bad channel according to his knowledge.There are two error criterions of codes for AVC. The criterion of average probability of error is equivalent to the assumption that jammer knows only the coding scheme before his acting whereas the criterion of maximum probability of error is equivalent to the assumption that jammer knows not only the coding scheme but also message to be transmitted.In the paper we propose a new model: the jammer who wiretaps the input of the AVC by a wiretap channel, wants to change the states of the AVC in order to disturb the communication according to the information that it receive. Basing this model, we determine the definition of a symmetrizable AVC and the capacity of AVC for average probability of error, and conclusion that the capacity of a symmetrizable AVC for average probability of error is zero. In addition, we point out the condition that the capacity of AVC with input or state constraint is zero. Finally, three examples are listed to explain these conclusions as mentioned above. We will find the capacity of AVC with inputs and states constraint relate to the wiretap channel according to the first example. Meanwhile, the assert that the capacity of AVC is zero while the corresponding mutual information is positive is possible from the other two example. According to the third example, we find that the condition which t the capacity of AVC with input or state constraint is zero relates whether inputs constraint is stronger than states constraint when these two constraints are same in forms.