Error Exponents of Typical Random Codes of Source-Channel Coding

Abstract

The error exponent of the typical random code (TRC) in a communication scenario of source-channel coding with side information at the decoder is the main objective of this work. We derive a lower bound, which is at least as large as the random binning-coding exponent due to Merhav (2016), and we show numerically that it may be strictly larger. We deduce the exponents of the TRCs in two special cases: Slepian-Wolf (SW) source coding and joint source-channel coding. Each of these models is further studied in order to provide deeper intuition concerning the behavior of the typical random code. We also propose an alternative expression for the error exponent of typical random binning in SW model, which is given by an optimization over four parameters only, instead of a computationally heavy optimization over probability distributions.