  This paper explores the possibilities and limitations of error correction by
the structural simplicity of error mechanisms. Specifically, we consider
channel models, called \emph{samplable additive channels}, in which (a) errors
are efficiently sampled without the knowledge of the coding scheme or the
transmitted codeword; (b) the entropy of the error distribution is bounded; and
(c) the number of errors introduced by the channel is unbounded. For the
channels, several negative and positive results are provided. Assuming the
existence of one-way functions, there are samplable additive errors of entropy
$n^{\epsilon}$ for $\epsilon \in (0,1)$ that are pseudorandom, and thus not
correctable by efficient coding schemes. It is shown that there is an oracle
algorithm that induces a samplable distribution over $\{0,1\}^n$ of entropy $m
= \omega( \log n)$ that is not pseudorandom, but is uncorrectable by efficient
schemes of rate less than $1 - m/n - o(1)$. The results indicate that
restricting error mechanisms to be efficiently samplable and not pseudorandom
is insufficient for error correction. As positive results, some conditions are
provided under which efficient error correction is possible.
