  Typical random codes (TRC) in a communication scenario of source coding with
side information at the decoder is the main subject of this work. We study the
semi-deterministic code ensemble, which is a certain variant of the ordinary
random binning code ensemble. In this code ensemble, the relatively small type
classes of the source are deterministically partitioned into the available bins
in a one-to-one manner. As a consequence, the error probability decreases
dramatically. The random binning error exponent and the error exponent of the
TRC are derived and proved to be equal to one another in a few important
special cases. We show that the performance under optimal decoding can be
attained also by certain universal decoders, e.g., the stochastic likelihood
decoder with an empirical entropy metric. Moreover, we discuss the trade-offs
between the error exponent and the excess-rate exponent for the typical random
semi-deterministic code and characterize its optimal rate function. We show
that for any pair of correlated information sources, both error and excess-rate
probabilities are exponentially vanishing when the blocklength tends to
infinity.
