  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 x=(x_1,...,x_n)
bit-by-bit over a communication channel. The adversarial jammer can view the
transmitted bits x_i one at a time, and can change up to a p-fraction of them.
However, the decisions of the jammer must be made in an online or causal
manner. Namely, for each bit x_i the jammer's decision on whether to corrupt it
or not (and on how to change it) must depend only on x_j for j <= i. This is in
contrast to the "classical" adversarial jammer which may base its decisions on
its complete knowledge of x. We present a non-trivial upper bound on the amount
of information that can be communicated. We show that the achievable rate can
be asymptotically no greater than min{1-H(p),(1-4p)^+}. Here H(.) is the binary
entropy function, and (1-4p)^+ equals 1-4p for p < 0.25, and 0 otherwise.
