  This paper is concerned with the problem of error-free communication over the
i.i.d. duplication channel which acts on a transmitted sequence $ x_1 \cdots
x_n $ by inserting a random number of copies of each symbol $ x_i $ next to the
original symbol. The random variables representing the numbers of inserted
copies at each position $ i $ are independent and take values in $ \{0, 1,
\ldots, r\} $, where $ r $ is a fixed parameter. A more general model in which
blocks of $ \ell $ consecutive symbols are being duplicated, and which is
inspired by DNA-based data storage systems wherein the stored molecules are
subject to tandem-duplication mutations, is also analyzed. A construction of
optimal codes correcting all patterns of errors of this type is described, and
the zero-error capacity of the duplication channel---the largest rate at which
information can be transmitted through it in an error-free manner---is
determined for each $ \ell $ and $ r $.
