In this work we consider the communication of information in the presence of
a causal adversarial jammer. In the setting under study, a sender wishes to
communicate a message to a receiver by transmitting a codeword (x1,...,xn)
bit-by-bit over a communication channel. The sender and the receiver do not
share common randomness. The adversarial jammer can view the transmitted bits
xi one at a time, and can change up to a p-fraction of them. However, the
decisions of the jammer must be made in a causal manner. Namely, for each bit
xi the jammer's decision on whether to corrupt it or not must depend only on
xj for j≤i. This is in contrast to the "classical" adversarial
jamming situations in which the jammer has no knowledge of (x1,...,xn), or
knows (x1,...,xn) completely. In this work, we present upper bounds (that
hold under both the average and maximal probability of error criteria) on the
capacity which hold for both deterministic and stochastic encoding schemes.Comment: To appear in the IEEE Transactions on Information Theory; shortened
version appeared at ISIT 201