Trade-offs Between Error Exponents and Excess-Rate Exponents of Typical Slepian-Wolf Codes

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 derive the TRC error exponent for fixed-rate random binning and show that at relatively high rates, the TRC deviates significantly from the optimal code. We discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random variable-rate code and characterize its optimal rate function. We show that the error exponent of the typical random variable-rate code may be strictly higher than in fixed-rate coding. We propose a new code, the semi-deterministic ensemble, which is a certain variant of the variable-rate code, and show that it dramatically improves upon the later: it is proved that the trade-off function between the error exponent and the excess-rate exponent for the typical random semi-deterministic code may be strictly higher than the same trade-off for the variable-rate code. Moreover, we show that the performance under optimal decoding can be attained also by different universal decoders: the minimum empirical entropy decoder and the generalized (stochastic) likelihood decoder with an empirical entropy metric.