  This paper examines the maximum code rate achievable by a data-driven
communication system over some unknown discrete memoryless channel in the
finite blocklength regime. A class of channel codes, called learning-based
channel codes, is first introduced. Learning-based channel codes include a
learning algorithm to transform the training data into a pair of encoding and
decoding functions that satisfy some statistical reliability constraint.
Data-dependent achievability and converse bounds in the non-asymptotic regime
are established for this class of channel codes. It is shown analytically that
the asymptotic expansion of the bounds for the maximum achievable code rate of
the learning-based channel codes are tight for sufficiently large training
data.
