Optimum Tradeoffs Between the Error Exponent and the Excess-Rate Exponent of Variable-Rate Slepian-Wolf Coding

We analyze the asymptotic performance of ensembles of random binning Slepian-Wolf codes, where each type class of the source might have a different coding rate. In particular, we first provide the exact encoder excess rate exponent as well as the decoder error exponent. Then, using the error exponent expression, we determine the optimal rate function, namely, the minimal rate for each type class needed to satisfy a given requirement on the decoder error exponent. The resulting excess rate exponent is then evaluated for the optimal rate function. Alternating minimization algorithms are provided for the calculation of both the optimal rate function and the excess rate exponent. It is thus exemplified that, compared to fixed-rate coding, larger error exponents may be achieved using variable-rate coding, at the price of a finite excess rate exponent. Index Terms Slepian-Wolf coding, method of types, error exponents, excess rate exponent, alternating minimization, source uncertainty.