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In the $q$-ary online (or "causal") channel coding model, a sender wishes tocommunicate a message to a receiver by transmitting a codeword $\mathbf{x}=(x_1,\ldots,x_n) \in \{0,1,\ldots,q-1\}^n$ symbol by symbol via a channellimited to at most $pn$ errors and/or $p^{*} n$ erasures. The channel is"online" in the sense that at the $i$th step of communication the channeldecides whether to corrupt the $i$th symbol or not based on its view so far,i.e., its decision depends only on the transmitted symbols $(x_1,\ldots,x_i)$.This is in contrast to the classical adversarial channel in which thecorruption is chosen by a channel that has a full knowledge on the sentcodeword $\mathbf{x}$.  In this work we study the capacity of $q$-ary online channels for a combinedcorruption model, in which the channel may impose at most $pn$ {\em errors} andat most $p^{*} n$ {\em erasures} on the transmitted codeword. The onlinechannel (in both the error and erasure case) has seen a number of recentstudies which present both upper and lower bounds on its capacity. In thiswork, we give a full characterization of the capacity as a function of $q,p$,and $p^{*}$.

The Capacity of Online (Causal) $q$-ary Error-Erasure Channels