  In the binary online (or "causal") channel coding model, a sender wishes to
communicate a message to a receiver by transmitting a codeword $\mathbf{x}
=(x_1,\ldots,x_n) \in \{0,1\}^n$ bit by bit via a channel limited to at most
$pn$ corruptions. The channel is "online" in the sense that at the $i$th step
of communication the channel decides whether to corrupt the $i$th bit or not
based on its view so far, i.e., its decision depends only on the transmitted
bits $(x_1,\ldots,x_i)$. This is in contrast to the classical adversarial
channel in which the error is chosen by a channel that has a full knowledge on
the sent codeword $\mathbf{x}$.
  In this work we study the capacity of binary online channels for two
corruption models: the {\em bit-flip} model in which the channel may flip at
most $pn$ of the bits of the transmitted codeword, and the {\em erasure} model
in which the channel may erase at most $pn$ bits of the transmitted codeword.
Specifically, for both error models we give a full characterization of the
capacity as a function of $p$.
  The online channel (in both the bit-flip and erasure case) has seen a number
of recent studies which present both upper and lower bounds on its capacity. In
this work, we present and analyze a coding scheme that improves on the
previously suggested lower bounds and matches the previously suggested upper
bounds thus implying a tight characterization.
