  In this work we consider a communication problem in which a sender, Alice,
wishes to communicate with a receiver, Bob, over a channel controlled by an
adversarial jammer, James, who is {\em myopic}. Roughly speaking, for
blocklength $n$, the codeword $X^n$ transmitted by Alice is corrupted by James
who must base his adversarial decisions (of which locations of $X^n$ to corrupt
and how to corrupt them) not on the codeword $X^n$ but on $Z^n$, an image of
$X^n$ through a noisy memoryless channel. More specifically, our communication
model may be described by two channels. A memoryless channel $p(z|x)$ from
Alice to James, and an {\it Arbitrarily Varying Channel} from Alice to Bob,
$p(y|x,s)$ governed by a state $X^n$ determined by James. In standard
adversarial channels the states $S^n$ may depend on the codeword $X^n$, but in
our setting $S^n$ depends only on James's view $Z^n$.
  The myopic channel captures a broad range of channels and bridges between the
standard models of memoryless and adversarial (zero-error) channels. In this
work we present upper and lower bounds on the capacity of myopic channels. For
a number of special cases of interest we show that our bounds are tight. We
extend our results to the setting of {\em secure} communication in which we
require that the transmitted message remain secret from James. For example, we
show that if (i) James may flip at most a $p$ fraction of the bits communicated
between Alice and Bob, and (ii) James views $X^n$ through a binary symmetric
channel with parameter $q$, then once James is "sufficiently myopic" (in this
case, when $q>p$), then the optimal communication rate is that of an adversary
who is "blind" (that is, an adversary that does not see $X^n$ at all), which is
$1-H(p)$ for standard communication, and $H(q)-H(p)$ for secure communication.
A similar phenomenon exists for our general model of communication.
