  We analyze the optimal trade-off between the error exponent and the
excess-rate exponent for variable-rate Slepian-Wolf codes. In particular, we
first derive upper (converse) bounds on the optimal error and excess-rate
exponents, and then lower (achievable) bounds, via a simple class of
variable-rate codes which assign the same rate to all source blocks of the same
type class. Then, using the exponent bounds, we derive bounds on the optimal
rate functions, namely, the minimal rate assigned to each type class, needed in
order to achieve a given target error exponent. The resulting excess-rate
exponent is then evaluated. Iterative algorithms are provided for the
computation of both bounds on the optimal rate functions and their excess-rate
exponents. The resulting Slepian-Wolf codes bridge between the two extremes of
fixed-rate coding, which has minimal error exponent and maximal excess-rate
exponent, and average-rate coding, which has maximal error exponent and minimal
excess-rate exponent.
